Estudo e implementação do Algoritmo de Buchberger na linguagem UserRPL para a calculadora gráfica HP 50g

Abstract

In this work we study the algebraic concepts and results that support Gröbner's theory of bases and the Buchberger algorithm that allows the effective calculation of these. The theory is established with respect to a polynomial ring in an arbitrary number of variables with coefficients on any one body. Emphasis is given to issues related to monomial order, division algorithm, monomial ideals, Dickson's lemma and Hilbert's basis theorem. As a matter of curiosity, an implementation of the Buchberger algorithm is developed as originally described in [Buchberger, 1985] in the UserRPL language for the HP 50g Graphing Calculator and explores its technical and computational properties. This implementation provides support for polynomials with complex coefficients in an arbitrary number of variables with pre-defined canonical polynomial ordering and also programmable by the user.