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Partial algorithms for satellite unknowns determination

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Abstract

The concept of satellite unknowns with respect to a set of selected unknowns in linear homogeneous differential systems was introduced earlier by the author of this paper, and an algorithm for satellite unknowns testing was proposed. On one of the stages of this algorithm, it is required to compare Picard–Vessiot extensions of two differential systems constructed in the course of the algorithm operation. The commonly accepted method of solving this problem, which is based on Hrushovski’s algorithm, has rather high algorithmic complexity, which hampers its use in practice. In the paper, some partial algorithms for satellite unknowns testing are described. These algorithms are not always applicable but have relatively low computational complexity and can be implemented in computer algebra systems.

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References

  1. Panferov, A.A., Determination of satellite unknowns in linear differential systems, Proc. of Int. Conf. “Computer Algebra,” Moscow, 2016, pp. 79–81.

    Google Scholar 

  2. Minchenko, A., Ovchinnikov, A., and Singer, M.F., Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations, Int. Math. Res. Notices, 2015, vol. 215, no. 7, pp. 1733–1793.

    MathSciNet  MATH  Google Scholar 

  3. Hrushovski, E., Computing the Galois group of a linear differential equation, Banach Center Publ., 2002, vol. 58, pp. 97–138.

    Article  MathSciNet  MATH  Google Scholar 

  4. van der Put, M. and Singer, M.F., Galois theory of linear differential equations, in Grundlehren der mathematischen Wissenschaften, 328, Heidelberg: Springer, 2003.

    Google Scholar 

  5. Abramov, S.A. and Bronstein, M., Solving linear systems of differential and difference equations with respect to a part of the unknowns, Comput. Math. Math. Phys., 2006, vol. 46, no. 2, pp. 218–230.

    Article  MathSciNet  MATH  Google Scholar 

  6. Barkatou, M.A. and Pfluegel, E., On the equivalence problem of linear differential systems and its application for factoring completely reducible systems, Proc. of ISSAC 1998, 1998, pp. 268–275.

    Google Scholar 

  7. Panferov, A.A., Differential equation systems with selected part of the unknowns, Program. Comput. Software, 2015, vol. 41, no. 2, pp. 90–97.

    Article  MathSciNet  MATH  Google Scholar 

  8. Panferov, A.A., Partitions of the set of selected unknowns in linear differential–algebraic systems, Program. Comput. Software, 2016, vol. 42, no. 2, pp. 84–89.

    Article  MathSciNet  MATH  Google Scholar 

  9. Beckermann, M., Cheng, H., and Labahn, G., Fraction-free row reduction of matrices of Ore polynomials, J. Symbolic Computation, 2006, vol. 41, no. 5, pp. 513–543.

    Article  MathSciNet  MATH  Google Scholar 

  10. Barkatou, M., El Bacha, C., Labahn, G., and Pflugel, E., On simultaneous row and column reduction of higher-order linear differential systems, J. Symbolic Computation, 2013, vol. 49, pp. 45–64.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

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

    A. A. Panferov

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

    A. A. Panferov

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  1. A. A. Panferov
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Correspondence to A. A. Panferov.

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Original Russian Text © A.A. Panferov, 2017, published in Programmirovanie, 2017, Vol. 43, No. 2.

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Panferov, A.A. Partial algorithms for satellite unknowns determination. Program Comput Soft 43, 119–125 (2017). https://doi.org/10.1134/S0361768817020098

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