Computation and applications of the Newton polyhedrons
We consider the multivariate Laurent polynomial f (X) = Sigma a(Q)X(Q), Q epsilon D with coefficients a(Q) epsilon R or C and D is some set in Z(n). The set D = D(f) = {Q: a(Q) not equal 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.). (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
newton polyhedron systems of differential polynomials intersections of normal cones truncated systems