Sobre a integração indefinida de funções racionais complexas: teoria e implementação de algoritmos racionais
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-Ostrograds...
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| Formato: | Dissertação |
| Idioma: | por |
| Publicado em: |
Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/jspui/handle/123456789/20055 |
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| Resumo: | 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 |
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