Notes on symmetries and reductions of algebraic equations

TL;DR

This paper explores symmetries and reduction techniques for algebraic equations, providing transformations that preserve or simplify equations, with examples demonstrating their application and potential use as test problems for numerical methods.

Contribution

It introduces specific transformations that preserve or reduce algebraic equations, offering new tools for analysis and testing numerical algorithms.

Findings

Transformations that preserve algebraic equation forms

Methods to reduce the degree of algebraic equations

Examples illustrating the application of these transformations

Abstract

Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative examples are provided. The obtained results and solutions can be used as test problems for numerical methods of solving algebraic equations.