# Absolute root separation

## TL;DR

This paper improves bounds on the absolute root separation of polynomials with integer coefficients and reports experimental results indicating current bounds may be overly conservative.

## Contribution

The authors enhance existing bounds for absolute root separation and provide experimental evidence suggesting these bounds can be tightened.

## Key findings

- Improved theoretical bounds for root separation.
- Experimental data indicating bounds are overly pessimistic.
- Potential for tighter bounds based on empirical results.

## Abstract

The absolute separation of a polynomial is the minimum nonzero difference between the absolute values of its roots. In the case of polynomials with integer coefficients, it can be bounded from below in terms of the degree and the height (the maximum absolute value of the coefficients) of the polynomial. We improve the known bounds for this problem and related ones. Then we report on extensive experiments in low degrees, suggesting that the current bounds are still very pessimistic.