Computing Gröbner Bases and Free Resolutions of OI-Modules

2023/03/12 by Michael R. Morrow, Morrow, Michael, Uwe Nagel +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2303.06725

openalex publication_date 2023/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a sequence of related modules M_n defined over a sequence of related polynomial rings, one may ask how to simultaneously compute a finite Gröbner basis for each M_n. Furthermore, one may ask how to simultaneously compute the module of syzygies of each M_n. In this paper we address both questions. Working in the setting of OI-modules over a Noetherian polynomial OI-algebra, we provide OI-analogues of Buchberger's Criterion, Buchberger's Algorithm for computing Gröbner bases, and Schreyer's Theorem for computing syzygies. We also establish a stabilization result for Gröbner bases.

Cited by

• Equivariant Free Resolutions of Sequences of Symmetric Module

Related

• The OIGroebnerBases Package for Macaulay2
• Analogs of Gröbner Bases in Polynomial Rings over a Ring
• Notes on Gröbner Bases and Free Resolutions of Modules over Solvable Polynomial Algebras
• Analysis of computing Gröbner bases and Gröbner degenerations via theory of signatures
• Gröbner Bases of Modules and Faugère's F₄ Algorithm in Isabelle/HOL