ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 10 Aug 2018 01:42:18 +0200generating the ring for schoof's division polynomialshttps://ask.sagemath.org/question/43301/generating-the-ring-for-schoofs-division-polynomials/ hello,
i want to generate the ring $F_p[x,y]/(y^2-x^3-ax-b)$, which is necessary to compute the division polynomials in schoof's algorithm to compute the amount of elements of a elliptic curve of the form $y^2=x^3+ax+b$ over $F_p$.
I already tried this:
R.<x,y>=PolynomialRing(Zmod(p))
F=R.quo(y^2-x^3-ax-b)
x,y=F.gens()
When i computed some division polynomials in the generated F and matched them with division polynomials which sage computed by this:
F=Zmod(p)
E=EllipticCurve(F,[a,b])
E.division_polynomial()
i saw that my computed division polynomials must be wrong. Does anyone have an idea for generating the Ring $F_p[x,y]/(y^2-x^3-ax-b)$ or generating a "pseudo" elliptic curve in sage, because this code
F=Zmod(p)
E=EllipticCurve(F,[a,b])
E.division_polynomial()
doesn't work if $p$ isn't prime of course.
Fri, 10 Aug 2018 01:42:18 +0200https://ask.sagemath.org/question/43301/generating-the-ring-for-schoofs-division-polynomials/