Subresultants in Multiple Roots

TL;DR

This paper extends formulas for subresultants to polynomials with multiple roots, providing new theoretical insights and closed-form expressions in both univariate and multivariate cases.

Contribution

It introduces novel Poisson-like formulas and closed-form expressions for subresultants in polynomials with multiple roots, expanding previous work to more complex root structures.

Findings

Extended Poisson-like formulas for multiple roots

Derived closed-form formulas in univariate case

Generalized results to multivariate polynomials

Abstract

We extend our previous work on Poisson-like formulas for subresultants in roots to the case of polynomials with multiple roots in both the univariate and multivariate case, and also explore some closed formulas in roots for univariate polynomials in this multiple roots setting.