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In this paper we consider disjoint decomposition of algebraic and non-linearpartial differential systems of equations and inequations into so-called simplesubsystems. We exploit Thomas decomposition ideas and develop them into a newalgorithm. For algebraic systems simplicity means triangularity, squarefreenessand non-vanishing initials. For differential systems the algorithm provides notonly algebraic simplicity but also involutivity. The algorithm has beenimplemented in Maple.

Thomas Decomposition of Algebraic and Differential Systems