# A new general formula for the Cauchy Index on an interval with Subresultants

## TL;DR

This paper introduces a novel formula for calculating the Cauchy index of rational functions on any interval, utilizing subresultant polynomials, and simplifies computations by reducing the number of subresultants needed.

## Contribution

The paper provides a new general formula for the Cauchy index that removes endpoint restrictions and optimizes the number of subresultants involved.

## Key findings

- The formula applies to any interval without endpoint conditions.
- It reduces the number of subresultants needed in certain cases.
- The approach simplifies the computation of the Cauchy index.

## Abstract

We present a new formula for the Cauchy index of a rational function on an interval using subresultant polynomials. There is no condition on the endpoints of the interval and the formula also involves in some cases less subresultant polynomials.