Points on schemes¶
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class
sage.schemes.generic.point.SchemePoint(S, parent=None)¶ Bases:
sage.structure.element.ElementBase class for points on a scheme, either topological or defined by a morphism.
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scheme()¶ Return the scheme on which self is a point.
EXAMPLES:
sage: from sage.schemes.generic.point import SchemePoint sage: S = Spec(ZZ) sage: P = SchemePoint(S) sage: P.scheme() Spectrum of Integer Ring
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class
sage.schemes.generic.point.SchemeRationalPoint(f)¶ Bases:
sage.schemes.generic.point.SchemePointINPUT:
f- a morphism of schemes
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morphism()¶
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class
sage.schemes.generic.point.SchemeTopologicalPoint(S)¶ Bases:
sage.schemes.generic.point.SchemePointBase class for topological points on schemes.
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class
sage.schemes.generic.point.SchemeTopologicalPoint_affine_open(u, x)¶ Bases:
sage.schemes.generic.point.SchemeTopologicalPointINPUT:
u– morphism with domain an affine scheme \(U\)x– topological point on \(U\)
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affine_open()¶ Return the affine open subset U.
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embedding_of_affine_open()¶ Return the embedding from the affine open subset U into this scheme.
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point_on_affine()¶ Return the scheme point on the affine open U.
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class
sage.schemes.generic.point.SchemeTopologicalPoint_prime_ideal(S, P, check=False)¶ Bases:
sage.schemes.generic.point.SchemeTopologicalPointINPUT:
S– an affine schemeP– a prime ideal of the coordinate ring of \(S\), or anything that can be converted into such an ideal
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prime_ideal()¶ Return the prime ideal that defines this scheme point.
EXAMPLES:
sage: from sage.schemes.generic.point import SchemeTopologicalPoint_prime_ideal sage: P2.<x, y, z> = ProjectiveSpace(2, QQ) sage: pt = SchemeTopologicalPoint_prime_ideal(P2, y*z-x^2) sage: pt.prime_ideal() Ideal (-x^2 + y*z) of Multivariate Polynomial Ring in x, y, z over Rational Field
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sage.schemes.generic.point.is_SchemeRationalPoint(x)¶
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sage.schemes.generic.point.is_SchemeTopologicalPoint(x)¶