COHERENT, REGULAR AND SIMPLE SYSTEMS IN ZERO DECOMPOSITIONS OF PARTIAL DIFFERENTIAL SYSTEMS

This paper studies triangular differential systems arising from various decompositions of partial differential polynomial systems. In theoretical aspects, we emphasizeon translating differential problems into purely algebraic ones. Rosenfeld's lemma is extended to a more general setting; relations between passivity and coherence are clarified;regular systems and simple systems are generalized and proposed, respectively. In algorithmic aspects, we review the Ritt-Wu and Seidenberg algorithms, and outline a methodfor decomposing a differential polynomial system into simple ones. Some applications arealso discussed.