Module: sage.schemes.generic.scheme
Author Log:
Module-level Functions
x) |
Return True if
is an affine scheme.
sage: is_AffineScheme(5) False sage: E = Spec(QQ) sage: is_AffineScheme(E) True
x) |
Return True if
is a scheme.
sage: is_Scheme(5) False sage: X = Spec(QQ) sage: is_Scheme(X) True
Class: AffineScheme
Functions: hom
self, x, [Y=None]) |
Return the scheme morphism from self to Y defined by x.
If Y is not given, try to determine from context.
We construct the inclusion from
into
induced by the inclusion from
into
.
sage: X = Spec(Q) sage: X.hom(Z.hom(Q)) Affine Scheme morphism: From: Spectrum of Rational Field To: Spectrum of Integer Ring Defn: Coercion morphism: From: Integer Ring To: Rational Field
Class: Scheme
self, X) |
Functions: base_extend,
base_morphism,
base_ring,
base_scheme,
category,
coordinate_ring,
dimension,
hom,
identity_morphism,
point,
point_homset,
point_set,
structure_morphism
self, Y) |
Y is either a scheme in the same category as self or a ring.
self) |
Return the coordinate ring of this scheme, if defined. Otherwise raise a ValueError.
self) |
Return the relative dimension of this scheme over its base.
self, x, [Y=None]) |
Return the scheme morphism from self to Y defined by x. If x is a scheme, try to determine a natural map to x.
If Y is not given, try to determine Y from context.
self, S) |
Return the set of S-valued points of this scheme.
self) |
Same as self.base_morphism().
Special Functions: __add__,
__call__,
__cmp__,
__div__,
_Hom_,
_homset_class,
_point_class,
_point_morphism_class
self) |
If S is a ring or scheme, return the set
of
-valued
points on
. If
is a list or tuple or just the coordinates,
return a point in
, where
is the base scheme of self.
sage: A = AffineSpace(2, QQ)
We create some point sets:
sage: A(QQ) Set of Rational Points of Affine Space of dimension 2 over Rational Field sage: A(RR) Set of Rational Points over Real Field with 53 bits of precision of Affine Space of dimension 2 over Rational Field sage: A(NumberField(x^2+1)) Set of Rational Points over Number Field in a with defining polynomial x^2 + 1 of Affine Space of dimension 2 over Rational Field sage: A(GF(7)) Traceback (most recent call last): ... ValueError: There must be a natural map S --> R, but S = Rational Field and R = Finite Field of size 7
We create some points:
sage: A(QQ)([1,0]) (1, 0)
We create the same point by giving the coordinates of the point directly.
sage: A( 1,0 ) (1, 0)
self, Y) |
Return the base extension of self to Y.
sage: A = AffineSpace(3, Z) sage: A Affine Space of dimension 3 over Integer Ring sage: A/Q Affine Space of dimension 3 over Rational Field sage: A/GF(7) Affine Space of dimension 3 over Finite Field of size 7
self, Y, [cat=True], [check=None]) |
Return the set of scheme morphisms from self to Y.