Effective Whitney Stratification of Real Algebraic Varieties
Martin Helmer, Anton Leykin, and Vidit Nanda

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.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Numerical Analysis Techniques · Algebraic Geometry and Number Theory
