Výsledky vyhledávání - "Prebet, Rémi"

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Algebraic Tools for Computing Polynomial Loop Invariants

Autor: Bayarmagnai, Erdenebayar, Mohammadi, Fatemeh, Prébet, Rémi

Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution. Consequently, the gen

Externí odkaz: http://arxiv.org/abs/2405.09232

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Computing roadmaps in unbounded smooth real algebraic sets II: algorithm and complexity

Autor: Prébet, Rémi, Din, Mohab Safey El, Schost, Éric

A roadmap for an algebraic set $V$ defined by polynomials with coefficients in some real field, say $\mathbb{R}$, is an algebraic curve contained in $V$ whose intersection with all connected components of $V\cap\mathbb{R}^{n}$ is connected. These obj

Externí odkaz: http://arxiv.org/abs/2402.03111

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Algorithm for connectivity queries on real algebraic curves

Autor: Islam, Md Nazrul, Poteaux, Adrien, Prébet, Rémi

We consider the problem of answering connectivity queries on a real algebraic curve. The curve is given as the real trace of an algebraic curve, assumed to be in generic position, and being defined by some rational parametrizations. The query points

Externí odkaz: http://arxiv.org/abs/2302.11347

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Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry

Autor: Chablat, Damien, Prébet, Rémi, Din, Mohab Safey El, Salunkhe, Durgesh, Wenger, Philippe

Cuspidal robots are robots with at least two inverse kinematic solutions that can be connected by a singularity-free path. Deciding the cuspidality of generic 3R robots has been studied in the past, but extending the study to six-degree-of-freedom ro

Externí odkaz: http://arxiv.org/abs/2203.04578

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Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results

Autor: Prébet, Rémi, Din, Mohab Safey El, Schost, Éric

Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is tackled through

Externí odkaz: http://arxiv.org/abs/2203.03961

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