Characteristic set method for differential-difference polynomial systems
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. (C) 2009 Elsevier Ltd. All rights reserved.
characteristic set differential and difference polynomial irreducible ascending chain perfect ideal membership problem regular ascending chain zero decomposition algorithm