Description
The
newtonPolytope of
f is the convex hull of its exponent vectors in nspace, where n is the number of variables in the ring.
Consider the Vandermond determinant in 3 variables:
i1 : R = QQ[a,b,c]
o1 = R
o1 : PolynomialRing

i2 : f = (ab)*(ac)*(bc)
2 2 2 2 2 2
o2 = a b  a*b  a c + b c + a*c  b*c
o2 : R

If we compute the Newton polytope we get a hexagon in
QQ^3.
i3 : P = newtonPolytope f
o3 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 6
number of rays => 0
number of vertices => 6
o3 : Polyhedron
