Axioms for a theory of signature bases - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Symbolic Computation Year : 2024

Axioms for a theory of signature bases

Abstract

Twenty years after the discovery of the F5 algorithm, Gr\"obner bases with signatures are still challenging to understand and to adapt to different settings. This contrasts with Buchberger's algorithm, which we can bend in many directions keeping correctness and termination obvious. I propose an axiomatic approach to Gr\"obner bases with signatures with the purpose of uncoupling the theory and the algorithms, and giving general results applicable in many different settings (e.g. Gr\"obner for submodules, F4-style reduction, noncommutative rings, non-Noetherian settings, etc.).
Fichier principal
Vignette du fichier
gb.pdf (924.76 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Licence : CC BY - Attribution

Dates and versions

hal-03830003 , version 1 (26-10-2022)
hal-03830003 , version 2 (28-11-2023)
hal-03830003 , version 3 (08-01-2024)

Licence

Attribution

Identifiers

Cite

Pierre Lairez. Axioms for a theory of signature bases. Journal of Symbolic Computation, 2024, 123, pp.102275. ⟨10.1016/j.jsc.2023.102275⟩. ⟨hal-03830003v3⟩
47 View
19 Download

Altmetric

Share

Gmail Facebook X LinkedIn More