def _call_(self, x):
"""
Construct a scheme from the data in ``x``
EXAMPLES:
Let us first construct the category of schemes::
sage: S = Schemes(); S
Category of schemes
We create a scheme from a ring::
sage: X = S(ZZ); X # indirect doctest
Spectrum of Integer Ring
We create a scheme from a scheme (do nothing)::
sage: S(X)
Spectrum of Integer Ring
We create a scheme morphism from a ring homomorphism.x::
sage: phi = ZZ.hom(QQ); phi
Ring Coercion morphism:
From: Integer Ring
To: Rational Field
sage: f = S(phi); f # indirect doctest
Affine Scheme morphism:
From: Spectrum of Rational Field
To: Spectrum of Integer Ring
Defn: Ring Coercion morphism:
From: Integer Ring
To: Rational Field
sage: f.domain()
Spectrum of Rational Field
sage: f.codomain()
Spectrum of Integer Ring
sage: S(f) # indirect doctest
Affine Scheme morphism:
From: Spectrum of Rational Field
To: Spectrum of Integer Ring
Defn: Ring Coercion morphism:
From: Integer Ring
To: Rational Field
"""
from sage.schemes.generic.scheme import is_Scheme
if is_Scheme(x):
return x
from sage.schemes.generic.morphism import is_SchemeMorphism
if is_SchemeMorphism(x):
return x
from sage.rings.morphism import is_RingHomomorphism
from sage.rings.ring import CommutativeRing
from sage.schemes.generic.spec import Spec
if isinstance(x, CommutativeRing):
return Spec(x)
elif is_RingHomomorphism(x):
A = Spec(x.codomain())
return A.hom(x)
else:
raise TypeError("No way to create an object or morphism in %s from %s"%(self, x))
def _call_(self, x):
"""
Construct a scheme from the data in ``x``
EXAMPLES:
Let us first construct the category of schemes::
sage: S = Schemes(); S
Category of schemes
We create a scheme from a ring::
sage: X = S(ZZ); X # indirect doctest
Spectrum of Integer Ring
We create a scheme from a scheme (do nothing)::
sage: S(X)
Spectrum of Integer Ring
We create a scheme morphism from a ring homomorphism.x::
sage: phi = ZZ.hom(QQ); phi
Ring Coercion morphism:
From: Integer Ring
To: Rational Field
sage: f = S(phi); f # indirect doctest
Affine Scheme morphism:
From: Spectrum of Rational Field
To: Spectrum of Integer Ring
Defn: Ring Coercion morphism:
From: Integer Ring
To: Rational Field
sage: f.domain()
Spectrum of Rational Field
sage: f.codomain()
Spectrum of Integer Ring
sage: S(f) # indirect doctest
Affine Scheme morphism:
From: Spectrum of Rational Field
To: Spectrum of Integer Ring
Defn: Ring Coercion morphism:
From: Integer Ring
To: Rational Field
"""
from sage.schemes.generic.scheme import is_Scheme
if is_Scheme(x):
return x
from sage.schemes.generic.morphism import is_SchemeMorphism
if is_SchemeMorphism(x):
return x
from sage.rings.morphism import is_RingHomomorphism
from sage.rings.commutative_ring import is_CommutativeRing
from sage.schemes.generic.spec import Spec
if is_CommutativeRing(x):
return Spec(x)
elif is_RingHomomorphism(x):
A = Spec(x.codomain())
return A.hom(x)
else:
raise TypeError(
"No way to create an object or morphism in %s from %s" %
(self, x))
def _call_(self, x):
"""
Construct a scheme from the data in ``x``
EXAMPLES:
Let us first construct the category of schemes::
sage: S = Schemes(); S
Category of schemes
We create a scheme from a ring::
sage: X = S(ZZ); X # indirect doctest
Spectrum of Integer Ring
We create a scheme from a scheme (do nothing)::
sage: S(X)
Spectrum of Integer Ring
We create a scheme morphism from a ring homomorphism.x::
sage: phi = ZZ.hom(QQ); phi
Natural morphism:
From: Integer Ring
To: Rational Field
sage: f = S(phi); f # indirect doctest
Affine Scheme morphism:
From: Spectrum of Rational Field
To: Spectrum of Integer Ring
Defn: Natural morphism:
From: Integer Ring
To: Rational Field
sage: f.domain()
Spectrum of Rational Field
sage: f.codomain()
Spectrum of Integer Ring
sage: S(f) # indirect doctest
Affine Scheme morphism:
From: Spectrum of Rational Field
To: Spectrum of Integer Ring
Defn: Natural morphism:
From: Integer Ring
To: Rational Field
"""
from sage.schemes.generic.scheme import is_Scheme
if is_Scheme(x):
return x
from sage.schemes.generic.morphism import is_SchemeMorphism
if is_SchemeMorphism(x):
return x
from sage.rings.ring import CommutativeRing
from sage.schemes.generic.spec import Spec
from sage.categories.map import Map
from sage.categories.all import Rings
if isinstance(x, CommutativeRing):
return Spec(x)
elif isinstance(x, Map) and x.category_for().is_subcategory(Rings()):
# x is a morphism of Rings
A = Spec(x.codomain())
return A.hom(x)
else:
raise TypeError("No way to create an object or morphism in %s from %s"%(self, x))
