Deterministic genericity for polynomial ideals. (May 2018)

• Record Type: Journal Article
• Authors: Hashemi, Amir; Schweinfurter, Michael; Seiler, Werner M.
• Is Part Of: Journal of symbolic computation. Volume 86(2018)
• Page Start: 20
• Page End: 50
• Publication Date: 2018-05
• Subjects: Polynomial ideals -- Deterministic algorithms -- Gröbner bases -- Pommaret bases -- Generic positions -- Generic initial ideals -- Strongly stable ideals -- Stable ideals -- Quasi stable ideals -- Componentwise stability -- β-maximal position -- Noether position; 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.2017.03.008
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent algebraic characterisations are provided. It is shown that in characteristic zero the corresponding generic positions can be obtained with a simple deterministic algorithm. In positive characteristic, only adapted stable positions are reachable except for quasi-stability which is obtainable in any characteristic.