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 zero decomposition. The method employs top-down elimination with splitting and the formation of subresultant regular subchains as basic operation.