Computation and applications of the Newton polyhedrons Original Research Article

We consider the multivariate Laurent polynomialf(X)=∑aQXQ, Q∈Dwith coefficients aQ∈R or C and D is some set in Zn. The set D=D(f)={Q: aQ≠0} is called the support of the polynomial f(X). The convex hull M=M(f) of the set D is called the Newton polyhedron of the polynomial f(X). There are important correspondences between properties of the polynomial f(X) and of its Newton polyhedron M(f) that were studied by Bruno, Soleev, Khovansgfkii and others. We propose algorithms and the computer program for computation of the Newton polyhedron of any polynomial, and for computation of all elements of this polyhedron (vertices, edges, faces, etc.).