Bulletin of the Australian Mathematical Society

Table of Contents - August 1997 - Volume 56, Issue 01  

Research Article

Computing the topological degree of polynomial maps

Takis Sakkalisa1 and Zenon Ligatsikasa1

a1 Department of Mathematics Agricultural University of Athens Athens 118 55 Greece e-mail: gmat2sap@auadec.aua.ariadne-t.gr

Abstract

Let C be a cube in Rn+1 and let F = (f1, …, fn+1) be a polynomial vector field. In this note we propose a recursive algorithm for the computation of the degree of F on C. The main idea of the algorithm is that the degree of F is equal to the algebraic sum of the degrees of the map (f1, f2, …, fi−1, fi, fi+1, …, fn+1) over all sides of C, thereby reducing an (n + 1)–dimensional problem to an n–dimensional one.

(Received September 02 1996)