Gröbner Bases on $\Sigma$-Algebras

Abstract

Copilot said: In this text, we develop a theory of Gröbner bases for $\Sigma$-algebras. To do so, we first give introductory notions on Gröbner bases, and on $\Sigma$-algebras. Moreover, we propose a method to represent certain monomial orderings of $\Sigma$-polynomial algebras via infinite matrices. Within this setting, and despite the non-Noetherianity, we present an algorithm to compute Gröbner bases whenever feasible. Finally, we illustrate these concepts with an example and provide implementations of the proposed algorithms.