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Beyond the First Class of Analytic Complexity

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Computer Algebra in Scientific Computing (CASC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11077))

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Abstract

We investigate the notion of analytic complexity of a bivariate holomorphic function by means of computer algebra tools. An estimate from below on the number of terms in the differential polynomials defining classes of analytic complexity is established. We provide an algorithm which allows one to explicitly compute the differential membership criteria for certain families of bivariate analytic functions in the second complexity class. The presented algorithm is implemented in the computer algebra system Singular 4-1-1.

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Acknowledgments

This research has been performed in the framework of the basic part of the scientific research state task in the field of scientific activity of the Ministry of Education and Science of the Russian Federation, project No. 2.9577.2017/8.9.

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Authors and Affiliations

  1. Plekhanov Russian University, Stremyanny 36, Moscow, 125993, Russia

    T. M. Sadykov

Authors
  1. T. M. Sadykov
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Correspondence to T. M. Sadykov .

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Editors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Werner M. Seiler

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Sadykov, T.M. (2018). Beyond the First Class of Analytic Complexity. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2018. Lecture Notes in Computer Science(), vol 11077. Springer, Cham. https://doi.org/10.1007/978-3-319-99639-4_23

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  • DOI: https://doi.org/10.1007/978-3-319-99639-4_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99638-7

  • Online ISBN: 978-3-319-99639-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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