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OldPolyhedra :: newtonPolytope

newtonPolytope -- computes the Newton polytope of a polynomial

Synopsis

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
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

Ways to use newtonPolytope :

For the programmer

The object newtonPolytope is a method function.