Programming and Computer Software

, Volume 33, Issue 3, pp 132–138 | Cite as

Improved universal denominators

  • S. A. Abramov
  • S. P. Polyakov


The paper presents an algorithm for improvement (degree reduction) of universal denominators, which are used, for example, for constructing rational solutions of linear differential and difference systems with polynomial coefficients. A variant of Zeilberger’s algorithm is described; it uses construction of universal denominator instead of application of Gosper’s algorithm.


Rational Solution Solution Component Degree Reduction Irreducible Factor Difference Case 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abramov, S.A., Rational Solutions for Linear Differential and Difference Equations with Polynomial Coefficients, Zh. Vychisl. Mat. Mat. Fiz., 1989, vol. 29, no. 11, pp. 1611–1620 [Comput. Math. Math. Phys. (Engl. Transl.), 1989, vol. 29, no. 6, pp. 7–12].zbMATHMathSciNetGoogle Scholar
  2. 2.
    Abramov, S.A. and Barkatou, M.A., Rational Solutions of First Order Linear Difference Systems, Proc. ISSAC’98, 1998, pp. 124–131.Google Scholar
  3. 3.
    Barkatou, M.A., On Rational Solutions of Systems of Linear Differential Equations, J. Symb. Comput., 1999, vol. 28, pp. 547–567.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Abramov, S.A., EG-Eliminations, J. Differ. Equ. Appl., 1999, vol. 5, pp. 393–433.zbMATHMathSciNetGoogle Scholar
  5. 5.
    Abramov, S.A. and Bronstein, M., On Solutions of Linear Functional Systems, Proc. ISSAC’2001, 2001, pp. 1–6.Google Scholar
  6. 6.
    Abramov, S.A., A Direct Algorithm to Compute Rational Solutions of First-Order Linear q-Difference Systems, Discrete Math., 2002, vol. 246, pp. 3–12.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Khmel’nov, D.E., Improved Algorithms for Solving Difference and q-Difference Equations, Programmirovaniye, 2000, vol. 26, no. 2, pp. 70–78 [Program. Comp. Soft. (Engl. Transl.), 2000, vol. 26, no. 2, pp. 107–115].MathSciNetGoogle Scholar
  8. 8.
    Van Hoeij, M., Rational Solutions of Linear Difference Equations, Proc. of ISSAC’98, 1998, pp. 120–123.Google Scholar
  9. 9.
    Zeilberger, D., The Method of Creative Telescoping, J. Symb. Comput., 1991, vol.11, pp. 195–204.zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Gosper, R.W., Decision Procedures of Indefinite Hypergeometric Summation, Proc. Natl. Acad. Sci. USA, 1978, vol. 75, pp. 40–42.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Polyakov, S.P., On Homogeneous Zeilberger Recurrences, Adv. Appl. Math. (in press).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • S. A. Abramov
    • 1
  • S. P. Polyakov
    • 1
  1. 1.Computing CenterRussian Academy of SciencesMoscowRussia

Personalised recommendations