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

查看全文 作　　者：LI Ziming(Institute Of Algorithms and Scientific Computing, German National Research Centerfor Information Technology, D-52754 Sankt Augustin, Germany)WANG Dongming(LEIBNIZ-IMAG, 46, Avenue Felix Viallet,38031 Grenoble Cedex, France) 出　　处：《Systems Science and Mathematical Sciences》索引1999年第12卷第S1期,共18页 摘　　要：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. 关 键 词：COHERENT set geometric theorem proving irreducible TRIANGULAR SYSTEM partial differential polynomial SYSTEM REGULAR SYSTEM SIMPLE SYSTEM TRIANGULAR SYSTEM ZERO decomposition.