On Sat, Apr 10, 2010 at 5:08 PM, Kenneth A. Ribet <[email protected]> wrote: > Hi, > > I'd like to present Lenstra's elliptic curve factoring method to a class. > This means that I'd like to define an elliptic curve over Integers(N), where > N is composite, and then add points on that curve in sage. I may be doing > something stupid, but I'm getting a NotImplementedError with the method I'm > using: > > sage: E=EllipticCurve([0,Mod(1,59)]); E > Elliptic Curve defined by y^2 = x^3 + 1 over Ring of integers modulo 59 > sage: E([0,1]) > (0 : 1 : 1) > sage: E=EllipticCurve([0,Mod(1,5963)]); E > Elliptic Curve defined by y^2 = x^3 + 1 over Ring of integers modulo 5963 > sage: E([0,1]) > Traceback (most recent call last): > ... > NotImplementedError > > Is there a workaround? Does an alternative approach allow the desired > computations? > > Thanks much in advance!
You can see how I do this in the code samples in Chapter 6.3 of my elementary number theory book: http://wstein.org/ent/ent.pdf The key trick is: sage: R = Integers(2010) sage: # Make Sage think that R is a field sage: R.is_field = lambda : True sage: E = EllipticCurve(R, [0,1]) sage: E Elliptic Curve defined by y^2 = x^3 + 1 over Ring of integers modulo 2010 William -- William -- 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-support URL: http://www.sagemath.org To unsubscribe, reply using "remove me" as the subject.
