Density of real and complex decomposable univariate polynomials

TL;DR

This paper estimates the density of neighborhoods around the algebraic variety of decomposable univariate polynomials over real and complex fields, providing insights into their geometric distribution.

Contribution

It introduces a method to quantify the density of decomposable polynomials near their algebraic variety over real and complex numbers.

Findings

Density estimates for decomposable polynomials over reals and complex numbers

Quantitative analysis of polynomial decomposability

Insights into the geometric structure of polynomial varieties

Abstract

We estimate the density of tubes around the algebraic variety of decomposable univariate polynomials over the real and the complex numbers.