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Computing Level Lines of a Polynomial on the Plane

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Abstract

Application of the method of computing the location of all types of level lines of a real polynomial on the real plane is demonstrated. The theory underlying this method is based on methods of local and global analysis by the means of power geometry and computer algebra. Three nontrivial examples of computing level lines of real polynomials on the real plane are discussed in detail. The following computer algebra algorithms are used: factorization of polynomials, computation of the Gröbner basis, construction of the Newton polygon, and representation of an algebraic curve on a plane. It is shown how computational difficulties can be overcome.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    A. D. Bruno & A. B. Batkhin

  2. Moscow Institute of Physics and Technology (National Research University), 141700, Dolgoprudnyi, Moscow oblast, Russia

    A. B. Batkhin

  3. Samarkand State University, 140104, Samarkand, Uzbekistan

    Z. Kh. Khaidarov

Authors
  1. A. D. Bruno
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  2. A. B. Batkhin
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  3. Z. Kh. Khaidarov
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Correspondence to A. D. Bruno, A. B. Batkhin or Z. Kh. Khaidarov.

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The authors declare that they have no conflicts of interest.

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Translated by A. Klimontovich

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Bruno, A.D., Batkhin, A.B. & Khaidarov, Z.K. Computing Level Lines of a Polynomial on the Plane. Program Comput Soft 49, 69–85 (2023). https://doi.org/10.1134/S0361768823020068

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  • DOI: https://doi.org/10.1134/S0361768823020068

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