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Tropical Newton–Puiseux Polynomials

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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 introduce tropical Newton–Puiseux polynomials admitting rational exponents. A resolution of a tropical hypersurface is defined by means of a tropical Newton–Puiseux polynomial. A polynomial complexity algorithm for resolubility of a tropical curve is designed. The complexity of resolubility of tropical prevarieties of arbitrary codimensions is studied.

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Acknowledgments

The author is grateful to the grant RSF 16-11-10075 and to MCCME for inspiring atmosphere.

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Authors and Affiliations

  1. CNRS, Mathématiques, Université de Lille, 59655, Villeneuve d’Ascq, France

    Dima Grigoriev

Authors
  1. Dima Grigoriev
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Correspondence to Dima Grigoriev .

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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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Grigoriev, D. (2018). Tropical Newton–Puiseux Polynomials. 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_12

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  • DOI: https://doi.org/10.1007/978-3-319-99639-4_12

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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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