Difference indices of quasi-prime difference algebraic systems. (July 2018)

• Record Type: Journal Article
• Authors: Wang, Jie
• Is Part Of: Journal of symbolic computation. Volume 87(2018)
• Page Start: 1
• Page End: 13
• Publication Date: 2018-07
• Subjects: primary 12H10 -- secondary 68W30; Difference index -- Order of difference ideal -- Hilbert–Levin regularity -- Difference ideal membership problem; 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.2017.05.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: This paper is devoted to studying difference indices of quasi-prime difference algebraic systems. We define the quasi dimension polynomial of a quasi-prime difference algebraic system. Based on this, we give the definition of the difference index of a quasi-prime difference algebraic system through a family of pseudo-Jacobian matrices. Some properties of difference indices are proved. In particular, an upper bound for difference indices is given. As applications, an upper bound for the Hilbert–Levin regularity and an effective difference ideal membership theorem for quasi-prime difference algebraic systems are deduced.