Points on schemes#
- class sage.schemes.generic.point.SchemePoint(S, parent=None)#
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
INPUT:
f
- a morphism of schemes
- morphism()#
- class sage.schemes.generic.point.SchemeTopologicalPoint(S)#
Bases:
sage.schemes.generic.point.SchemePoint
Base class for topological points on schemes.
- class sage.schemes.generic.point.SchemeTopologicalPoint_affine_open(u, x)#
Bases:
sage.schemes.generic.point.SchemeTopologicalPoint
INPUT:
u
– morphism with domain an affine scheme \(U\)x
– topological point on \(U\)
- 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
INPUT:
S
– an affine schemeP
– a prime ideal of the coordinate ring of \(S\), or anything that can be converted into such an ideal
- 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
- sage.schemes.generic.point.is_SchemeRationalPoint(x)#
- sage.schemes.generic.point.is_SchemeTopologicalPoint(x)#