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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
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/20055 |
| Date | 12 June 2015 |
| Creators | Grilo, Daniel de Souza |
| Contributors | 21402190824, http://lattes.cnpq.br/7895700958229353, Pereira, Edgar Silva, 31502482053, http://lattes.cnpq.br/0470193971644313, Trevisan, Vilmar, 29647860030, http://lattes.cnpq.br/0319183112661354, Cohen, Nir |
| Publisher | Universidade Federal do Rio Grande do Norte, PROGRAMA DE P?S-GRADUA??O EM MATEM?TICA APLICADA E ESTAT?STICA, UFRN, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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