Characteristic set method for differential-difference polynomial systems

Authors:
X. S. Gao;J. Van der Hoeven;C. M. Yuan;G. L. Zhang
Affiliations:
KLMM, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China;CNRS, Département de Mathématiques, Université Paris-Sud 91405 Orsay Cedex, France;KLMM, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China;KLMM, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China
Venue:
Journal of Symbolic Computation
Year:
2009

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Abstract

In 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.