Uma introdução à base de Gröbner

Abstract

In this work, we will develop a study in the area of Commutative Algebra, focusing on results related to a special topic known as the Gröbner Basis. The main subjects addressed include polynomial rings in several variables, highlighting how we can establish a monomial order and the division algorithm in the ring K[x1, . . . , xn]. The knowledge acquired throughout the first chapter will serve as the foundation for the study of this basis. In particular, we will analyze the importance and application of Buchberger’s algorithm, used to determine a Gröbner Basis. Finally, we will seek to apply the developed theory to the resolution of nonlinear systems, addressing practical examples such as the map coloring problem and road network systems.