Jacobian of a Hyperelliptic curve of Genus 2¶
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class
sage.schemes.hyperelliptic_curves.jacobian_g2.
HyperellipticJacobian_g2
(C)¶ Bases:
sage.schemes.hyperelliptic_curves.jacobian_generic.HyperellipticJacobian_generic
TESTS:
sage: from sage.schemes.jacobians.abstract_jacobian import Jacobian_generic sage: P2.<x, y, z> = ProjectiveSpace(QQ, 2) sage: C = Curve(x^3 + y^3 + z^3) sage: J = Jacobian_generic(C); J Jacobian of Projective Plane Curve over Rational Field defined by x^3 + y^3 + z^3 sage: type(J) <class 'sage.schemes.jacobians.abstract_jacobian.Jacobian_generic_with_category'>
Note: this is an abstract parent, so we skip element tests:
sage: TestSuite(J).run(skip =["_test_an_element", "_test_elements", "_test_elements_eq_reflexive", "_test_elements_eq_symmetric", "_test_elements_eq_transitive", "_test_elements_neq", "_test_some_elements"])
sage: Jacobian_generic(ZZ) Traceback (most recent call last): ... TypeError: Argument (=Integer Ring) must be a scheme. sage: Jacobian_generic(P2) Traceback (most recent call last): ... ValueError: C (=Projective Space of dimension 2 over Rational Field) must have dimension 1. sage: P2.<x, y, z> = ProjectiveSpace(Zmod(6), 2) sage: C = Curve(x + y + z) sage: Jacobian_generic(C) Traceback (most recent call last): ... TypeError: C (=Projective Plane Curve over Ring of integers modulo 6 defined by x + y + z) must be defined over a field.
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kummer_surface
()¶
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