A Syzygial Method for Equidimensional Decomposition

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2024Embargo end date: 01 Sep 2024 France Publisher:Elsevier BVJournal:Journal of Symbolic Computation, volume 131, page 102,455 (issn: 0747-7171,

Copyright policy )Funded by:DFG | unidentified, DFG | Symbolic Tools in Mathema...

Authors: Mohr, Rafael;

doi: 10.2139/ssrn.4973742 , 10.1016/j.jsc.2025.102455 , 10.48550/arxiv.2409.17785

arXiv: 2409.17785

A Syzygial Method for Equidimensional Decomposition

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Abstract

Based on a theorem by Vasconcelos, we give an algorithm for equidimensional decomposition of algebraic sets using syzygy computations via Gröbner bases. This algorithm avoids the use of elimination, homological algebra and processing the input equations one-by-one present in previous algorithms. We experimentally demonstrate the practical interest of our algorithm compared to the state of the art.

15 pages

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France

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Keywords

[MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC], Computer Science - Symbolic Computation, FOS: Computer and information sciences, equidimensional decomposition, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], effective algebraic geometry, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Symbolic Computation (cs.SC), Syzygies, resolutions, complexes and commutative rings, Gröbner basis

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