def __init__(self, X, coordinates, check=True):
r"""
See :class:`SchemeMorphism_toric_coordinates_field` for documentation.
TESTS::
sage: fan = FaceFan(lattice_polytope.octahedron(2))
sage: P1xP1 = ToricVariety(fan)
sage: P1xP1(1,2,3,4)
[1 : 2 : 3 : 4]
"""
# Convert scheme to its set of points over the base ring
if scheme.is_Scheme(X):
X = X(X.base_ring())
super(SchemeMorphism_toric_coordinates_field, self).__init__(X)
if check:
# Verify that there are the right number of coords
# Why is it not done in the parent?
if is_SchemeMorphism(coordinates):
coordinates = list(coordinates)
if not isinstance(coordinates, (list, tuple)):
raise TypeError("coordinates must be a scheme point, list, "
"or tuple. Got %s" % coordinates)
d = X.codomain().ambient_space().ngens()
if len(coordinates) != d:
raise ValueError("there must be %d coordinates! Got only %d: "
"%s" % (d, len(coordinates), coordinates))
# Make sure the coordinates all lie in the appropriate ring
coordinates = Sequence(coordinates, X.value_ring())
# Verify that the point satisfies the equations of X.
X.codomain()._check_satisfies_equations(coordinates)
self._coords = coordinates
def __init__(self, X, v, check=True):
if scheme.is_Scheme(X):
X = X(X.base_ring())
SchemeMorphism.__init__(self, X)
if check:
# Verify that there are the right number of coords
d = X.codomain().ambient_space().ngens()
if len(v) != d:
raise TypeError, \
"Argument v (=%s) must have %s coordinates."%(v, d)
if is_SchemeMorphism(v):
v = list(v)
if not isinstance(v,(list,tuple)):
raise TypeError, \
"Argument v (= %s) must be a scheme point, list, or tuple."%str(v)
# Make sure the coordinates all lie in the appropriate ring
v = Sequence(v, X.value_ring())
# Verify that the point satisfies the equations of X.
X.codomain()._check_satisfies_equations(v)
self._coords = v
def __init__(self, X, v, check=True):
if scheme.is_Scheme(X):
X = X(X.base_ring())
SchemeMorphism.__init__(self, X)
if check:
from sage.schemes.elliptic_curves.ell_point import EllipticCurvePoint_field # TODO: fix circular ref.
d = X.codomain().ambient_space().ngens()
if is_SchemeMorphism(v) or isinstance(v, EllipticCurvePoint_field):
v = list(v)
elif v is infinity:
v = [0] * (d)
v[1] = 1
if not isinstance(v,(list,tuple)):
raise TypeError, \
"Argument v (= %s) must be a scheme point, list, or tuple."%str(v)
if len(v) != d and len(v) != d-1:
raise TypeError, "v (=%s) must have %s components"%(v, d)
#v = Sequence(v, X.base_ring())
v = Sequence(v, X.value_ring())
if len(v) == d-1: # very common special case
v.append(1)
n = len(v)
all_zero = True
for i in range(n):
if v[n-1-i]:
all_zero = False
c = v[n-1-i]
if c == 1:
break
for j in range(n-i):
v[j] /= c
break
if all_zero:
raise ValueError, "%s does not define a valid point since all entries are 0"%repr(v)
X.codomain()._check_satisfies_equations(v)
self._coords = v
