Points on schemes

class sage.schemes.generic.point.SchemePoint(S)

Bases: sage.structure.element.Element

Base class for points on a scheme, either topological or defined by a morphism.

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
class sage.schemes.generic.point.SchemeRationalPoint(f)

Bases: sage.schemes.generic.point.SchemePoint

morphism()
class sage.schemes.generic.point.SchemeTopologicalPoint(S)
Bases: sage.schemes.generic.point.SchemePoint
class sage.schemes.generic.point.SchemeTopologicalPoint_affine_open(u, x)

Bases: sage.schemes.generic.point.SchemeTopologicalPoint

affine_open()
Return the affine open subset U.
embedding_of_affine_open()
Return the embedding from the affine open subset U into this scheme.
point_on_affine()
Return the scheme point on the affine open U.
class sage.schemes.generic.point.SchemeTopologicalPoint_prime_ideal(S, P, check=False)

Bases: sage.schemes.generic.point.SchemeTopologicalPoint

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()
Principal ideal (-x^2 + y*z) of Multivariate Polynomial Ring in x, y, z over Rational Field
sage.schemes.generic.point.is_SchemeRationalPoint(x)
sage.schemes.generic.point.is_SchemeTopologicalPoint(x)

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