def _element_constructor_(self, x, check=True):
r"""
Construct a :class:`ChowCycle`.
INPUT:
- ``x`` -- a cone of the fan, a toric divisor, or a valid
input for
:class:sage.modules.fg_pid.fgp_module.FGP_Module_class`.
- ``check`` -- bool (default: ``True``). See
:class:sage.modules.fg_pid.fgp_module.FGP_Module_class`.
EXAMPLES::
sage: dP6 = toric_varieties.dP6()
sage: A = dP6.Chow_group()
sage: cone = dP6.fan(dim=1)[4]
sage: A(cone)
( 0 | 0, 1, 0, 0 | 0 )
sage: A(Cone(cone)) # isomorphic but not identical to a cone of the fan!
( 0 | 0, 1, 0, 0 | 0 )
sage: A( dP6.K() )
( 0 | -1, -2, -2, -1 | 0 )
"""
fan = self._variety.fan()
if is_Cone(x):
cone = fan.embed(x)
return self.element_class(self, self._cone_to_V(cone), False)
if is_ToricDivisor(x):
v = sum(x.coefficient(i)*self._cone_to_V(onecone)
for i,onecone in enumerate(fan(1)))
return self.element_class(self, v, False)
return super(ChowGroup_class,self)._element_constructor_(x, check)
def get_filtration(self, ray=None):
r"""
Return the filtration associated to the ``ray``.
INPUT:
- ``ray`` -- Integer, a `N`-lattice point, a one-dimensional
cone, or ``None`` (default). Specifies a ray of the fan of
the toric variety, either via its index or its generator.
OUTPUT:
The filtered vector space associated to the given ``ray``. If
no ray is specified, all filtrations are returned.
EXAMPLES::
sage: TX = toric_varieties.dP6().sheaves.tangent_bundle()
sage: TX.get_filtration(0)
QQ^2 >= QQ^1 >= 0
sage: TX.get_filtration([-1, -1])
QQ^2 >= QQ^1 >= 0
sage: TX.get_filtration(TX.variety().fan(1)[0])
QQ^2 >= QQ^1 >= 0
sage: TX.get_filtration()
Filtrations
N(-1, -1): QQ^2 >= QQ^1 >= 0
N(-1, 0): QQ^2 >= QQ^1 >= 0
N(0, -1): QQ^2 >= QQ^1 >= 0
N(0, 1): QQ^2 >= QQ^1 >= 0
N(1, 0): QQ^2 >= QQ^1 >= 0
N(1, 1): QQ^2 >= QQ^1 >= 0
"""
if ray is None:
return self._filt
X = self.variety()
fan = X.fan()
if is_Cone(ray):
if ray.dim() != 1:
raise ValueError('not a one-dimensional cone')
ray = ray.ray(0)
elif ray in ZZ:
ray = fan.ray(ray)
else:
N = fan.lattice()
ray = N(ray)
ray.set_immutable()
return self._filt.get_filtration(ray)
def get_filtration(self, ray=None):
r"""
Return the filtration associated to the ``ray``.
INPUT:
- ``ray`` -- Integer, a `N`-lattice point, a one-dimensional
cone, or ``None`` (default). Specifies a ray of the fan of
the toric variety, either via its index or its generator.
OUTPUT:
The filtered vector space associated to the given ``ray``. If
no ray is specified, all filtrations are returned.
EXAMPLES::
sage: TX = toric_varieties.dP6().sheaves.tangent_bundle()
sage: TX.get_filtration(0)
QQ^2 >= QQ^1 >= 0
sage: TX.get_filtration([-1, -1])
QQ^2 >= QQ^1 >= 0
sage: TX.get_filtration(TX.variety().fan(1)[0])
QQ^2 >= QQ^1 >= 0
sage: TX.get_filtration()
Filtrations
N(-1, -1): QQ^2 >= QQ^1 >= 0
N(-1, 0): QQ^2 >= QQ^1 >= 0
N(0, -1): QQ^2 >= QQ^1 >= 0
N(0, 1): QQ^2 >= QQ^1 >= 0
N(1, 0): QQ^2 >= QQ^1 >= 0
N(1, 1): QQ^2 >= QQ^1 >= 0
"""
if ray is None:
return self._filt
X = self.variety()
fan = X.fan()
if is_Cone(ray):
if ray.dim() != 1:
raise ValueError('not a one-dimensional cone')
ray = ray.ray(0)
elif ray in ZZ:
ray = fan.ray(ray)
else:
N = fan.lattice()
ray = N(ray)
ray.set_immutable()
return self._filt.get_filtration(ray)