def _iterate_PointCollection(self, start, stop, step):
"""
Iterate over the reflexive polytopes.
INPUT:
- ``start``, ``stop``, ``step`` -- integers specifying the
range to iterate over.
OUTPUT:
A generator for PPL-based lattice polyhedra.
EXAMPLES::
sage: from sage.geometry.polyhedron.palp_database import PALPreader
sage: polygons = PALPreader(2)
sage: iter = polygons._iterate_PointCollection(0,4,2)
sage: next(iter)
[ 1, 0],
[ 0, 1],
[-1, -1]
in Ambient free module of rank 2 over the principal ideal domain Integer Ring
"""
from sage.modules.free_module import FreeModule
N = FreeModule(ZZ, self._dim)
from sage.geometry.point_collection import PointCollection
for vertices in self._iterate_list(start, stop, step):
yield PointCollection(vertices, module=N)
def fan_2d_cyclically_ordered_rays(fan):
"""
Return the rays of a 2-dimensional ``fan`` in cyclic order.
INPUT:
- ``fan`` -- a 2-dimensional fan.
OUTPUT:
A :class:`~sage.geometry.point_collection.PointCollection`
containing the rays in one particular cyclic order.
EXAMPLES::
sage: rays = ((1, 1), (-1, -1), (-1, 1), (1, -1))
sage: cones = [(0,2), (2,1), (1,3), (3,0)]
sage: fan = Fan(cones, rays)
sage: fan.rays()
N( 1, 1),
N(-1, -1),
N(-1, 1),
N( 1, -1)
in 2-d lattice N
sage: from sage.geometry.fan_isomorphism import fan_2d_cyclically_ordered_rays
sage: fan_2d_cyclically_ordered_rays(fan)
N(-1, -1),
N(-1, 1),
N( 1, 1),
N( 1, -1)
in 2-d lattice N
TESTS::
sage: fan = Fan(cones=[], rays=[], lattice=ZZ^2)
sage: from sage.geometry.fan_isomorphism import fan_2d_cyclically_ordered_rays
sage: fan_2d_cyclically_ordered_rays(fan)
Empty collection
in Ambient free module of rank 2 over the principal ideal domain Integer Ring
"""
assert fan.lattice_dim() == 2
import math
rays = [(math.atan2(r[0], r[1]), r) for r in fan.rays()]
rays = [r[1] for r in sorted(rays)]
from sage.geometry.point_collection import PointCollection
return PointCollection(rays, fan.lattice())