Programming and Computer Software

, Volume 37, Issue 2, pp 78–86 | Cite as

Rational solutions of linear difference equations: Universal denominators and denominator bounds

Article

Abstract

Complexities of some well-known algorithms for finding rational solutions of linear difference equations with polynomial coefficients are studied.

References

  1. 1.
    Abramov, S.A., Computer Algebra Problems Associated with Searching Polynomial Solutions of Linear Differential and Difference Equations, Vestn. Mosk. Univ., Ser. 15 Vychisl. Mat. Kibernetika, 1989, no. 3, pp. 53–60 [Moscow Univ. Comput. Math. Cybernet. (Engl. Transl.), 1989, no. 3, pp. 63–80].Google Scholar
  2. 2.
    Abramov, S.A., Rational Solutions of 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, pp. 7–12].MATHMathSciNetGoogle Scholar
  3. 3.
    Abramov, S.A., Rational Solutions of Linear Differential and Difference Equations with Polynomial Coefficients, Programmirovanie, 1995, no. 6, pp. 3–11 [Program. Comp. Soft. (Engl. Transl.), 1995, vol. 21, pp. 273–278].Google Scholar
  4. 4.
    Abramov, S.A., Lectures on Algorithm Complexity, Moscow: MTsNMO, 2009.Google Scholar
  5. 5.
    Abramov, S.A. and Barkatou, M., Rational Solutions of First Order Linear Difference Systems, Proc. of ISSAC’98, 1998, pp. 124–131.Google Scholar
  6. 6.
    Abramov, S.A., Bronstein, M., and Petkovšek, M., On Polynomial Solutions of Linear Operator Equations, Proc. of ISSAC’95, 1995, pp. 290–295.Google Scholar
  7. 7.
    Abramov, S.A., Gheffar, A., and Khmelnov, D.E., Factorization of Polynomials and GCD Computations for Finding Universal Denominators, Proc. of CASC’2010, 2010, pp. 4–18.Google Scholar
  8. 8.
    Barkatou, M., Rational Solutions of Matrix Difference Equations: Problem of Equivalence and Factorization, Proc. of ISSAC’99, 1999, pp. 277–282.Google Scholar
  9. 9.
    Gheffar, A., Linear Differential, Difference and q-Difference Homogeneous Equations Having no Rational Solutions, ACM Commun. Comput. Algebra, 2010, vol. 44, no. 3, pp. 78–83.Google Scholar
  10. 10.
    Gheffar, A. and Abramov, S., Valuations of Rational Solutions of Linear Difference Equations at Irreducible Polynomials, Adv. Appl. Math., 2011 (in press).Google Scholar
  11. 11.
    Van Hoeij, M., Rational Solutions of Linear Difference Equations, Proc. of ISSAC’98, 1998, pp. 120–123.Google Scholar
  12. 12.
    Knuth, D.E., Big Omicron and Big Omega and Big Theta, ACM SIGACT News, 1976, vol. 8, no. 2, pp. 18–23.CrossRefGoogle Scholar
  13. 13.
    Petkovšek, M., Wilf, H.S., and Zeilberger, D., A = B, Peters, 1996.Google Scholar
  14. 14.

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Dorodnicyn Computing CenterRussian Academy of SciencesMoscowRussia
  2. 2.XLIMUniversit@e de Limoges, CNRSLimogesFrance

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