SYMBOLIC ALGORITHM FOR FINDING ZEROS OF A SYSTEM OF OLOMORPHIC FUNCTIONS

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Abstract

Based on the Bochner–Martinelli integral representation, an algorithm for determining the number of zeros of a system of holomorphic functions is developed. We search for zeros of the system in a polycube. The use of computer algebra methods in this problem is due to the computational complexity of the developed algorithms and final results. The algorithm is implemented in Maple, which makes it possible to significantly facilitate the necessary computations.

About the authors

V. I. KUZOVATOV

Siberian Federal University

Email: kuzovatov@yandex.ru
Krasnoyarsk, Russia

A. A. KYTMANOV

MIREA – Russian Technological University; Laboratory of Artificial Intelligence, Neurotechnology, and Business Analytic

Email: aakytm@gmail.com
Moscow, Russia; Moscow, Russia

E. K. MYSHKINA

Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences

Author for correspondence.
Email: elfifenok@mail.ru
Krasnoyarsk, Russia

References

  1. Ортега Дж., Рейнболдт В. Итерационные методы решения нелинейных систем уравнений со многими неизвестными. М.: Мир, 1975.
  2. Айзенберг Л.А., Южаков А.П. Интегральные представления и вычеты в многомерном комплексном анализе. Новосибирск: Наука, 1979.
  3. Шабат Б.В. Введение в комплексный анализ. Функции нескольких переменных. Ч. 2. СПб.: Лань, 2004.

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Copyright (c) 2023 В.И. Кузоватов, А.А. Кытманов, Е.К. Мышкина