Decomposing polynomial systems into simple systems

A simple system is a pair of multivariate polynomial sets (one set for equations and the other for inequations) ordered in triangular form, in which every polynomial is squarefree and has non-vanishing leading coefficient with respect to its leading variable. This paper presents a method that decomposes any pair of polynomial sets into finitely many simple systems with an associated aero decomposition. The method employs top-down elimination with splitting and the formation of subresultant regular subchains as basic operation. (C) 1998 Academic Press Limited.