Sharedsupport / 2016-02-10-082355-ellcurve-ring.sagewsOpen in CoCalc
Authors: Harald Schilly, ℏal Snyder, William A. Stein
License: GNU General Public License v3.0
Description: Examples for support purposes.
E = EllipticCurve('389a') E
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 2*x over Rational Field
R = E.coordinate_ring(); R
Quotient of Multivariate Polynomial Ring in x, y, z over Rational Field by the ideal (-x^3 - x^2*z + y^2*z + 2*x*z^2 + y*z^2)
S = PolynomialRing(E.base_field(), 'a,b,c')
p = R.cover_ring().hom(S.gens())(R.defining_ideal().gens()[0]) p
-a^3 - a^2*c + b^2*c + 2*a*c^2 + b*c^2
S.quotient(p)
Quotient of Multivariate Polynomial Ring in a, b, c over Rational Field by the ideal (-a^3 - a^2*c + b^2*c + 2*a*c^2 + b*c^2)