On the Bivariate Symmetric Polynomials and Their Application

Document Type : Expository article (original)

Authors

Zeinab Saeidian ¹

Reza Kahkeshani ²

¹ Department of Mathematics, University of Kashan, Kashan, Iran

² Kashan University,Kashan,Iran

10.22067/tmsj.2025.93722.1065

Abstract

In this paper, we first introduce and investigate the symmetric polynomials and then, the features and underlying theorems are expressed.
 
In addition, we discuss applications of these polynomials in solving equations, systems of equations, inequalities, inverse equations, and divisibility.
 
The main objective of this research is to explain the prominent role of bivariate symmetric polynomials in different fields and provide practical examples to understand these issues better.‎

Keywords

Symmetric polynomial

System of equations

Inverse equation

Divisibility

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