Fundamentals and Applications of Gröbner Bases in Solving Polynomial Equations

Abstract

This review article examines research on Gröbner bases applied to systems of polynomial equations, with the aim of presenting a comprehensive review of their applications in solving these systems. The study, based on a qualitative approach, covers 24 citations selected from 30 research found and uses Google Scholar for the search, addressing topics such as Gröbner bases, mathematical learning, computational thinking, algebra, polynomial equation solving, technology and mathematics education. New educational technologies in mathematics education go beyond a simple computer; however, the computer remains a fundamental tool in computer algebra. Gröbner bases facilitate the solution of polynomial equations and are an essential tool in computer algebra and other areas, allowing to solve various algebraic difficulties. This article provides an overview of Gröbner bases applied to systems of polynomial equations, highlighting key theoretical and educational aspects for the academic community.