sage: ZZ Integer Ring sage: a = ZZ(5); b = ZZ(7); a+b 12 sage: QQ Rational Field sage: QQ(3/4) + QQ(2/3) 17/12 sage: R = IntegerModRing(12) sage: print R Ring of integers modulo 12 sage: R(7) + R(8) 3 sage: R = FiniteField(7) sage: print R Finite Field of size 7 sage: R(4)*R(5) 6
sage: E = EllipticCurve([-36,0]) sage: E Elliptic Curve defined by y^2 = x^3 - 36*x over Rational Field sage: P = E([-3,9]) # or use E.gens(proof=False) sage: P + P (25/4 : -35/8 : 1)
sage: E = EllipticCurve([-36,0]) sage: P = plot(E,rgbcolor=(0,0,1)) sage: pnt = E([-3,9]) sage: pnt2 = 2*pnt sage: c1 = point(pnt, pointsize=100) sage: c2 = point(pnt2, rgbcolor=(1,0,0), pointsize=100) sage: show(P + c1 + c2)
William Stein 2006-07-07