Description
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
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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
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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
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