Module: sage.schemes.generic.morphism
Scheme morphism
Author Log:
Module-level Functions
f) |
Class: PyMorphism
self, parent) |
Functions: category,
codomain,
domain,
is_endomorphism
Special Functions: __init__,
__pow__,
_composition_,
_repr_,
_repr_defn,
_repr_type
Class: SchemeMorphism
self, parent) |
Functions: glue_along_domains
self, other) |
Assuming that self and other are open immersions with the same domain, return scheme obtained by gluing along the images.
We construct a scheme isomorphic to the projective line over
by gluing two copies of
minus a point.
sage: R.<x,y> = PolynomialRing(QQ, 2) sage: S.<xbar, ybar> = R.quotient(x*y - 1) sage: Rx = PolynomialRing(QQ, 'x') sage: i1 = Rx.hom([xbar]) sage: Ry = PolynomialRing(QQ, 'y') sage: i2 = Ry.hom([ybar]) sage: Sch = Schemes() sage: f1 = Sch(i1) sage: f2 = Sch(i2)
Now f1 and f2 have the same domain, which is a
minus a point.
We glue along the domain:
sage: P1 = f1.glue_along_domains(f2) sage: P1 Scheme obtained by gluing X and Y along U, where X: Spectrum of Univariate Polynomial Ring in x over Rational Field Y: Spectrum of Univariate Polynomial Ring in y over Rational Field U: Spectrum of Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x*y - 1)
sage: a, b = P1.gluing_maps() sage: a Affine Scheme morphism: From: Spectrum of Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x*y - 1) To: Spectrum of Univariate Polynomial Ring in x over Rational Field Defn: Ring morphism: From: Univariate Polynomial Ring in x over Rational Field To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x*y - 1) Defn: x |--> xbar sage: b Affine Scheme morphism: From: Spectrum of Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x*y - 1) To: Spectrum of Univariate Polynomial Ring in y over Rational Field Defn: Ring morphism: From: Univariate Polynomial Ring in y over Rational Field To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x*y - 1) Defn: y |--> ybar
Special Functions: __init__,
_repr_type
Class: SchemeMorphism_abelian_variety_coordinates_field
Special Functions: __mul__
Class: SchemeMorphism_affine_coordinates
Input:
sage: A = AffineSpace(2, QQ) sage: A(1,2) (1, 2)
self, X, v, [check=True]) |
Special Functions: __init__
Class: SchemeMorphism_coordinates
Functions: scheme
Special Functions: __cmp__,
__getitem__,
__iter__,
__tuple__,
_latex_,
_repr_
Class: SchemeMorphism_id
sage: X = Spec(ZZ) sage: X.identity_morphism() Scheme endomorphism of Spectrum of Integer Ring Defn: Identity map
self, X) |
Special Functions: __init__,
_repr_defn
Class: SchemeMorphism_on_points
Special Functions: __call__,
_repr_defn
Class: SchemeMorphism_on_points_affine_space
self, parent, polys, [check=True]) |
Functions: defining_polynomials
Special Functions: __init__
Class: SchemeMorphism_on_points_projective_space
self, parent, polys, [check=True]) |
Functions: defining_polynomials
Special Functions: __init__
Class: SchemeMorphism_projective_coordinates_field
Input:
sage: P = ProjectiveSpace(3, RR) sage: P(2,3,4,5) (0.400000000000000 : 0.600000000000000 : 0.800000000000000 : 1.00000000000000)
sage: P = ProjectiveSpace(3, QQ) sage: P(0,0,0,0) Traceback (most recent call last): ... ValueError: [0, 0, 0, 0] does not define a valid point since all entries are 0
self, X, v, [check=True]) |
Special Functions: __init__
Class: SchemeMorphism_projective_coordinates_ring
self, X, v, [check=True]) |
Special Functions: __init__
Class: SchemeMorphism_spec
sage: R.<x> = PolynomialRing(QQ) sage: phi = R.hom([QQ(7)]); phi Ring morphism: From: Univariate Polynomial Ring in x over Rational Field To: Rational Field Defn: x |--> 7
sage: X = Spec(QQ); Y = Spec(R) sage: f = X.hom(phi); f Affine Scheme morphism: From: Spectrum of Rational Field To: Spectrum of Univariate Polynomial Ring in x over Rational Field Defn: Ring morphism: From: Univariate Polynomial Ring in x over Rational Field To: Rational Field Defn: x |--> 7
sage: f.ring_homomorphism() Ring morphism: From: Univariate Polynomial Ring in x over Rational Field To: Rational Field Defn: x |--> 7
self, parent, phi, [check=True]) |
Functions: ring_homomorphism
Special Functions: __call__,
__init__,
_repr_defn,
_repr_type
Class: SchemeMorphism_structure_map
self, parent) |
Input:
Special Functions: __init__,
_repr_defn