Computing minimal finite free resolutions
type: Item
instance of: scholarly article
title: Computing minimal finite free resolutions
zbMATH Open document ID: 0906.13006
DOI: 10.1016/S0022-4049(97)00007-8
author: A. Capani
author: Gabriel de Dominicis
author: Gianfranco Niesi
author: Lorenzo Robbiano
published in: Journal of Pure and Applied Algebra
publication date: 1999-02-18T00:00:00Z
review text: An algorithm to construct a minimal resolution for a graded submodule \(M\) of a free graded module over a polynomial ring is presented. Let \(m_1,\dots,m_d\) be a minimal basis of \(M\). The peculiarity of the proposed algorithm consists in the successive construction of the minimal basis for \(\text{Syz} (m_1, \dots, m_d)\) at every step in the process of running Buchberger's algorithm to obtain the Gröbner basis. Additional improvements, e.g., using the Poincaré series are indicated. Results of the computation for several examples are presented.
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13D40
zbMATH DE Number: 1025692
zbMATH Keywords: syzygies
zbMATH Keywords: Buchberger's algorithm
zbMATH Keywords: Gröbner basis
zbMATH Keywords: Poincaré series
describes a project that uses: SINGULAR
describes a project that uses: CoCoA
describes a project that uses: Macaulay2
MaRDI profile type: Publication
cites work: Gröbner bases and primary decomposition in polynomial rings in one variable over Dedekind domains
cites work: Q4317713
cites work: On an implementation of standard bases and syzygies in SINGULAR
cites work: SINGULAR: A computer algebra system for singularity theory, algebraic geometry and commutative algebra
cites work: New constructive methods in classical ideal theory
cites work: Q3222965
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description: scientific article; zbMATH DE number 1025692