Bracket Polynomial Expression of Discriminant-Resultants as SL2-invariant

TL;DR

This paper introduces a bracket polynomial expression linking discriminants and resultants of binary forms, providing an algebraic proof of their independence with applications in dynamical systems.

Contribution

It presents a novel bracket polynomial formulation for intermediate terms between discriminant and resultant, and proves their algebraic independence.

Findings

Bracket polynomial expression for intermediate terms

Algebraic proof of independence of these terms

Application to dynamical systems theory

Abstract

We give a bracket polynomial expression for intermediate terms between discriminant and resultant for pair of binary forms. As an application of the bracket polynomial expression, we give an algebraic proof of the algebraic independence of intermediate terms, which was shown in the theory of dynamical systems.