System of Resultants as a collection of coefficients of a unique Resultant

TL;DR

This paper presents an explicit formula for the system of Resultants of multiple homogeneous polynomials, providing a new way to compute these algebraic objects in polynomial systems.

Contribution

It introduces a novel explicit formula for the system of Resultants as a collection of coefficients of a unique Resultant, advancing algebraic computation methods.

Findings

Derived an explicit formula for the system of Resultants.

Unified the system of Resultants with a single resultant expression.

Enhanced computational techniques for polynomial systems.

Abstract

I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables.