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On testing the existence of universal denominators for partial differential and difference equations

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Abstract

We consider the problem of testing the existence of a universal denominator for partial differential or difference equations with polynomial coefficients and prove its algorithmic undecidability. This problem is closely related to finding rational function solutions in that the construction of a universal denominator is a part of the algorithms for finding solutions of such form for ordinary differential and difference equations.

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    S. V. Paramonov

  2. Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    S. V. Paramonov

Authors
  1. S. V. Paramonov
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Correspondence to S. V. Paramonov.

Additional information

Original Russian Text © S.V. Paramonov, 2017, published in Programmirovanie, 2017, Vol. 43, No. 2.

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Paramonov, S.V. On testing the existence of universal denominators for partial differential and difference equations. Program Comput Soft 43, 126–129 (2017). https://doi.org/10.1134/S0361768817020104

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  • DOI: https://doi.org/10.1134/S0361768817020104

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