Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2016-03-10T20:29:20Z No. of bitstreams: 1 DanielDeSouzaGrilo_DISSERT.pdf: 1196405 bytes, checksum: 8dadb4e2bfb538ecb800a9fe227ec252 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2016-03-17T00:40:14Z (GMT) No. of bitstreams: 1 DanielDeSouzaGrilo_DISSERT.pdf: 1196405 bytes, checksum: 8dadb4e2bfb538ecb800a9fe227ec252 (MD5) / Made available in DSpace on 2016-03-17T00:40:14Z (GMT). No. of bitstreams: 1 DanielDeSouzaGrilo_DISSERT.pdf: 1196405 bytes, checksum: 8dadb4e2bfb538ecb800a9fe227ec252 (MD5) Previous issue date: 2015-06-12 / Apresentamos algoritmos de integra??o indefinida de fun??es racionais sobre subcorpos dos complexos, a partir de uma abordagem alg?brica. Estudamos o algoritmo local de Bernoulli e algoritmos racionais de integra??o para a classe de fun??es em quest?o, a saber, os algoritmos de Hermite; Horowitz-Ostrogradsky; Rothstein-Trager e Lazard-Rioboo-Trager. Estudamos tamb?m o algoritmo de Rioboo para convers?o de logaritmos envolvendo extens?es complexas para fun??es arco tangente reais, quando estes logaritmos surgem da integra??o de fun??es racionais com coeficientes reais. Conclu?mos fornecendo pseudoc?digos e c?digos para implementa??o no software Maxima relativos aos algoritmos estudados neste trabalho, e, al?m disso, a algoritmos para c?lculo de mdc de polin?mios; decomposi??o em fra??es parciais; fatora??o livres de quadrados; c?lculo de subresultantes, entre outros algoritmos acess?rios ao trabalho. Ser? tamb?m apresentado no ap?ndice o algoritmo de Zeilberger-Almkvist para integra??o de fun??es hiperexponenciais, bem como seu pseudoc?digo e c?digo para Maxima. Como alternativa aos algoritmos de Rothstein-Trager e Lazard-Rioboo-Trager, apresentamos ainda um c?digo para o algoritmo de Bernoulli para denominadores livres de quadrados; e outro para o algoritmo de Czichowski, ainda que este n?o seja estudado em detalhes no trabalho, devido ?s bases te?ricas necess?rias para o seu entendimento, as quais se encontram fora do escopo deste trabalho. Diversos exemplos s?o fornecidos de modo a demonstrar o o funcionamento dos algoritmos de integra??o deste trabalho. / We present indefinite integration algorithms for rational functions over subfields of the complex numbers, through an algebraic approach. We study the local algorithm of Bernoulli and rational algorithms for the class of functions in concern, namely, the algorithms of Hermite; Horowitz-Ostrogradsky; Rothstein-Trager and Lazard-Rioboo-Trager. We also study the algorithm of Rioboo for conversion of logarithms involving complex extensions into real arctangent functions, when these logarithms arise from the integration of rational functions with real coefficients. We conclude presenting pseudocodes and codes for implementation in the software Maxima concerning the algorithms studied in this work, as well as to algorithms for polynomial gcd computation; partial fraction decomposition; squarefree factorization; subresultant computation, among other side algorithms for the work. We also present the algorithm of Zeilberger-Almkvist for integration of hyperexpontential functions, as well as its pseudocode and code for Maxima. As an alternative for the algorithms of Rothstein-Trager and Lazard-Rioboo-Trager, we yet present a code for Benoulli?s algorithm for square-free denominators; and another for Czichowski?s algorithm, although this one is not studied in detail in the present work, due to the theoretical basis necessary to understand it, which is beyond this work?s scope. Several examples are provided in order to illustrate the working of the integration algorithms in this text