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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
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Abstract |
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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
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Mathematical Subject Classification
Primary: 14-04
Secondary: 13N05, 14Q15, 65D05, 65L80
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Supplementary materialAlgorithms 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
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Authors |
| Justin Chen | |
| School of Mathematics Georgia Institute of Technology Atlanta, GA United States |
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| Yairon Cid-Ruiz | |
| Department of Mathematics: Algebra
and Geometry Ghent University Gent Belgium |
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| Marc Härkönen | |
| School of Mathematics Georgia Institute of Technology Atlanta, GA United States |
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| Robert Krone | |
| Department of Mathematics UC Davis Davis, CA United States |
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| Anton Leykin | |
| School of Mathematics Georgia Institute of Technology Atlanta, GA United States |
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