# newtonPolytope -- computes the Newton polytope of a polynomial

## Synopsis

• Usage:
P = newtonPolytope f
• Inputs:
• f,
• Outputs:

## 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 = P o3 : Polyhedron

## Ways to use newtonPolytope :

• "newtonPolytope(RingElement)"

## For the programmer

The object newtonPolytope is .