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# newtonPolytope -- computes the Newton polytope of a polynomial

- Usage:
    `P = newtonPolytope f`
- Inputs:
  - f, a ring element
- Outputs:
  - P, a convex polyhedron

## 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 a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Polyhedra/documentation/old_documentation.m2:3006:0.