Noetherian operators and primary decomposition. (May 2022)

• Record Type: Journal Article
• Authors: Chen, Justin; Härkönen, Marc; Krone, Robert; Leykin, Anton
• Is Part Of: Journal of symbolic computation. Volume 110(2022)
• Page Start: 1
• Page End: 23
• Publication Date: 2022-05
• Subjects: 14Q15 -- 14-04 -- 13N05 -- 65L80 -- 65D05; Noetherian operators -- Inverse systems -- Primary decomposition; 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.2021.09.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Noetherian operators are differential operators that encode primary components of a polynomial ideal. We develop a framework, as well as algorithms, for computing Noetherian operators with local dual spaces, both symbolically and numerically. For a primary ideal, such operators provide an alternative representation to one given by a set of generators. This description fits well with numerical algebraic geometry, taking a step toward the goal of numerical primary decomposition.