def _init_from_Hrepresentation(self,
ieqs,
eqns,
minimize=True,
verbose=False):
"""
Construct polyhedron from H-representation data.
INPUT:
- ``ieqs`` -- list of inequalities. Each line can be specified
as any iterable container of
:meth:`~sage.geometry.polyhedron.base.base_ring` elements.
- ``eqns`` -- list of equalities. Each line can be specified
as any iterable container of
:meth:`~sage.geometry.polyhedron.base.base_ring` elements.
- ``verbose`` -- boolean (default: ``False``). Whether to print
verbose output for debugging purposes.
TESTS::
sage: p = Polyhedron(ambient_dim=2, backend='field')
sage: from sage.geometry.polyhedron.backend_field import Polyhedron_field
sage: Polyhedron_field._init_from_Hrepresentation(p, [(1, 2, 3)], [])
"""
from sage.geometry.polyhedron.double_description_inhomogeneous import Hrep2Vrep, Vrep2Hrep
V = Hrep2Vrep(self.base_ring(), self.ambient_dim(), ieqs, eqns)
H = Vrep2Hrep(self.base_ring(), self.ambient_dim(), V.vertices, V.rays,
V.lines)
self._init_Vrepresentation_backend(V)
self._init_Hrepresentation_backend(H)
def _init_from_Vrepresentation(self, vertices, rays, lines,
minimize=True, verbose=False):
"""
Construct polyhedron from V-representation data.
INPUT:
- ``vertices`` -- list of points. Each point can be specified
as any iterable container of
:meth:`~sage.geometry.polyhedron.base.base_ring` elements.
- ``rays`` -- list of rays. Each ray can be specified as any
iterable container of
:meth:`~sage.geometry.polyhedron.base.base_ring` elements.
- ``lines`` -- list of lines. Each line can be specified as
any iterable container of
:meth:`~sage.geometry.polyhedron.base.base_ring` elements.
- ``verbose`` -- boolean (default: ``False``). Whether to print
verbose output for debugging purposes.
EXAMPLES::
sage: p = Polyhedron(ambient_dim=2, backend='field')
sage: from sage.geometry.polyhedron.backend_field import Polyhedron_field
sage: Polyhedron_field._init_from_Vrepresentation(p, [(0,0)], [], [])
"""
from sage.geometry.polyhedron.double_description_inhomogeneous import Hrep2Vrep, Vrep2Hrep
H = Vrep2Hrep(self.base_ring(), self.ambient_dim(), vertices, rays, lines)
V = Hrep2Vrep(self.base_ring(), self.ambient_dim(),
H.inequalities, H.equations)
self._init_Vrepresentation_backend(V)
self._init_Hrepresentation_backend(H)