Computing the V-saturation of finitely-generated submodules of V[X]m where V is a valuation domain. (January 2016)

• Record Type: Journal Article
• Authors: Ducos, Lionel; Monceur, Samiha; Yengui, Ihsen
• Is Part Of: Journal of symbolic computation. Volume 72(2016)
• Page Start: 196
• Page End: 205
• Publication Date: 2016-01
• Subjects: Saturation -- Coherence -- Echelon matrix -- Syzygies -- Valuation domains; 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.2015.02.006
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Recently, Lombardi, Quitté and Yengui have given a Gröbner-free algorithm which computes theV -saturation of any finitely generated submodule of V [ X ] n, whereV is a valuation domain. The goal of this paper is to clarify this algorithm, to give precise complexity bounds, and a complete submodule membership test for the saturation. As application, we give precise degree bounds on syzygies over V [ X ] .