def _morphism(self, *args, **kwds):
r"""
Construct a morphism determined by action on points of ``self``.
INPUT:
- same as for
:class:`~sage.schemes.toric.morphism.SchemeMorphism_polynomial_toric_variety`.
OUTPUT:
- :class:`~sage.schemes.toric.morphism.SchemeMorphism_polynomial_toric_variety`.
TESTS::
sage: P1xP1 = toric_varieties.P1xP1()
sage: P1xP1.inject_variables()
Defining s, t, x, y
sage: P1 = P1xP1.subscheme(s - t)
sage: H = P1.Hom(P1xP1)
sage: H([s, s, x, y])
Scheme morphism:
From: Closed subscheme of 2-d CPR-Fano toric variety
covered by 4 affine patches defined by:
s - t
To: 2-d CPR-Fano toric variety covered by 4 affine patches
Defn: Defined on coordinates by sending [s : t : x : y] to
[s : s : x : y]
sage: sbar, tbar, xbar, ybar = P1.coordinate_ring().gens()
sage: P1._morphism(H, [sbar, sbar, xbar, ybar])
Scheme morphism:
From: Closed subscheme of 2-d CPR-Fano toric variety
covered by 4 affine patches defined by:
s - t
To: 2-d CPR-Fano toric variety covered by 4 affine patches
Defn: Defined on coordinates by sending [s : t : x : y] to
[t : t : x : y]
"""
from sage.schemes.toric.morphism import SchemeMorphism_polynomial_toric_variety
return SchemeMorphism_polynomial_toric_variety(*args, **kwds)
def _element_constructor_(self, x, check=True):
"""
Construct a scheme morphism.
INPUT:
- `x` -- anything that defines a morphism of toric
varieties. A matrix, fan morphism, or a list or tuple of
homogeneous polynomials that define a morphism.
- ``check`` -- boolean (default: ``True``) passed onto
functions called by this to be more careful about input
argument type checking
OUTPUT:
The morphism of toric varieties determined by ``x``.
EXAMPLES:
First, construct from fan morphism::
sage: dP8.<t,x0,x1,x2> = toric_varieties.dP8()
sage: P2.<y0,y1,y2> = toric_varieties.P2()
sage: hom_set = dP8.Hom(P2)
sage: fm = FanMorphism(identity_matrix(2), dP8.fan(), P2.fan())
sage: hom_set(fm) # calls hom_set._element_constructor_()
Scheme morphism:
From: 2-d CPR-Fano toric variety covered by 4 affine patches
To: 2-d CPR-Fano toric variety covered by 3 affine patches
Defn: Defined by sending Rational polyhedral fan in 2-d lattice N
to Rational polyhedral fan in 2-d lattice N.
A matrix will automatically be converted to a fan morphism::
sage: hom_set(identity_matrix(2))
Scheme morphism:
From: 2-d CPR-Fano toric variety covered by 4 affine patches
To: 2-d CPR-Fano toric variety covered by 3 affine patches
Defn: Defined by sending Rational polyhedral fan in 2-d lattice N
to Rational polyhedral fan in 2-d lattice N.
Alternatively, one can use homogeneous polynomials to define morphisms::
sage: P2.inject_variables()
Defining y0, y1, y2
sage: dP8.inject_variables()
Defining t, x0, x1, x2
sage: hom_set([x0,x1,x2])
Scheme morphism:
From: 2-d CPR-Fano toric variety covered by 4 affine patches
To: 2-d CPR-Fano toric variety covered by 3 affine patches
Defn: Defined on coordinates by sending [t : x0 : x1 : x2] to
[x0 : x1 : x2]
A morphism of the coordinate ring will also work::
sage: ring_hom = P2.coordinate_ring().hom([x0,x1,x2], dP8.coordinate_ring())
sage: ring_hom
Ring morphism:
From: Multivariate Polynomial Ring in y0, y1, y2 over Rational Field
To: Multivariate Polynomial Ring in t, x0, x1, x2 over Rational Field
Defn: y0 |--> x0
y1 |--> x1
y2 |--> x2
sage: hom_set(ring_hom)
Scheme morphism:
From: 2-d CPR-Fano toric variety covered by 4 affine patches
To: 2-d CPR-Fano toric variety covered by 3 affine patches
Defn: Defined on coordinates by sending [t : x0 : x1 : x2] to
[x0 : x1 : x2]
"""
from sage.schemes.toric.morphism import SchemeMorphism_polynomial_toric_variety
if isinstance(x, (list, tuple)):
return SchemeMorphism_polynomial_toric_variety(self,
x,
check=check)
from sage.categories.map import Map
from sage.categories.all import Rings
if isinstance(x, Map) and x.category_for().is_subcategory(Rings()):
# x is a morphism of Rings
assert x.domain() is self.codomain().coordinate_ring()
assert x.codomain() is self.domain().coordinate_ring()
return SchemeMorphism_polynomial_toric_variety(self,
x.im_gens(),
check=check)
if is_Matrix(x):
x = FanMorphism(x, self.domain().fan(), self.codomain().fan())
if isinstance(x, FanMorphism):
if x.is_dominant():
from sage.schemes.toric.morphism import SchemeMorphism_fan_toric_variety_dominant
return SchemeMorphism_fan_toric_variety_dominant(self,
x,
check=check)
else:
from sage.schemes.toric.morphism import SchemeMorphism_fan_toric_variety
return SchemeMorphism_fan_toric_variety(self, x, check=check)
raise TypeError(
"x must be a fan morphism or a list/tuple of polynomials")
