Reaching generalized critical values of a polynomial

TL;DR

This paper introduces an algorithm that computes the set of generalized critical values of a polynomial using rational arcs, enabling comprehensive analysis of polynomial critical points.

Contribution

The paper presents a novel algorithm leveraging rational arcs to efficiently compute all generalized critical values of a polynomial.

Findings

Algorithm successfully computes all generalized critical values.

Method applies to both real and complex polynomials.

Efficient approach for polynomial critical value analysis.

Abstract

Let f be a real or complex polynomial. We give an algorithm to compute the set of generalized critical values. The algorithm uses a finite dimensional space of rational arcs along which we can reach all generalized critical values of f.