COMPUTING THE CONNECTED COMPONENTS OF THE COMPLEMENT TO THE AMOEBA OF A POLYNOMIAL IN SEVERAL COMPLEX VARIABLES

T. A. ZHUKOV; Жуков Т. А.; T. M. SADYKOV; Садыков Т. М.

doi:10.31857/S0132347423020164

COMPUTING THE CONNECTED COMPONENTS OF THE COMPLEMENT TO THE AMOEBA OF A POLYNOMIAL IN SEVERAL COMPLEX VARIABLES

作者: ZHUKOV T.¹, SADYKOV T.¹
隶属关系:
1. Plekhanov Russian University of Economics
期: 编号 2 (2023)
页面: 36-45
栏目: КОМПЬЮТЕРНАЯ АЛГЕБРА
URL: https://journals.rcsi.science/0132-3474/article/view/137618
DOI: https://doi.org/10.31857/S0132347423020164
EDN: https://elibrary.ru/MHCDUI
ID: 137618

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详细

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 computed amoebas and their cross-sections in higher dimensions. The correctness and running time of the proposed algorithms are tested using 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.

作者简介

T. ZHUKOV

Plekhanov Russian University of Economics

Email: Zhukov.TA@rea.ru
Moscow, Russia

T. SADYKOV

Plekhanov Russian University of Economics

编辑信件的主要联系方式.
Email: Sadykov.TM@rea.ru
Moscow, Russia

参考

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