A new interpolation algorithm for computing dixon resultants

Abstract

Given a system of polynomial equations with parameters, we present a new interpolation algorithm for computing its Dixon resultant R. Our algorithm interpolates the monic square-free factors of R one at a time from monic univariate polynomial images of R using sparse rational function interpolation. We have implemented our new Dixon resultant algorithm in Maple with some subroutines coded in C for efficiency. Experimental results show that our algorithm significantly outperforms Zippel's sparse interpolation algorithm.