An Efficient Method for Computing Resultant Systems

Abstract

A resultant system of a finite set of polynomials in two homogeneous variables is a finite set of polynomials in the coefficients of the original polynomials whose vanishing is a necessary and sufficient condition for the original polynomials to have a common non-trivial zero. We present an efficient general method for computing resultant systems. If there are s polynomials and each has degree at most d, the resultant system will have O(s 2 d) polynomials, each of which will have degree at most d 2 .