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TitleCharacteristic set method for differential–difference polynomial systems
Author(s) Xiao Shan Gao, Svante Janson, C.M. Yuan, G.L. Zhang
TypeArticle in Journal
AbstractIn this paper, we present a characteristic set method for mixed differential and difference polynomial systems. We introduce the concepts of coherent, regular, proper irreducible, and strongly irreducible ascending chains and study their properties. We give an algorithm which can be used to decompose the zero set for a finitely generated differential and difference polynomial sets into the union of the zero sets of regular and consistent ascending chains. As a consequence, we solve the perfect ideal membership problem for differential and difference polynomials.
KeywordsCharacteristic set, Differential and difference polynomial, Regular ascending chain Irreducible ascending chain, Zero decomposition algorithm Perfect ideal membership problem
URL http://www.sciencedirect.com/science/article/pii/S0747717109000145
JournalJournal of Symbolic Computation
Pages1137 - 1163
NoteEffective Methods in Algebraic Geometry
Translation No
Refereed No