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Indefinite summation of rational functions with factorization of denominators

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Abstract

A computer algebra algorithm for indefinite summation of rational functions based on complete factorization of denominators is proposed. For a given f, the algorithm finds two rational functions g, r such that f = g(x + 1) − g(x) + r and the degree of the denominator of r is minimal. A modification of the algorithm is also proposed that additionally minimizes the degree of the denominator of g. Computational complexity of the algorithms without regard to denominator factorization is shown to be O(m 2), where m is the degree of the denominator of f.

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  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

    S. P. Polyakov

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  1. S. P. Polyakov
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Original Russian Text © S.P. Polyakov, 2011, published in Programmirovanie, 2011, Vol. 37, No. 4.

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Polyakov, S.P. Indefinite summation of rational functions with factorization of denominators. Program Comput Soft 37, 322–325 (2011). https://doi.org/10.1134/S0361768811060077

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  • DOI: https://doi.org/10.1134/S0361768811060077

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