Sistemas de equações polinomiais e base de Gröbner

• Autor(a) principal: Vilanova, Fábio Fontes
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFS
• Texto Completo: https://ri.ufs.br/handle/riufs/6524
• topic: Sistemas de equações polinomiais; Algoritmo extendido da divisão; Ideais Monomiais; Bases de Hilbert; Algoritmo de Buchberger; Base de Gröbner; Coloração de mapas; Sudoku; Polynomial equation systems; Division extended algorithm; Monomial ideals; Hilbert Base; Buchberger´s algorithm; Gröbner basis; Map coloring; Sudoku; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The main objective of this dissertation is to present an algebraic method capable of determining a solution, if any, of a non linear polynomial equation systems using Gröbner basis. In order to accomplish that, we first present some concepts and theorems linked to polynomial rings with several undetermined and monomial ideals where we highlight the division extended algorithm, the Hilbert Basis and the Buchberger´s algorithm. Beyond that, using basics of Elimination and Extension Theorems, we present an algebraic solution to the map coloring that use 3 colors as well as a general solution to the Sudoku puzzle.