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Algorithmic Computation of Polynomial Amoebas

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Computer Algebra in Scientific Computing (CASC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9890))

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Abstract

We present algorithms for computation and visualization of polynomial amoebas, their contours, compactified amoebas and sections of three-dimensional amoebas by two-dimensional planes. We also provide a method and an algorithm for the computation of polynomials whose amoebas exhibit the most complicated topology among all polynomials with a fixed Newton polytope. The presented algorithms are implemented in computer algebra systems Matlab 8 and Mathematica 9.

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Acknowledgements

This research was supported by the state order of the Ministry of Education and Science of the Russian Federation for Siberian Federal University (task 1.1462.2014/K), by grant of the Government of the Russian Federation for investigations under the guidance of the leading scientists of the Siberian Federal University (contract No. 14.Y26.31.0006) and by the Russian Foundation for Basic Research, projects 15-31-20008-mol_a_ved and 16-41-240764-r_a.

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Authors and Affiliations

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

    D. V. Bogdanov & T. M. Sadykov

  2. Siberian Federal University, Svobodny 79, Krasnoyarsk, 660041, Russia

    A. A. Kytmanov

Authors
  1. D. V. Bogdanov
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  2. A. A. Kytmanov
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  3. T. M. Sadykov
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Corresponding author

Correspondence to T. M. Sadykov .

Editor information

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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Bogdanov, D.V., Kytmanov, A.A., Sadykov, T.M. (2016). Algorithmic Computation of Polynomial Amoebas. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2016. Lecture Notes in Computer Science(), vol 9890. Springer, Cham. https://doi.org/10.1007/978-3-319-45641-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-45641-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45640-9

  • Online ISBN: 978-3-319-45641-6

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