2025

• Fast evaluation and root finding for polynomials with floating-point coefficients. Rémi Imbach, Guillaume Moroz. Journal of Symbolic Computation, vol. 127, pages 102372, 2025-03. [hal] [pdf]

• A Subquadratic Algorithm for Computing the L1-distance between Two Terrains. Pankaj K. Agarwal, Boris Aronov, Guillaume Moroz. Research report, 2025-01. [hal] [pdf]

2024

• Algebraic data structures and approximations for efficient geometric modeling. Guillaume Moroz. Accreditation to supervise research, 2024-12. [hal] [pdf]

• Sparse Tensors and Subdivision Methods for Finding the Zero Set of Polynomial Equations. Guillaume Moroz. Proceedings of the 26th International Workshop on Computer Algebra in Scientific Computing, 2024-09. [hal] [pdf]

• Towards the Computation of Stabilizing Controllers of Multidimensional Systems. Thomas Cluzeau, Guillaume Moroz, Alban Quadrat. IFAC-Papers online, vol. 58, 2024-08. [hal] [pdf]

2023

• Fast evaluation and root finding for polynomials with floating-point coefficients. Rémi Imbach, Guillaume Moroz. ISSAC ’23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, 2023-07. [hal] [pdf]

2022

• Fast High-Resolution Drawing of Algebraic Curves. Nuwan Herath Mudiyanselage, Guillaume Moroz, Marc Pouget. ISSAC 2022 - International Symposium on Symbolic and Algebraic Computation, pages 449-458, 2022-07. [hal] [pdf]

• New data structure for univariate polynomial approximation and applications to root isolation, numerical multipoint evaluation, and other problems. Guillaume Moroz. 2021 IEEE 62nd Annual Symposimum on Foundations of Computer Science (FOCS), 2022-02. [hal] [pdf]

2021

• Fast Guaranteed Drawing of High Degree Algebraic Curves. Nuwan Herath Mudiyanselage, Guillaume Moroz, Marc Pouget. Research report, 2021-12. [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, vol. 394, pages 113553, 2021-10. [hal] [pdf]

• Computational real algebraic geometry and applications to robotics. Guillaume Moroz. Doctoral, 2021-03. [hal] [pdf]

• Fast real and complex root-finding methods for well-conditioned polynomials. Guillaume Moroz. Research report, 2021-02. [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. Vol. 20 no. 1(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. Lecture Notes in Computer Science, 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. Proceedings of the ASME 2016 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. Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, 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]

• 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]

• 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]

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]

• 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]

• 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]

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. New Trends in Mechanism Science: Analysis and Design, 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. Proceedings of 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]

pwpoly

This software was written by Rémi Imbach under my direction, based on a new algorithm I designed. It contains approximately 40,000 lines of code. It is currently being integrated into Maple 2024. Associated publication. APP: IDDN.FR.001.360018.000.S.P.2021.000.10000. (2023).

hefroots

This software was written with Rémi Imbach, based on an initial prototype I developed in C. It contains approximately 40,000 lines of code. It is integrated in Maple 2023 along with earoots. Associated publication. APP: IDDN.FR.001.360018.000.S.P.2021.000.10000. (2022).

earoots

This C software uses the Ehrlich-Aberth method to find complex roots of polynomials in double precision. It contains approximately 1500 lines of code. The code was written to leverage auto-vectorization. This software is notably integrated with hefroots into Maple 2023. APP: IDDN.FR.001.190035.000.S.P.2022.000.10000. (2022).

voxelize

This software, developed in C++, allowed me to explore a new technique mixing subdivision algorithms and multipoint evaluation. It contains approximately 7000 lines of code. It supports my research and that of some colleagues. Publication 1, Publication 2. DOI: 10.5281/zenodo.3562432. (2019).

clenshaw

This Python software explores multipoint evaluation techniques combined with Marching Cube-type algorithms for visualizing algebraic surfaces and curves. It contains approximately 2000 lines of code. Associated publication. (2019).

fast_polynomial

This library of about 2000 lines written in Cython is intended for a wide audience (researchers, engineers). After compiling the polynomial to be evaluated, the evaluation is as fast or faster than various specialized software for fast evaluation and composition of polynomials (FLINT, Maple, Magma, etc.). Moreover, it is designed to be easily extensible by other users. Associated preprint. (2013)

Siropa Library

I developed this software during my post-doctorate in Nantes and maintain it for research colleagues in robotics who continue to use it. It contains approximately 10,000 lines of code. Documentation available here. Associated publications: Publication 1, Publication 2. APP: IDDN.FR.001.140015.000.S.P.2017.000.20600. (2010).

RD

This software decomposes a system of polynomial equations into equidimensional components. Each output component is represented as a list of equations and a list of inequations. The codimension of a component is exactly the number of polynomials in the equations list. Furthermore, outside the zeros of the inequations, the zeros of the equations coincide with the component. Associated publication. (2008).

DV

This Maple package deals with systems of polynomial equations and inequations depending on parameters. Since Maple version 12, this program has been integrated into the RootFinding[Parametric] library. It allows for the certified solving of parameterized polynomial systems. Associated publication. (2008).