Abstract

In this paper, a zero decomposition algorithm based on characteristic set methods are developed in reflexive difference and differential polynomial systems. The “generalized term order” is used to deal with negative exponents of difference operators in DD-polynomials and the reduction of two DD-polynomials is discussed. We introduce the concept of characteristic set in reflexive DD-polynomial systems and propose a algorithm which can be used to decompose the zero set of a finitely generated reflexive DD-polynomial set into the union of zero sets of coherent chains. Keywords-Characteristic set; Reflexive difference and differential polynomials; Generalized term order; Zero decomposition algorithm

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