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Computing the Connected Components of the Complement to the Amoeba of a Polynomial in Several Complex Variables

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Abstract

In this paper, we propose a method for computing and visualizing the amoeba of a Laurent polynomial in several complex variables, which is applicable in arbitrary dimension. The algorithms developed based on this method are implemented as a free web service (http://amoebas.ru), which enables interactive computation of amoebas for polynomials in two variables, as well as provides a set of precomputed amoebas and their cross-sections in higher dimensions. The correctness and running time of the proposed algorithms are tested against a set of optimal polynomials in two, three, and four variables, which are generated using Mathematica computer algebra system. The developed program code makes it possible, in particular, to generate optimal hypergeometric polynomials in an arbitrary number of variables supported in an arbitrary zonotope given by a set of generating vectors.

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Funding

This work was supported by the Russian Science Foundation, grant no. 22-21-00556 (https://rscf.ru/project/22-21-00556).

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Authors and Affiliations

  1. Plekhanov Russian University of Economics, Stremyannyi per. 36, 117997, Moscow, Russia

    T. A. Zhukov & T. M. Sadykov

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  1. T. A. Zhukov
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  2. T. M. Sadykov
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Correspondence to T. A. Zhukov or T. M. Sadykov.

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The authors declare that they have no conflicts of interest.

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Translated by Yu. Kornienko

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Zhukov, T.A., Sadykov, T.M. Computing the Connected Components of the Complement to the Amoeba of a Polynomial in Several Complex Variables. Program Comput Soft 49, 91–99 (2023). https://doi.org/10.1134/S0361768823020159

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  • DOI: https://doi.org/10.1134/S0361768823020159

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