def __init__(self, parent, phi, check=True):
"""
The Python constuctor.
See :class:`SchemeMorphism_structure_map` for details.
TESTS::
sage: from sage.schemes.generic.morphism import SchemeMorphism_spec
sage: SchemeMorphism_spec(Spec(QQ).Hom(Spec(ZZ)), ZZ.hom(QQ))
Affine Scheme morphism:
From: Spectrum of Rational Field
To: Spectrum of Integer Ring
Defn: Ring Coercion morphism:
From: Integer Ring
To: Rational Field
"""
SchemeMorphism.__init__(self, parent)
if check:
if not is_RingHomomorphism(phi):
raise TypeError("phi (=%s) must be a ring homomorphism" % phi)
if phi.domain() != parent.codomain().coordinate_ring():
raise TypeError("phi (=%s) must have domain %s"
% (phi, parent.codomain().coordinate_ring()))
if phi.codomain() != parent.domain().coordinate_ring():
raise TypeError("phi (=%s) must have codomain %s"
% (phi, parent.domain().coordinate_ring()))
self.__ring_homomorphism = phi
def __init__(self, parent, phi, check=True):
"""
The Python constuctor.
See :class:`SchemeMorphism_structure_map` for details.
TESTS::
sage: from sage.schemes.generic.morphism import SchemeMorphism_spec
sage: SchemeMorphism_spec(Spec(QQ).Hom(Spec(ZZ)), ZZ.hom(QQ))
Affine Scheme morphism:
From: Spectrum of Rational Field
To: Spectrum of Integer Ring
Defn: Ring Coercion morphism:
From: Integer Ring
To: Rational Field
"""
SchemeMorphism.__init__(self, parent)
if check:
if not is_RingHomomorphism(phi):
raise TypeError("phi (=%s) must be a ring homomorphism" % phi)
if phi.domain() != parent.codomain().coordinate_ring():
raise TypeError("phi (=%s) must have domain %s"
% (phi, parent.codomain().coordinate_ring()))
if phi.codomain() != parent.domain().coordinate_ring():
raise TypeError("phi (=%s) must have codomain %s"
% (phi, parent.domain().coordinate_ring()))
self.__ring_homomorphism = phi
def __init__(self, parent, polys, check=True):
"""
The Python constructor.
See :class:`SchemeMorphism_polynomial` for details.
EXAMPLES::
sage: A2.<x,y> = AffineSpace(QQ,2)
sage: H = A2.Hom(A2)
sage: H([x-y, x*y])
Scheme endomorphism of Affine Space of dimension 2 over Rational Field
Defn: Defined on coordinates by sending (x, y) to
(x - y, x*y)
"""
if check:
if not isinstance(polys, (list, tuple)):
raise TypeError("polys (=%s) must be a list or tuple"%polys)
source_ring = parent.domain().coordinate_ring()
target = parent._codomain.ambient_space()
if len(polys) != target.ngens():
raise ValueError("there must be %s polynomials"%target.ngens())
try:
polys = [source_ring(poly) for poly in polys]
except TypeError:
raise TypeError("polys (=%s) must be elements of %s"%(polys,source_ring))
if isinstance(source_ring, QuotientRing_generic):
lift_polys = [f.lift() for f in polys]
else:
lift_polys = polys
polys = Sequence(lift_polys)
self._polys = polys
SchemeMorphism.__init__(self, parent)
def __init__(self, parent, polys, check=True):
"""
The Python constructor.
See :class:`SchemeMorphism_polynomial` for details.
EXAMPLES::
sage: A2.<x,y> = AffineSpace(QQ,2)
sage: H = A2.Hom(A2)
sage: H([x-y, x*y])
Scheme endomorphism of Affine Space of dimension 2 over Rational Field
Defn: Defined on coordinates by sending (x, y) to
(x - y, x*y)
"""
if check:
if not isinstance(polys, (list, tuple)):
raise TypeError("polys (=%s) must be a list or tuple"%polys)
source_ring = parent.domain().coordinate_ring()
target = parent._codomain.ambient_space()
if len(polys) != target.ngens():
raise ValueError("there must be %s polynomials"%target.ngens())
try:
polys = [source_ring(poly) for poly in polys]
except TypeError:
raise TypeError("polys (=%s) must be elements of %s"%(polys,source_ring))
if isinstance(source_ring, QuotientRing_generic):
lift_polys = [f.lift() for f in polys]
else:
lift_polys = polys
polys = Sequence(lift_polys)
self._polys = polys
SchemeMorphism.__init__(self, parent)
def __init__(self, parent, codomain=None):
"""
The Python constructor.
EXAMPLES::
sage: X = Spec(ZZ)
sage: Hom = X.Hom(X)
sage: from sage.schemes.generic.morphism import SchemeMorphism
sage: f = SchemeMorphism(Hom)
sage: type(f)
<class 'sage.schemes.generic.morphism.SchemeMorphism'>
"""
if codomain is not None:
parent = Hom(parent, codomain)
if not isinstance(parent, Homset):
raise TypeError("parent (=%s) must be a Homspace"%parent)
Element.__init__(self, parent)
self.domain = ConstantFunction(parent.domain())
self._codomain = parent.codomain()
self.codomain = ConstantFunction(self._codomain)
def __init__(self, parent, codomain=None):
"""
The Python constructor.
EXAMPLES::
sage: X = Spec(ZZ)
sage: Hom = X.Hom(X)
sage: from sage.schemes.generic.morphism import SchemeMorphism
sage: f = SchemeMorphism(Hom)
sage: type(f)
<class 'sage.schemes.generic.morphism.SchemeMorphism'>
"""
if codomain is not None:
parent = Hom(parent, codomain)
if not isinstance(parent, Homset):
raise TypeError("parent (=%s) must be a Homspace"%parent)
Element.__init__(self, parent)
self.domain = ConstantFunction(parent.domain())
self._codomain = parent.codomain()
self.codomain = ConstantFunction(self._codomain)
