def _find_isomorphism_to_subreflexive_polytope(self):
"""
Find an isomorphism to a sub-polytope of a maximal reflexive
polytope.
OUTPUT:
A tuple consisting of the ambient reflexive polytope, the
subpolytope, and the embedding of ``self`` into the ambient
polytope.
EXAMPLES::
sage: from sage.geometry.polyhedron.ppl_lattice_polytope import LatticePolytope_PPL
sage: polygon = LatticePolytope_PPL((0,0,2,1),(0,1,2,0),(2,3,0,0),(2,0,0,3))
sage: polygon._find_isomorphism_to_subreflexive_polytope()
(A 2-dimensional lattice polytope in ZZ^2 with 3 vertices,
A 2-dimensional lattice polytope in ZZ^2 with 4 vertices,
The map A*x+b with A=
[ 1 1]
[ 0 1]
[-1 -1]
[ 1 0]
b =
(-1, 0, 3, 0))
sage: ambient, sub, embedding = _
sage: ambient.vertices()
((0, 0), (0, 3), (3, 0))
sage: sub.vertices()
((0, 1), (3, 0), (0, 3), (1, 0))
"""
from ppl_lattice_polygon import sub_reflexive_polygons
from sage.geometry.polyhedron.lattice_euclidean_group_element import (
LatticePolytopesNotIsomorphicError,
LatticePolytopeNoEmbeddingError,
)
for p, ambient in sub_reflexive_polygons():
try:
return (ambient, p, p.find_isomorphism(self))
except LatticePolytopesNotIsomorphicError:
pass
from sage.geometry.polyhedron.lattice_euclidean_group_element import LatticePolytopeNoEmbeddingError
raise LatticePolytopeNoEmbeddingError("not a sub-polytope of a reflexive polygon")
def _find_isomorphism_to_subreflexive_polytope(self):
"""
Find an isomorphism to a sub-polytope of a maximal reflexive
polytope.
OUTPUT:
A tuple consisting of the ambient reflexive polytope, the
subpolytope, and the embedding of ``self`` into the ambient
polytope.
EXAMPLES::
sage: from sage.geometry.polyhedron.ppl_lattice_polytope import LatticePolytope_PPL
sage: polygon = LatticePolytope_PPL((0,0,2,1),(0,1,2,0),(2,3,0,0),(2,0,0,3))
sage: polygon._find_isomorphism_to_subreflexive_polytope()
(A 2-dimensional lattice polytope in ZZ^2 with 3 vertices,
A 2-dimensional lattice polytope in ZZ^2 with 4 vertices,
The map A*x+b with A=
[ 1 1]
[ 0 1]
[-1 -1]
[ 1 0]
b =
(-1, 0, 3, 0))
sage: ambient, sub, embedding = _
sage: ambient.vertices()
((0, 0), (0, 3), (3, 0))
sage: sub.vertices()
((0, 1), (3, 0), (0, 3), (1, 0))
"""
from ppl_lattice_polygon import sub_reflexive_polygons
from sage.geometry.polyhedron.lattice_euclidean_group_element import \
LatticePolytopesNotIsomorphicError, LatticePolytopeNoEmbeddingError
for p, ambient in sub_reflexive_polygons():
try:
return (ambient, p, p.find_isomorphism(self))
except LatticePolytopesNotIsomorphicError:
pass
from sage.geometry.polyhedron.lattice_euclidean_group_element import \
LatticePolytopeNoEmbeddingError
raise LatticePolytopeNoEmbeddingError(
'not a sub-polytope of a reflexive polygon')