Configuratrix and Resultant

TL;DR

This paper derives an explicit formula for the resultant of n quadratic equations derived from a symmetric cubic polynomial, with applications to Finslerian geometry.

Contribution

It provides a novel explicit expression for the resultant of symmetric quadratic equations from a cubic polynomial, advancing algebraic and geometric analysis.

Findings

Explicit resultant formula for symmetric cubic polynomial equations

Application to Finslerian space analysis

Enhanced understanding of algebraic solutions in geometric contexts

Abstract

In this paper, we obtain an explicit expression for the resultant of n quadratic algebraic equations dS/dx_1 = 0,..., dS/dx_n = 0, where S is a cubic polynomial in n variables, symmetric under permutations of its arguments. Application of this result to the study of Finslerian spaces is discussed.