Certified Numerical Real Root Isolation for Bivariate Polynomial Systems.

In this paper, we present a new method for isolating real roots of a bivariate polynomial system. Our method is a subdivision method which is based on real root isolation of univariate polynomials and analyzing the local geometrical properties of the given system. We propose the concept of the orthogonal monotone system in a box and use it to determine the uniqueness and the existence of a simple real zero of the system in the box. We implement our method to isolate the real zeros of a given bivariate polynomial system. The experiments show the effectivity and efficiency of our method, especially for systems with high degrees and sparse terms. Our method also works for non-polynomial systems.