On Oct 5, 3:36 pm, James Parson <par...@hood.edu> wrote: > Dear sage-support, > > I was playing with some elliptic-curves calculations in Sage 4.5.3, > and I came across (or, rather, cooked up) the following, which puzzled > me: > > sage: K = QuadraticField(8,'a') > sage: E = EllipticCurve([K(0),0,0,-1,0]) > sage: P = E([-1,0]) > sage: P.division_points(2) > [] > sage: P.is_divisible_by(2) > True > > Is this the intended behavior? From the source code, it looks as if > P.is_divisible_by(2) just checks whether the x-coordinate of the > system of equations for dividing P by 2 can be solved over K. The > division_points method does the full check of whether the system has a > solution over K. Shouldn't is_divisible_by do the same thing? > > Thanks for any clarification you can offer.
It is a bug -- well spotted. In this case the x-coordinates of the points Q such that 2*Q=P are the roots of x^2 + 2*x - 1 which are a/ 2-1 and -a/2-1, but the y-coordinates are not in the field. I will make a bug trac ticket for this, and write a patch for it. John Cremona > > Regards, > > James Parson -- 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
