Can the base ring of a polyhedron be restricted?
I have a polyhedron
P with rational vertices
sage: A = matrix([[1,0,0],[1,0,2],[1,1,1],[1,3/2,0]]) sage: A [ 1 0 0] [ 1 0 2] [ 1 1 1] [ 1 3/2 0] sage: P = Polyhedron(A) sage: P A 2-dimensional polyhedron in QQ^3 defined as the convex hull of 4 vertices
If we scale
P by a factor of two, then we get a lattice polytope.
sage: (2*P).is_lattice_polytope() True
However, the base ring of
P is still
sage: (2*P).parent() Polyhedra in QQ^3
2*P is a lattice polytope it seems like it should be possible to restrict the base ring of
ZZ. Is this possible?