def _make_ToricVariety(self, name, coordinate_names):
"""
Construct a toric variety and cache the result.
INPUT:
- ``name`` -- string. One of the pre-defined names in the
``toric_varieties_rays_cones`` data structure.
- ``coordinate_names`` -- A string describing the names of the
homogeneous coordinates of the toric variety.
OUTPUT:
A :class:`toric variety
<sage.schemes.generic.toric_variety.ToricVariety_field>`.
EXAMPLES::
sage: toric_varieties.A1() # indirect doctest
1-d affine toric variety
"""
rays, cones = toric_varieties_rays_cones[name]
if coordinate_names is None:
dict_key = "_cached_" + name
else:
import toric_variety
coordinate_names = toric_variety.normalize_names(coordinate_names, len(rays), toric_variety.DEFAULT_PREFIX)
dict_key = "_cached_" + name + "_" + "_".join(coordinate_names)
if dict_key not in self.__dict__:
fan = Fan(cones, rays, check=self._check)
self.__dict__[dict_key] = ToricVariety(fan, coordinate_names=coordinate_names)
return self.__dict__[dict_key]
def _make_CPRFanoToricVariety(self, name, coordinate_names):
"""
Construct a (crepant partially resolved) Fano toric variety
and cache the result.
INPUT:
- ``name`` -- string. One of the pre-defined names in the
``toric_varieties_rays_cones`` data structure.
- ``coordinate_names`` -- A string describing the names of the
homogeneous coordinates of the toric variety.
OUTPUT:
A :class:`CPR-Fano toric variety
<sage.schemes.generic.fano_toric_variety.CPRFanoToricVariety_field>`.
EXAMPLES::
sage: toric_varieties.P2() # indirect doctest
2-d CPR-Fano toric variety covered by 3 affine patches
"""
rays, cones = toric_varieties_rays_cones[name]
if coordinate_names is None:
dict_key = "_cached_" + name
else:
import toric_variety
coordinate_names = toric_variety.normalize_names(coordinate_names, len(rays), toric_variety.DEFAULT_PREFIX)
dict_key = "_cached_" + name + "_" + "_".join(coordinate_names)
if dict_key not in self.__dict__:
polytope = LatticePolytope(matrix(rays).transpose())
points = map(tuple, polytope.points().columns())
ray2point = [points.index(r) for r in rays]
charts = [[ray2point[i] for i in c] for c in cones]
self.__dict__[dict_key] = CPRFanoToricVariety(
Delta_polar=polytope,
coordinate_points=ray2point,
charts=charts,
coordinate_names=coordinate_names,
check=self._check,
)
return self.__dict__[dict_key]
