Some criteria for Gröbner bases and their applications. (May 2019)

• Record Type: Journal Article
• Authors: Liu, Jinwang; Li, Dongmei; Liu, Weijun
• Is Part Of: Journal of symbolic computation. Volume 92(2019)
• Page Start: 15
• Page End: 21
• Publication Date: 2019-05
• Subjects: Polynomial ring -- Gröbner basis -- Polynomial composition; 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.2017.11.016
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We consider the following two problems: Let f and g be two polynomials over a field K . P1. When is { f + s, g + t } a Gröbner basis for all s, t ∈ K ? P2. When is { f λ, g σ } a Gröbner basis for all λ, σ ∈ N ? We provide a simpler proof of Hoon's criterion for P1 and a new criterion for P2. The two criteria are applied to the theory of Gröbner bases under composition.