12 citations · 40 across the 14 of their papers we have counts for
14 papers
Singularity Analysis for the Perspective-Four and Five-Line Problems
Jorge García Fontán, Abhilash Nayak, Sébastien Briot +1
This paper deals with image-based visual servoing and pose estimation by observing four and five lines. Our main interest is to determine the relative configurations of the camera…
Optimized Gröbner basis algorithms for maximal determinantal ideals and critical point computations
Sriram Gopalakrishnan, Vincent Neiger, Mohab Safey El Din
Given polynomials and , all in for some field , we consider the problem of computing the critical points of the restriction of …
Solving parameter-dependent semi-algebraic systems
Louis Gaillard, Mohab Safey El Din
We consider systems of polynomial equations and inequalities in where and $\boldsymbol{y} = (y_1,…
Faster real root decision algorithm for symmetric polynomials
George Labahn, Cordian Riener, Mohab Safey El Din +2
In this paper, we consider the problem of deciding the existence of real solutions to a system of polynomial equations having real coefficients, and which are invariant under the a…
A Direttissimo Algorithm for Equidimensional Decomposition
Christian Eder, Pierre Lairez, Rafael Mohr +1
We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension.…
Fast Algorithms for Discrete Differential Equations
Alin Bostan, Hadrien Notarantonio, Mohab Safey El Din
Discrete Differential Equations (DDEs) are functional equations that relate polynomially a power series in with polynomial coefficients in a "catalytic" variable a…
Refined Algorithms for Ideals of Minors of Square Matrices
Sriram Gopalakrishnan, Vincent Neiger, Mohab Safey El Din
We consider the problem of computing a grevlex Gröbner basis for the set of minors of size of an matrix of generic linear forms over a field of charact…
Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry
Damien Chablat, Rémi Prébet, Mohab Safey El Din +2
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 st…
Exact SOHS decompositions of trigonometric univariate polynomials with Gaussian coefficients
Victor Magron, Mohab Safey El Din, Markus Schweighofer +1
Certifying the positivity of trigonometric polynomials is of first importance for design problems in discrete-time signal processing. It is well known from the Riesz-Fejéz spectral…
Computing the volume of compact semi-algebraic sets
Pierre Lairez, Marc Mezzarobba, Mohab Safey El Din
Let be a compact basic semi-algebraic set defined as the real solution set of multivariate polynomial inequalities with rational coefficients. We design an algorithm…
SPECTRA -- a Maple library for solving linear matrix inequalities in exact arithmetic
Mohab Safey El Din, Didier Henrion, Simone Naldi +2
This document describes our freely distributed Maple library {\sc spectra}, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear m…
Determinantal sets, singularities and application to optimal control in medical imagery
Bernard Bonnard, Jean-Charles Faugère, Alain Jacquemard +2
Control theory has recently been involved in the field of nuclear magnetic resonance imagery. The goal is to control the magnetic field optimally in order to improve the contrast b…
On the Complexity of Computing Gröbner Bases for Quasi-homogeneous Systems
Jean-Charles Faugère, Mohab Safey El Din, Thibaut Verron
Let $\K$ be a field and $(f_1, \ldots, f_n)\subset \K[X_1, \ldots, X_n]$ be a sequence of quasi-homogeneous polynomials of respective weighted degrees w.r.t a…
On the geometry of polar varieties
B. Bank, M. Giusti, J. Heintz +2
We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehens…