Bivariate Kolchin-type dimension polynomials of non-reflexive prime difference-differential ideals. The case of one translation. (January 2021)

• Record Type: Journal Article
• Authors: Levin, Alexander
• Is Part Of: Journal of symbolic computation. Volume 102(2020)
• Page Start: 173
• Page End: 188
• Publication Date: 2021-01
• Subjects: Difference-differential polynomial -- Reflexive closure -- Dimension polynomial -- Reduction -- Characteristic set; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.10.014
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We use the method of characteristic sets with respect to two term orderings to prove the existence and obtain a method of computation of a bivariate Kolchin-type dimension polynomial associated with a non-reflexive difference-differential ideal in the algebra of difference-differential polynomials with several basic derivations and one translation. In particular, we obtain a new proof and a method of computation of the dimension polynomial of a non-reflexive prime difference ideal in the algebra of difference polynomials over an ordinary difference field. As a consequence, it is shown that the reflexive closure of a prime difference polynomial ideal is the inverse image of this ideal under a power of the basic translation. We also discuss applications of our results to the analysis of systems of algebraic difference-differential equations.