2021

• New data structure for univariate polynomial approximation and applications to root isolation, numerical multipoint evaluation, and other problems. Guillaume Moroz. Research report, 2021-06. [hal] [pdf]

• Fast real and complex root-finding methods for well-conditioned polynomials. Guillaume Moroz. Research report, 2021-02. [hal] [pdf]

• Certified numerical algorithm for isolating the singularities of the plane projection of generic smooth space curves. George Krait, Sylvain Lazard, Guillaume Moroz, Marc Pouget. Journal of Computational and Applied Mathematics, 2021. [hal] [pdf]

• Optimal transport between determinantal point processes and application to fast simulation. Laurent Decreusefond, Guillaume Moroz. Modern Stochastics: Theory and Applications, vol. 8(2), pages 209-237, 2021. [hal] [pdf]

2020

• Isolating the singularities of the plane projection of a generic space curve. George Krait, Sylvain Lazard, Guillaume Moroz, Marc Pouget. Research report, 2020. [hal] [pdf]

• Using Maple to analyse parallel robots. Damien Chablat, Guillaume Moroz, Fabrice Rouillier, Philippe Wenger. Maple in Mathematics Education and Research, pages 50-64, 2020-02. [hal] [pdf]

2019

• Reliable Computation of the Singularities of the Projection in R3 of a Generic Surface of R4. Sény Diatta, Guillaume Moroz, Marc Pouget. MACIS 2019 - Mathematical Aspects of Computer and Information Sciences, 2019-11. [hal] [pdf]

• Evaluation of Chebyshev polynomials on intervals and application to root finding. Viviane Ledoux, Guillaume Moroz. Mathematical Aspects of Computer and Information Sciences 2019, 2019-11. [hal] [pdf]

• Numerical Algorithm for the Topology of Singular Plane Curves. George Krait, Sylvain Lazard, Guillaume Moroz, Marc Pouget. EuroCG 2019 - 35th European Workshop on Computational Geometry, 2019-03. [hal] [pdf]

2018

• Workspace, Joint space and Singularities of a family of Delta-Like Robot. Ranjan Jha, Damien Chablat, Luc Baron, Fabrice Rouillier, Guillaume Moroz. Mechanism and Machine Theory, vol. 127, pages 73-95, 2018-09. [hal] [pdf]

• Monotone Simultaneous Paths Embeddings in ℝ^d. David Bremner, Olivier Devillers, Marc Glisse, Sylvain Lazard, Giuseppe Liotta, Tamara Mchedlidze, Guillaume Moroz, Sue Whitesides, Stephen Wismath. Discrete Mathematics and Theoretical Computer Science, vol. 20(1), pages 1-11, 2018-01. [hal] [pdf]

• Reliable Location with Respect to the Projection of a Smooth Space Curve. Rémi Imbach, Guillaume Moroz, Marc Pouget. Reliable Computing, vol. 26, pages 13-55, 2018. [hal] [pdf]

2017

• Reliable location with respect to the projection of a smooth space curve. Rémi Imbach, Guillaume Moroz, Marc Pouget. Research Report, 2017-11. [hal] [pdf]

• Computing effectively stabilizing controllers for a class of nD systems. Yacine Bouzidi, Thomas Cluzeau, Guillaume Moroz, Alban Quadrat. The 20th World Congress of the International Federation of Automatic Control, vol. 50, pages 1847 - 1852, 2017-07. [hal] [pdf]

2016

• Quadric Arrangement in Classifying Rigid Motions of a 3D Digital Image. Kacper Pluta, Guillaume Moroz, Yukiko Kenmochi, Pascal Romon. The 18th International Workshop on Computer Algebra in Scientific Computing, vol. 9890, pages 426 - 443, 2016-09. [hal] [pdf]

• Influence of the trajectory planning on the accuracy of the orthoglide 5-axis. Ranjan Jha, Damien Chablat, Fabrice Rouillier, Guillaume Moroz. ASME International Design Engineering Technical Conference and the Computer and Information in Engineering Conference (IDETC/CIE), 2016-08. [hal] [pdf]

• A Fast Algorithm for Computing the Truncated Resultant. Guillaume Moroz, Éric Schost. ISSAC ’16, pages 341-348, 2016-07. [hal] [pdf]

• Computing the Distance between Piecewise-Linear Bivariate Functions. Guillaume Moroz, Boris Aronov. ACM Transactions on Algorithms, vol. 12(1), pages 3:1-3:13, 2016-02. [hal] [pdf]

• A certified numerical algorithm for the topology of resultant and discriminant curves. Rémi Imbach, Guillaume Moroz, Marc Pouget. Journal of Symbolic Computation, vol. 80, Part 2, pages 285-306, 2016. [hal] [pdf]

• Solving bivariate systems using Rational Univariate Representations. Yacine Bouzidi, Sylvain Lazard, Guillaume Moroz, Marc Pouget, Fabrice Rouillier, Michael Sagraloff. Journal of Complexity, vol. 37, pages 34-75, 2016. [hal] [pdf]

2015

• Numeric and Certified Isolation of the Singularities of the Projection of a Smooth Space Curve. Rémi Imbach, Guillaume Moroz, Marc Pouget. Proceedings of the 6th International Conferences on Mathematical Aspects of Computer and Information Sciences, 2015-10. [hal] [pdf]

• An algebraic method to check the singularity-free paths for parallel robots. Ranjan Jha, Damien Chablat, Fabrice Rouillier, Guillaume Moroz. International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, 2015-08. [hal] [pdf]

• Workspace and Singularity analysis of a Delta like family robot. Ranjan Jha, Damien Chablat, Fabrice Rouillier, Guillaume Moroz. 4th IFTOMM International Symposium on Robotics and Mechatronics, 2015-06. [hal] [pdf]

• Improved algorithms for solving bivariate systems via Rational Univariate Representations. Yacine Bouzidi, Sylvain Lazard, Guillaume Moroz, Marc Pouget, Fabrice Rouillier, Michael Sagraloff. Research Report, 2015-06. [hal] [pdf]

• Numeric certified algorithm for the topology of resultant and discriminant curves. Rémi Imbach, Guillaume Moroz, Marc Pouget. Research Report, 2015-04. [hal] [pdf]

2014

• Workspace and joint space analysis of the 3-RPS parallel robot. Damien Chablat, Ranjan Jha, Fabrice Rouillier, Guillaume Moroz. ASME 2013 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, vol. Volume 5A, pages 1-10, 2014-08. [hal] [pdf]

• Improved algorithm for computing separating linear forms for bivariate systems. Yacine Bouzidi, Sylvain Lazard, Guillaume Moroz, Marc Pouget, Fabrice Rouillier. ISSAC - 39th International Symposium on Symbolic and Algebraic Computation, 2014-07. [hal] [pdf]

• Non-singular assembly mode changing trajectories in the workspace for the 3-RPS parallel robot. Damien Chablat, Ranjan Jha, Fabrice Rouillier, Guillaume Moroz. Advances in Robot Kinematics, pages 149 - 159, 2014-06. [hal] [pdf]

2013

• Fast polynomial evaluation and composition. Guillaume Moroz. Technical Report, 2013-07. [hal] [pdf]

• The monotonicity of f-vectors of random polytopes. Olivier Devillers, Marc Glisse, Xavier Goaoc, Guillaume Moroz, Matthias Reitzner. Electronic Communications in Probability, vol. 18(23), pages 1-8, 2013. [hal] [pdf]

2012

• Infinite Boltzmann Samplers and Applications to Branching Processes. Olivier Bodini, Guillaume Moroz, Hanane Tafat-Bouzid. GASCom - 8th edition of the conference GASCom on random generation of combinatorial structures - 2012, 2012-06. [hal] [pdf]

• A Six-Dof Epicyclic-Parallel Manipulator. Chao Chen, Thibault Gayral, Stéphane Caro, Damien Chablat, Guillaume Moroz, Sajeeva Abeywardena. Journal of Mechanisms and Robotics, vol. 4(4), 2012-04. [hal] [pdf]

• Computing the Distance between Piecewise-Linear Bivariate Functions. Guillaume Moroz, Boris Aronov. SODA - Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms - 2012, 2012-01. [hal] [pdf]

• Solution regions in the parameter space of a 3-RRR decoupled robot for a prescribed workspace. Damien Chablat, Guillaume Moroz, Vigen Arakelian, Sébastien Briot, Philippe Wenger. Latest Advances in Robot Kinematics, pages 357-364, 2012-01. [hal] [pdf]

• The monotonicity of f-vectors of random polytopes. Olivier Devillers, Marc Glisse, Xavier Goaoc, Guillaume Moroz, Matthias Reitzner. Research Report, pages 10, 2012. [hal] [pdf]

• Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators. Montserrat Manubens, Guillaume Moroz, Damien Chablat, Philippe Wenger, Fabrice Rouillier. Journal of Mechanisms and Robotics, pages 1-10, 2012. [hal] [pdf]

2011

• Properness Defects of Projection and Minimal Discriminant Variety. Guillaume Moroz. Journal of Symbolic Computation, vol. 46(10), pages 1139 - 1157, 2011-10. [hal]

• A comparative study of 4-cable planar manipulators based on cylindrical algebraic decomposition. Damien Chablat, Erika Ottaviano, Guillaume Moroz. Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, pages 1-10, 2011-08. [hal] [pdf]

• The assembly modes of rigid 11-bar linkages. Ioannis Z. Emiris, Guillaume Moroz. IFToMM 2011 World Congress, 2011-06. [hal] [pdf]

• Uniqueness domains and non singular assembly mode changing trajectories. Damien Chablat, Guillaume Moroz, Philippe Wenger. International Conference on Robotics and Automation, pages 1-6, 2011. [hal] [pdf]

2010

• Singularity Analysis of a Six-dof Parallel Manipulator using Grassmann-Cayley Algebra and Gröbner Bases. Stéphane Caro, Guillaume Moroz, Thibault Gayral, Damien Chablat, Chao Chen. Brain, Body and Machine. Advances in Intelligent and Soft Computing, vol. 83, pages 341-352, 2010-11. [hal] [pdf]

• On the determination of cusp points of 3-RPR parallel manipulators. Guillaume Moroz, Fabrice Rouillier, Damien Chablat, Philippe Wenger. Mechanism and Machine Theory, vol. 45(11), pages 1555-1567, 2010-11. [hal] [pdf]

• Cusp points in the parameter space of RPR-2PRR parallel manipulators. Guillaume Moroz, Damien Chablat, Philippe Wenger, Fabrice Rouillier. 3rd European Conference on Mechanism Science : EUCOMES 2010, vol. 5, pages 29-37, 2010-09. [hal] [pdf]

2008

• Sur la décomposition réelle et algébrique des systèmes dépendant de paramètres. Guillaume Moroz. Theses, 2008-12. [hal] [pdf]

• Classification of the perspective-three-point problem, discriminant variety and real solving polynomial systems of inequalities. Jean-Charles Faugère, Guillaume Moroz, Fabrice Rouillier, Mohab Safey El Din. ISSAC 2008 - 21st International Symposium on Symbolic and Algebraic Computation, pages 79-86, 2008-07. [hal]

• Explicit classification of the 9 first Haas parametric systems. Guillaume Moroz, Fabrice Rouillier. ADG 2008 — Seventh International Workshop on Automated Deduction in Geometry, pages 1-1, 2008. [hal]

2007

• Regular Decompositions. Guillaume Moroz. Computer Mathematics: 8th Asian Symposium, ASCM 2007, Revised and Invited Papers, vol. 5081, pages 263-277, 2007-12. [hal]

2006

• Complexity of the Resolution of Parametric Systems of Polynomial Equations and Inequations. Guillaume Moroz. International Symposium on Symbolic and Algebraic Computation, pages 246-253, 2006-07. [hal]

• Complexity of Resolution of Parametric Systems of Polynomial Equations and Inequations. Guillaume Moroz. Research Report, 2006. [hal] [pdf]

fast_polynomial

Cette bibliothèque d’environ 2000 lignes écrite en cython est destinée à un large public (chercheur, ingénieur). Après compilation du polynôme à évaluer, l’évaluation est autant ou plus rapide que les différents logiciels spécialisés dans l’évaluation rapide et la composition rapide de polynômes (FLINT, Maple, Magma, etc.). De plus, il est conçu pour être aisément extensible par d’autres utilisateurs.

Siropa Toolbox

Cette bibliothèque d’environ 7500 lignes écrites en Maple s’adresse à des chercheurs en robotique, dans le but de les aider à décrire les configurations de mécanismes insolubles par d’autres programmes. Ce programme est basé sur des algorithmes symboliques et est complémentaire d’autres programmes comme ALIAS (analyse par intervalles), SinguLab (algèbre de Grassmann-Cayley).

RD

Ce logiciel permet de décomposer un système d’équations polynomiales en composantes equidimensionelles. Chaque composante en sortie est représentée sous la forme d’une liste d’équations et une liste d’inéquations. La codimension d’une composante est exactement le nombre de polynômes de la liste équations. De plus, en dehors des zéros des inéquations, les zéros des équations coïncident avec la composante.

DV

Ce package Maple traite les sytèmes d’équations et inéquations polynomiales dépendant de paramètres. Depuis la version 12 de Maple, ce programme est intégré à la bibliothèque RootFinding[Parametric]. Il permet la résolution certifiée de systèmes paramétrés polynomiaux.