The OIGroebnerBases Package for Macaulay2
Michael Morrow
TL;DR
The paper presents the OIGroebnerBases package for Macaulay2, enabling efficient computation of Gr"obner bases, syzygies, and resolutions for OI-modules over polynomial OI-algebras, extending classical algorithms to this setting.
Contribution
It introduces a new Macaulay2 package implementing OI-analogues of Buchberger's algorithm and Schreyer's theorem for OI-modules.
Findings
Efficient computation of Gr"obner bases for OI-modules.
Implementation of OI-analogues of classical algorithms.
Enhanced tools for algebraic computations in Noetherian polynomial OI-algebras.
Abstract
We introduce the package for working with OI-modules over Noetherian polynomial OI-algebras. The main methods implement OI-analogues of Buchberger's algorithm and Schreyer's theorem to compute Gr\"obner bases, syzygies and free resolutions of submodules of free OI-modules.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic structures and combinatorial models