Advertisement

Programming and Computer Software

, Volume 34, Issue 2, pp 95–100 | Cite as

Indefinite summation of rational functions with additional minimization of the summable part

  • S. P. Polyakov
Article

Abstract

An algorithm of indefinite summation of rational functions is proposed. For a given function f(x), it constructs a pair of rational functions g(x) and r(x) such that f(x) = g(x + 1) − g(x) + r(x), where the degree of the denominator of r(x) is minimal, and, when this condition is satisfied, the degree of the denominator of g(x) is also minimal.

Keywords

Rational Function Summable Part Minimum Degree Irreducible Factor Additional Minimization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gosper, R.W., Decision Procedures of Indefinite Hypergeometric Summation, Proc. Natl. Acad. Sci. USA, 1978, vol. 75, pp. 40–42.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Abramov, S.A., The Rational Component of the Solution of a First-Order Linear Recurrence Relation with a Rational Right-Hand Side, Zh. Vychisl. Mat. Mat. Fiz., 1975, vol. 15, pp. 1035–1039.zbMATHMathSciNetGoogle Scholar
  3. 3.
    Paule, P., Greatest Factorial Factorization and Symbolic Summation, J. Symbol. Comput., 1995, vol. 20, no. 3, pp. 235–268.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Pirastu, R., Algorithms for Indefinite Summation of Rational Functions in Maple, The Maple Tech. Newsletter, 1995, vol. 2, no. 1, pp. 1–12.Google Scholar
  5. 5.
    Pirastu, R. and Strehl, V., Rational Summation and Gosper-Petkovšek Representation, J. Symbolic Comput., 1995, vol. 20, pp. 617–635.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Abramov, S.A., Indefinite Sums of Rational Functions, Proc. ISSAC’95, Montreal: ACM, 1995, pp. 303–308.Google Scholar
  7. 7.
    Pirastu, R., A Note On the Minimality Problem in Indefinite Summation of Rational Functions, Actes du Se’minaire Lotharingien de Combinatoire, 31e session, 1994, Saint-Nabor: Publications de l’I.R.M.A, 1994/021, pp. 95–101.Google Scholar
  8. 8.
    Polyakov, S.P., Symbolic Additive Decomposition of Rational Functions, Programmirovanie, 2005, vol. 31, no. 2, pp. 15–21 [Programming Comput. Software (Engl. Transl.), 2005, vol. 31, no. 2, pp. 60–64].MathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  1. 1.Computing CenterRussian Academy of SciencesMoscowRussia

Personalised recommendations