38.3 Hyperelliptic curves over a general ring

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

is_HyperellipticCurve( C)

Class: HyperellipticCurve_generic

class HyperellipticCurve_generic
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_

_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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