Effective Whitney Stratification of Real Algebraic Varieties

TL;DR

This paper introduces new algorithms for computing Whitney stratifications of real algebraic varieties, utilizing conormal and polar techniques, and extends these methods to semialgebraic sets and algebraic maps.

Contribution

The paper presents novel algorithms for Whitney stratification of real algebraic varieties and extends these techniques to broader classes of semialgebraic sets and maps.

Findings

Algorithms successfully stratify complexifications of real varieties

Stratifications can be described by real polynomials

Methods applicable to semialgebraic sets and algebraic maps

Abstract

We describe new algorithms to compute Whitney stratifications of real algebraic varieties. Using either conormal or polar techniques, these algorithms stratify a complexification of a given real variety. We then show that the resulting stratification can be described by real polynomials. We also extend these methods to stratification problems involving the so-called full semialgebraic sets as well as real algebraic maps.