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In this paper, a linear univariate representation for the roots of azero-dimensional polynomial equation system is presented, where the roots ofthe equation system are represented as linear combinations of roots of severalunivariate polynomial equations. The main advantage of this representation isthat the precision of the roots can be easily controlled. In fact, based on thelinear univariate representation, we can give the exact precisions needed forroots of the univariate equations in order to obtain the roots of the equationsystem to a given precision. As a consequence, a root isolation algorithm for azero-dimensional polynomial equation system can be easily derived from itslinear univariate representation.

Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation