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01-04-2023

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

Authors: T. A. Zhukov, T. M. Sadykov

Published in: Programming and Computer Software | Issue 2/2023

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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.

previous article Symbolic Algorithm for Finding Zeros of a System of Holomorphic Functions

next article Symbolic-Numerical Implementation of the Galerkin Method for Approximate Solution of the Waveguide Diffraction Problem

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Title: Computing the Connected Components of the Complement to the Amoeba of a Polynomial in Several Complex Variables
Authors: T. A. Zhukov
T. M. Sadykov
Publication date: 01-04-2023
Publisher: Pleiades Publishing
Published in: Programming and Computer Software / Issue 2/2023
Print ISSN: 0361-7688
Electronic ISSN: 1608-3261
DOI: https://doi.org/10.1134/S0361768823020159

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