Module: sage.schemes.hyperelliptic_curves.hyperelliptic_generic
Hyperelliptic curves over a general ring
sage: P, x = PolynomialRing(GF(5),"x").objgen() sage: f = x^5 - 3*x^4 - 2*x^3 + 6*x^2 + 3*x - 1 sage: C = HyperellipticCurve(f); C Hyperelliptic Curve over Finite Field of size 5 defined by y^2 = x^5 + 2*x^4 + 3*x^3 + x^2 + 3*x + 4
sage: P, x = PolynomialRing(QQ,"x").objgen() sage: f = 4*x^5 - 30*x^3 + 45*x - 22 sage: C = HyperellipticCurve(f); C Hyperelliptic Curve over Rational Field defined by y^2 = 4*x^5 - 30*x^3 + 45*x - 22 sage: C.genus() 2
Module-level Functions
C) |
Class: HyperellipticCurve_generic
self, PP, f, [h=None], [names=None], [genus=None]) |
Functions: change_ring,
genus,
hyperelliptic_polynomials,
jacobian,
lift_x
Special Functions: __cmp__,
__init__,
_repr_
self) |
String representation hyperelliptic curves.
sage: P, x = PolynomialRing(QQ,"x").objgen() sage: f = 4*x^5 - 30*x^3 + 45*x - 22 sage: C = HyperellipticCurve(f); C Hyperelliptic Curve over Rational Field defined by y^2 = 4*x^5 - 30*x^3 + 45*x - 22 sage: C = HyperellipticCurve(f,names='u,v'); C Hyperelliptic Curve over Rational Field defined by v^2 = 4*u^5 - 30*u^3 + 45*u - 22
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