- PII
- S3034584725020052-1
- DOI
- 10.7868/S3034584725020052
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume / Issue number 2
- Pages
- 43-48
- Abstract
- Systems of nonalgebraic equations containing entire functions of several complex variables are considered. The number of real zeros of such systems is studied using computer algebra methods. For this purpose, a computer implementation of Newton’s recurrences and formulas for the resultant of the functions under study in Maple is proposed. The relevance of this problem is due to the fact that in applied problems, e.g., in the equations of chemical kinetics, it is necessary to determine the number of stationary states of the system.
- Keywords
- системы неалгебраических уравнений вещественные нули результант системы
- Date of publication
- 01.04.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 65
References
- 1. Kytmanov A.M., Khodos O.V. On the Roots of Systems of Transcendental Equations // Probl. Anal. Issues Anal. 2024. V. 13.№1. P. 37–49.
- 2. Гантмахер Ф.Р. Теория матриц. М.: Наука, 1967.
- 3. Gantmakher F.R. The Theory of Matrices, New York: Chelsea, 1959.
- 4. Krein M.G., Naimark M.A. The Method of Symmetric and Hermitian Forms in the Theory of the Separation of the Roots of Algebraic Equation // Linear Multilin. Algebra. 1981. V. 10.№4. P. 265–308.
- 5. Jury E.I. Inners and stability of dynamic system, Wiley, New York–London–Sydney–Toronto, 1974.
- 6. Чеботарев Н.Г. Собрание сочинений. Т. 2. Москва–Ленинград: АН СССР, 1949.
- 7. Chebotarev N.G. Collected Works, Moscow: Akad. Nauk SSSR, 1949, vol. 2 [in Russian].
- 8. Kytmanov A.M., Khodos O.V. On Localization of Zeros of an Entire Function of Finite Order of Growth // Complex Analysis and Operator Theory. 2017. V. 11.№2. P. 393–416.
- 9. Кытманов А.М. О числе вещественных корней систем уравнений // Известия вузов. Математика. 1991.№6. С. 20–23.
- 10. Kytmanov A.M. On the number of real roots od systems of equations, Izv. Vyssh. Uchebn. Zaved., Mat., 1991, no. 6, pp. 20–23.
- 11. Брюно А.Д., Батхин А.Б. Алгоритмы и программы вычисления корней многочлена от одной или двух неизвестных // Программирование. 2021. №5. С. 22–43.
- 12. Bruno A.D., Batkhin A.B. Algorithms and programs for calculating the roots of polynomial of one or two variables, Program. Comput. Software, 2021, vol. 47, no. 5, pp. 353–373.
- 13. Gohberg I.C., Heinig G. Resultant Matrix and its Generalization. I. Resultant Operator of Matrix Polynomial // Acta Scientiarum Mathematicarum. 1975. V. 72. P. 41–61.
- 14. Gohberg I.C., Heinig G. Resultant Matrix and its Generalization. II. Continual Analog of Resultant Matrix // Acta Mathematica Academiae Scientiarum Hungaricae. 1976. V. 28. P. 189–209.
- 15. Gohberg I.C., Lerer L.E. Resultant Operators of a Pair of Analytic Functions // Proceedings of the American Mathematical Society 1978. V. 72.№1. P. 65–73.
- 16. Gustafsson B., Tkachev V.G. The Resultant on Compact Riemann Surfaces // Communications in Mathematical Physics. 2009. V. 286. P. 313–358.
- 17. Морозов А.Ю., Шакиров Ш.Р. Новые и старые результаты в теории результантов // Теоретическая и математическая физика. 2010. Т. 163.№2. С. 222–257.
- 18. Morozov A.Yu., Shakirov Sh.R. New and old results in resultant theory, Theor. Math. Phys., 2010, vol. 163, no. 2, pp. 587–617.
- 19. Kytmanov A.M., Naprienko Ya.M. An approach to define the resultant of two entire functions // Journal Complex Variables and Elliptic Equations. 2017. V. 62.№2. P. 269–286.
- 20. Kytmanov A.M., Khodos O.V. An Approach to the Determination of the Resultant of Two Entire Functions // Russian Mathematics. 2018. V. 62.№4. P. 42–51.
- 21. Kytmanov A.M., Myshkina E.K. On Some Approach for Finding the Resultant of Two Entire Functions // J. Siberian Federal Univ. Math. Phys. 2019. V. 12. №4. P. 434–438.
- 22. Kuzovatov V.I., Myshkina E.K., Bushkova A.S. On an Approach to Finding Sums of Multiple Numerical Series // The Bulletin of Irkutsk State University. Series Mathematics. 2023. V. 46. P. 85–97.
- 23. Kytmanov A.M., Khodos O.V. On the Real Roots of Systems of Transcendental Equations // J. Siberian Federal Univ. Math. Phys. 2024. V. 17. № 3. P. 326–333.
- 24. Чирка Е.М. Комплексные аналитические множества. М.: Наука, 1985.
- 25. Chirka E.M. Complex Analytic Sets, Moscow: Nauka, 1985 [in Russian].
- 26. Kytmanov A.M., Myshkina E.K. On Finding the Resultant of Two Entire Functions // Probl. Anal. Issues Anal. 2020. V. 9.№3. P. 119–130.
- 27. Myshkina E.K. On a Formula for Calculating the Resultant of Two Entire Functions // J. Siberian Federal Univ. Math. Phys. 2022. V. 15.№1. P. 17–22.
- 28. Кытманов А.А. Об аналогах рекуррентных формул Ньютона // Известия вузов. Математика. 2009.№10. С. 40–50.
- 29. Kytmanov A.A. Analogs of recurrent Newton formulas, Russ. Math., 2009, vol. 53, no. 10, pp. 34–44.
- 30. Кытманов А.А. Алгоритм вычисления степенных сумм корней для класса систем нелинейных уравнений // Программирование. 2010.№2. С. 55–63.
- 31. Kytmanov A.A. An algorithm for calculating power sums of roots for a class of systems of nonlinear equations, Program. Comput. Software, 2010, vol. 36, no. 2, pp. 103–110.
