Solving degree, last fall degree, and related invariants. (January 2023)

• Record Type: Journal Article
• Authors: Caminata, Alessio; Gorla, Elisa
• Is Part Of: Journal of symbolic computation. Volume 114(2023)
• Page Start: 322
• Page End: 335
• Publication Date: 2023-01
• Subjects: 13P10 -- 13P15 -- 13P25 -- 68W30; Degree of regularity -- Castelnuovo–Mumford regularity -- Gröbner bases -- Last fall degree -- Solving degree; 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.2022.05.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper we study and relate several invariants connected to the solving degree of a polynomial system. This provides a rigorous framework for estimating the complexity of solving a system of polynomial equations via Gröbner bases methods. Our main results include a connection between the solving degree and the last fall degree and one between the degree of regularity and the Castelnuovo–Mumford regularity.