1. In you checking make sure that you have the correct polynomial satisfied by the field generator f:
sage: F.<f> = GF(11^2,'f') sage: f.minpoly() x^2 + 7*x + 2 2. You can define your curve more simply by sage: ff2 = EllipticCurve(F,[0,1]) 3. The code which computes the generators and group structure uses random points on the curve so will not give the same generators in different situations (I wrote that code!). I get sage: ff2.gens() [(9 : 9 : 1), (3*f + 9 : 5*f + 1 : 1)] I would be very surprised if you got points which did not satisfy the curve equation since Sage will refuse to construct points on the curve unless they do. You can check manually, of course: sage: (3*f+9)^3 + 1 == (5*f+1)^2 True sage: (F(9))^3 + 1 == (F(9))^2 True John Cremona On Wednesday, October 1, 2014 8:16:57 AM UTC+1, Padmanabhan Tr wrote: > > I am working with Elliptic curve in extended field. I tried to get points > / order in the group. I have copied a small code set & results from > notebook. The points obtained are not in the EC; I have checked it using a > Python program I coded for this. Is it a bug / wrong use of codes by me? > > F.<f> = GF(11^2,'f') > ff2 = EllipticCurve([0+f*0,1+f*0]) > ff2 > Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in f of size > 11^2 > fg =ff2.gens() > fg > [(8*f : 6*f + 6 : 1), (5*f + 8 : 3*f + 6 : 1)] > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
