On Oct 5, 8:04 pm, John Cremona <[email protected]> wrote: > This is now ticket #10076 (seehttp://trac.sagemath.org/sage_trac/ticket/10076)
There's a patch which fixes this bug on that ticket, ready for review. Thanks again for the bug report. John Cremona > > John Cremona > > On Oct 5, 8:01 pm, John Cremona <[email protected]> wrote: > > > > > > > > > On Oct 5, 3:36 pm, James Parson <[email protected]> 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 [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
