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We improve the local generic position method for isolating the real roots ofa zero-dimensional bivariate polynomial system with two polynomials and extendthe method to general zero-dimensional polynomial systems. The method mainlyinvolves resultant computation and real root isolation of univariate polynomialequations. The roots of the system have a linear univariate representation. Thecomplexity of the method is $\tilde{O}_B(N^{10})$ for the bivariate case, where$N=\max(d,\tau)$, $d$ resp., $\tau$ is an upper bound on the degree, resp., themaximal coefficient bitsize of the input polynomials. The algorithm iscertified with probability 1 in the multivariate case. The implementation showsthat the method is efficient, especially for bivariate polynomial systems.

A Generic Position Based Method for Real Root Isolation of Zero-Dimensional Polynomial Systems