Team : PolSys
Arrival date : 09/01/2020
- Sorbonne Université - LIP6
Boîte courrier 169
Couloir 26-00, Étage 3, Bureau 338
4 place Jussieu
75252 PARIS CEDEX 05
Tel: +33 1 44 27 71 30, Remi.Prebet (at) nulllip6.fr
Supervision : Mohab SAFEY EL DIN
Connectivity in semi-algebraic sets: algorithms, implementations and applications.
The goal of this PhD thesis is to design theoretical tools and to develop algorithms using them to solve connectivity problems on semi-algebraic sets. We rely on the concept of roadmaps which is a one-dimensional subset preserving the same properties of connectedness. Constructing roadmaps and knowing how to use them are the two major issues of this PhD thesis.
- N. Islam, A. Poteaux, R. Prébet : “Algorithm for connectivity queries on real algebraic curves”, ISSAC '23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, Tromsø, Norway (2023)
- R. Prébet, M. Safey El Din, E. Schost : “Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results”, Journal of Symbolic Computation, pp. 102234, (Elsevier) (2023)
- D. Chablat, R. Prébet, M. Safey El Din, D. Salunkhe, Ph. Wenger : “Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry”, ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, Lille, France (2022)