Skip to main content
SpringerLink
Log in

Improved Kolchin–Ritt Algorithm

  • Published:
Programming and Computer Software Aims and scope Submit manuscript

Abstract

An algorithm for computation of an extended characteristic sets for finitely generated differential ideals is suggested. This algorithm improves the well-known Kolchin–Ritt algorithm. The improvement is achieved through computing algebraic Gröbner bases on intermediate stages of the computation process. The rank of the extended characteristic set obtained is less than or equal to that of the set obtained by the Kolchin–Ritt algorithm. Examples demonstrating the rank reduction are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Ritt, J.F., Differential Algebra, New York: AMS, 1950.

    Google Scholar 

  2. Kolchin, E.R., Differential Algebra and Algebraic Groups, New York: Academic, 1973.

    Google Scholar 

  3. Wu, W.-T., On the Foundation of Algebraic Differential Geometry, System Sci. Math. Sci., 1989, vol. 2, pp. 289–312.

    Google Scholar 

  4. Boulier, F., Lazard, D., Ollivier, F., and Petitot, M., Representation for the Radical of a Finitely Generated Differential Ideal, Proc. of ISSAC'95, ACM, 1995, pp. 158–166.

  5. Mansfield, E. and Clarkson, P.A., Application of the Differential Algebra Package diffgrob2 to Classical Symmetries of Differential Equations, J. Symb. Comp., 1997, vol. 23, pp. 517–533.

    Google Scholar 

  6. Boulier, F., Lazard, D., Ollivier, F., and Petitot, M., Computing Representations for Radicals of Finitely Generated Differential Ideals, Tech. Report, LIFL, Université Lille I, 1997.

  7. Rosenfeld, A., Specializations in Differential Algebra, Trans. Am. Math. Soc., 1959, vol. 90, pp. 394–407.

    Google Scholar 

  8. Buchberger, B., Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory, Recent Trends in Multidimensional System Theory, Bose, N.K., Ed., Dordrecht: Reidel, 1985, pp. 184–232. Translated under the title Komp'yuternaya algebra. Simvol'nye i algebraicheskie vychisleniya, Moscow: Mir, 1986, pp. 331–372.

    Google Scholar 

  9. Mikhalev, A.V. and Pankrat'ev, E.V., Computer Algebra. Computation in Differential and Difference Algebra, Moscow: Mosk. Gos. Univ., 1989.

    Google Scholar 

  10. Hubert, E., Factorization-free Decomposition Algorithms in Differential Algebra, J. Symb. Comp., 2000, vol. 29, pp. 641–662.

    Google Scholar 

  11. Knuth, D.E., The Art of Computer Programming, vol. 2: Seminumerical Algorithms, Reading: Addison-Wesley, 1969. Translated under the title Iskusstvo programmirovaniya dlya EVM, tom 2: Poluchislennye algoritmy Moscow: Mir, 1977.

    Google Scholar 

  12. Carra'Ferro, G., Gröbner Bases and Differential Algebra, Lecture Notes in Computer Science, 1987, vol. 356, pp. 129–140.

    Google Scholar 

  13. Ollivier, F., Standard Bases of Differential Ideals, Lecture Notes in Computer Science, 1990, vol. 508, pp. 304–321.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Catania, Viale A. Doria 6, 95125, Catania, Italy

    G. Carra'Ferro

  2. Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia gerdt@jinr.ru

    V. P. Gerdt

Authors
  1. G. Carra'Ferro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. P. Gerdt
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carra'Ferro, G., Gerdt, V.P. Improved Kolchin–Ritt Algorithm. Programming and Computer Software 29, 83–87 (2003). https://doi.org/10.1023/A:1022996615890

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022996615890

Keywords

Search

Navigation