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 QQ
sage: (2*P).parent()
Polyhedra in QQ^3
Since 2*P
is a lattice polytope it seems like it should be possible to restrict the base ring of 2*P
to ZZ
. Is this possible?