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Noetherian operators in Macaulay2

Justin Chen, Yairon Cid-Ruiz, Marc Härkönen, Robert Krone and Anton Leykin

Vol. 12 (2022), 33–41
DOI: 10.2140/jsag.2022.12.33
Abstract

A primary module over a polynomial ring can be described by an algebraic variety and a finite set of Noetherian operators, which are vectors of differential operators with polynomial coefficients. We implement both symbolic and numerical algorithms to produce such a description in various scenarios, as well as routines for studying affine schemes and coherent sheaves through the prism of Noetherian operators and Macaulay dual spaces.

Keywords
commutative algebra, computational algebraic geometry, differential algebra, Noetherian operators, dual spaces, numerical algebraic geometry
Mathematical Subject Classification
Primary: 14-04
Secondary: 13N05, 14Q15, 65D05, 65L80
Supplementary material

Algorithms for computing local dual spaces and sets of Noetherian operators

Milestones
Received: 4 January 2021
Revised: 8 July 2022
Accepted: 26 September 2022
Published: 23 January 2023
Authors
Justin Chen
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
Yairon Cid-Ruiz
Department of Mathematics: Algebra and Geometry
Ghent University
Gent
Belgium
Marc Härkönen
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
Robert Krone
Department of Mathematics
UC Davis
Davis, CA
United States
Anton Leykin
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States