Application Domains
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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## Section: New Results

### Non-Linear Computational Geometry

Participants : Laurent Dupont, Nuwan Herath Mudiyanselage, George Krait, Sylvain Lazard, Viviane Ledoux, Guillaume Moroz, Marc Pouget.

#### Clustering Complex Zeros of Triangular Systems of Polynomials

This work, presented at the CASC'19 Conference [23], gives the first algorithm for finding a set of natural $ϵ$-clusters of complex zeros of a regular triangular system of polynomials within a given polybox in ${ℂ}^{n}$, for any given $ϵ>0$. Our algorithm is based on a recent near-optimal algorithm of Becker et al (2016) for clustering the complex roots of a univariate polynomial where the coefficients are represented by number oracles. Our algorithm is based on recursive subdivision. It is local, numeric, certified and handles solutions with multiplicity. Our implementation is compared to well-known homotopy solvers on various triangular systems. Our solver always gives correct answers, is often faster than the homotopy solvers that often give correct answers, and sometimes faster than the ones that give sometimes correct results.

In collaboration with R. Imbach and C. Yap (Courant Institute of Mathematical Sciences, New York University, USA).

#### Reliable Computation of the Singularities of the Projection in ${ℝ}^{3}$ of a Generic Surface of ${ℝ}^{4}$

In collaboration with Sény Diatta (University Assane Seck of Ziguinchor, Senegal)

#### Using Maple to analyse parallel robots

In collaboration with Philippe Wenger, Damien Chablat (Laboratoire des Sciences du Numérique de Nantes, UMR CNRS 6004) and Fabrice Rouillier (project team Ouragan )