[sage-support] Re: AttributeErrors in EllipticCurve classes
Oh wow, I didn't think the stuff was that new! I will make sure I get the new version and check it out soon. Thanks, John! --~--~-~--~~~---~--~~ 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://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: AttributeErrors in EllipticCurve classes
John, Hello again :-) While you're working on more elliptic curves stuff, what I could use is the following: I'd like to define points on curves by just providing the x-coordinate (and maybe an indicator of which of the possible two y-coordinates I want). When I do something like E = EllipticCurve(RR,[a,b]) P = E([xP,sqrt(xP^3+a*xP+b)]) it doesn't always work. Or is there a way of doing this already? Maike --~--~-~--~~~---~--~~ 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://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: AttributeErrors in EllipticCurve classes
You have E.lift_x(x0) which gives a point with x-coord x0 if there is one (else raises an error), or E.lift_x(x0,all=True) which gives a list of 0, 1 or 2 points with x-coord x0, or E.is_x_coord(x0). JEC 2008/9/3 Maike <[EMAIL PROTECTED]>: > > John, > > Hello again :-) While you're working on more elliptic curves stuff, > what I could use is the following: > I'd like to define points on curves by just providing the x-coordinate > (and maybe an indicator of which of the possible two y-coordinates I > want). When I do something like > > E = EllipticCurve(RR,[a,b]) > P = E([xP,sqrt(xP^3+a*xP+b)]) > > it doesn't always work. > > Or is there a way of doing this already? > > Maike > > > --~--~-~--~~~---~--~~ 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://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: AttributeErrors in EllipticCurve classes
Yeah right, I'll install that new version right now! --~--~-~--~~~---~--~~ 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://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: AttributeErrors in EllipticCurve classes
For example (using your notation) sage: a=3; b=5 sage: E = EllipticCurve(RR,[a,b]) sage: E Elliptic Curve defined by y^2 = x^3 + 3.00*x + 5.00 over Real Field with 53 bits of precision sage: xP=1 sage: P=E.lift_x(xP) sage: P (1.00 : 3.00 : 1.00) Support for elliptic curves over fields other than Q (the rationals), number fields and finite fields is limited. But you can do sage: E.plot() and see a nice picture. JEC 2008/9/3 Maike <[EMAIL PROTECTED]>: > > Yeah right, I'll install that new version right now! > > > --~--~-~--~~~---~--~~ 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://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: AttributeErrors in EllipticCurve classes
Maike, the trick is that integral points were only put into Sage in version 3.1.1. You must be looking at a more recent version of the reference manual. THere should be more elliptic curve goodies in 3.1.2, out any day now. As the integral points curve is all new, I would very much like someone to put it through its paces, so I hope you do that! I know that it runs ok on all the curves in the (large) database, conductors up to 13. (I would recommend installing the optional large elliptic curve database since then you get not only all the curves but also their ranks and generators directly.) John Cremona 2008/9/3 Maike <[EMAIL PROTECTED]>: > > Hi, > > I'm running Version 3.0.5 of Sage, and I just discovered the huge > elliptic curve functionality in the Sage reference manual. However, my > Sage doesn't know most of these nice functions. For example, > > sage: E=EllipticCurve([0,0,1,-7,6]) > sage: P1=E.point((2,0)); P2=E.point((-1,3)); P3=E.point((4,6)) > sage: a=E.integral_points([P1,P2,P3]); a > > gives me an error "EllipticCurve_rational_field' object has no > attribute 'integral_points'", although the code is copied directly > from the reference manual. > > Something like "import > sage.schemes.elliptic_curves.ell_rational_field" doesn't solve the > problem. > > What's the trick? Do I have to install/import extra packages or is > there anything else I've missed? > > Thanks! > Maike > > > --~--~-~--~~~---~--~~ 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://www.sagemath.org -~--~~~~--~~--~--~---
