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Communication Dans Un Congrès Année : 2020

Computing the real isolated points of an algebraic hypersurface

Résumé

Let $\mathbb{R}$ be the field of real numbers. We consider the problem of computing the real isolated points of a real algebraic set in $\mathbb{R}^n$ given as the vanishing set of a polynomial system. This problem plays an important role for studying rigidity properties of mechanism in material designs. In this paper, we design an algorithm which solves this problem. It is based on the computations of critical points as well as roadmaps for answering connectivity queries in real algebraic sets. This leads to a probabilistic algorithm of complexity $(nd)^{O(n\log(n))}$ for computing the real isolated points of real algebraic hypersurfaces of degree $d$. It allows us to solve in practice instances which are out of reach of the state-of-the-art.
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Dates et versions

hal-02920059 , version 1 (24-08-2020)

Identifiants

Citer

Huu Phuoc Le, Mohab Safey El Din, Timo de Wolff. Computing the real isolated points of an algebraic hypersurface. ISSAC '20: International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata / Virtual, Greece. pp.297-304, ⟨10.1145/3373207.3404049⟩. ⟨hal-02920059⟩
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