The newtonPolytope of f is the convex hull of its exponent vectors in n-space, 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 = (a-b)*(a-c)*(b-c) 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 |
The object newtonPolytope is a method function.