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# Fabrice Rouillier

104
Documents

## Presentation

![](https://who.rocq.inria.fr/Fabrice.Rouillier/images/fabrice.jpg) **Fabrice Rouillier** Research Director ![](https://who.rocq.inria.fr/Fabrice.Rouillier/images/inria.png) INRIA Paris research center Address Institut de Mathématiques de Jussieu Université Pierre et Marie Curie Paris VI 4, place Jussieu, F-75005 Paris. Office 15-25 503 Phone (+33) 6 73 19 35 15 E-mail Fabrice.Rouillier $at$ inria.fr Research interests Polynomial System Solving, Real Algebraic Geometry, Computational Geometry, Topology, and Applications. Keywords Zero-dimensional systems, Parametric Systems, Real Roots Classification(s), Exact Computations, Software, Robotics, Signal Processing.

## Publications

### Bounds for polynomials on algebraic numbers and application to curve topology

Discrete and Computational Geometry, 2022, 67, pp.631-697. ⟨10.1007/s00454-021-00353-w⟩
Journal articles

### PTOPO: Computing the Geometry and the Topology of Parametric Curves

Journal of Symbolic Computation, 2022, ⟨10.1016/j.jsc.2022.08.012⟩
Journal articles

### Computation of the $\mathcal{L} \infty$ -norm of finite-dimensional linear systems

Communications in Computer and Information Science, 2021
Journal articles

### PTOPO: A Maple package for the topology of parametric curves

ACM Communications in Computer Algebra, 2020, 54 (2), pp.49-52. ⟨10.1145/3427218.3427223⟩
Journal articles

### Certified Non-conservative Tests for the Structural Stability of Discrete Multidimensional Systems

Multidimensional Systems and Signal Processing, 2019, 30 (3), pp.31. ⟨10.1007/s11045-018-0596-y⟩
Journal articles

### Computing Chebyshev knot diagrams

Journal of Symbolic Computation, 2018, 86, pp.21. ⟨10.1016/j.jsc.2017.04.001⟩
Journal articles

### Workspace, Joint space and Singularities of a family of Delta-Like Robot

Mechanism and Machine Theory, 2018, 127, pp.73-95. ⟨10.1016/j.mechmachtheory.2018.05.004⟩
Journal articles

### Bivariate triangular decompositions in the presence of asymptotes

Journal of Symbolic Computation, 2017, 82, pp.123 - 133. ⟨10.1016/j.jsc.2017.01.004⟩
Journal articles

### Solving bivariate systems using Rational Univariate Representations

Journal of Complexity, 2016, 37, pp.34--75. ⟨10.1016/j.jco.2016.07.002⟩
Journal articles

### Character Varieties For SL(3,C): The Figure Eight Knot

Experimental Mathematics, 2016, 25 (2), pp.17. ⟨10.1080/10586458.2015.1068249⟩
Journal articles

### Representations of fundamental groups of 3-manifolds into PGL(3,C): Exact computations in low complexity

Geometriae Dedicata, 2015, 177 (1), pp.52. ⟨10.1007/s10711-014-9987-x⟩
Journal articles

### Separating linear forms and Rational Univariate Representations of bivariate systems

Journal of Symbolic Computation, 2015, 68, pp.84-119. ⟨10.1016/j.jsc.2014.08.009⟩
Journal articles

### Local rigidity for SL (3,C) representations of 3-manifolds groups

Experimental Mathematics, 2013, 22 (4), pp.10. ⟨10.1080/10586458.2013.832441⟩
Journal articles

### Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators

Journal of Mechanisms and Robotics, 2012, pp.1-10
Journal articles

### On the topology of real algebraic plane curves

Mathematics in Computer Science, 2010, 4 (1), pp.113-137. ⟨10.1007/s11786-010-0044-3⟩
Journal articles

### On the determination of cusp points of 3-R\underline{P}R parallel manipulators

Mechanism and Machine Theory, 2010, 45 (11), pp.1555-1567. ⟨10.1016/j.mechmachtheory.2010.06.016⟩
Journal articles

### The first rational Chebyshev knots

Journal of Symbolic Computation, 2010, 45 (12), pp.1341-1358. ⟨10.1016/j.jsc.2010.06.014⟩
Journal articles

### Comments on A blind Signal Separation Method for Multiuser Communications

IEEE Transactions on Signal Processing, 2007, 55 (5), pp.2355-2356. ⟨10.1109/tsp.2007.892716⟩
Journal articles

### Exhaustive approach to the coupling matrix synthesis problem and application to the design of high degree asymmetric filters

International Journal of RF and Microwave Computer-Aided Engineering, 2007, 17 (1), pp.4--12. ⟨10.1002/mmce.20190⟩
Journal articles

### Solving parametric polynomial systems

Journal of Symbolic Computation, 2007, 42 (6), pp.636-667. ⟨10.1016/j.jsc.2007.01.007⟩
Journal articles

### Using computer algebra to certify the global convergence of a numerical optimization process

Mathematics in Computer Science, 2007, 1 (2), pp.291-304. ⟨10.1007/s11786-007-0021-7⟩
Journal articles

### The implicit structure of ridges of a smooth parametric surface

Computer Aided Geometric Design, 2006, 23 (7), pp.582-598. ⟨10.1016/j.cagd.2006.04.002⟩
Journal articles

### Motivations for an arbitrary precision interval arithmetic and the MPFI library

Reliable Computing, 2005, 11 (4), pp.275-290. ⟨10.1007/s11155-005-6891-y⟩
Journal articles

### Efficient isolation of polynomial's real roots

Journal of Computational and Applied Mathematics, 2004, 162 (1), pp.33-50. ⟨10.1016/j.cam.2003.08.015⟩
Journal articles

### Real solving for positive dimensional systems

Journal of Symbolic Computation, 2002, 34 (6), pp.543-560. ⟨10.1006/jsco.2002.0563⟩
Journal articles

### Finding at least one point in each connected component of a real algebraic set defined by a single equation

Journal of Complexity, 2000, 16 (4), pp.716-750. ⟨10.1006/jcom.2000.0563⟩
Journal articles

### Solving Zero-Dimensional Systems through the Rational Univariate Representation

Applicable Algebra in Engineering, Communication and Computing, 1999, 9 (5), pp.433-461. ⟨10.1007/s002000050114⟩
Journal articles

### Design of regular nonseparable bidimensional wavelets using Grobner basis techniques

IEEE Transactions on Signal Processing, 1998, 46 (4), pp.845-856. ⟨10.1109/78.668541⟩
Journal articles

### Des formules de Bareiss à la réduction des formes quadratiques

Notes aux comptes rendus de l'académie des sciences, 1995, 320, pp.1273-1278
Journal articles

### On the Geometry and the Topology of Parametric Curves

ISSAC 2020 - International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata / Virtual, Greece
Conference papers

### Computation of the $\mathcal{L}_{\infty}$-norm of finite-dimensional linear systems

Maple Conference, Nov 2020, Waterloo, Canada
Conference papers

### On the effective computation of stabilizing controllers of 2D systems

Maple Conference, Oct 2019, Waterloo, Canada. pp.19, ⟨10.1007/978-3-030-41258-6_3⟩
Conference papers

### Explicit H∞ controllers for 4th order single-input single-output systems with parameters and their applications to the two mass-spring system with damping

IFAC 2017 Workshop Congress , Jul 2017, Toulouse, France
Conference papers

### Certified Algorithms for proving the structural stability of two dimensional systems possibly with parameters

MNTS 2016 - 22nd International Symposium on Mathematical Theory of Networks and Systems, Jul 2016, Minneapolis, United States
Conference papers

### Computing Real Roots of Real Polynomials ... and now For Real!

ISSAC '16 Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, Jul 2016, Waterloo, Canada. pp.7, ⟨10.1145/2930889.2930937⟩
Conference papers

### Influence of the trajectory planning on the accuracy of the orthoglide 5-axis

ASME International Design Engineering Technical Conference and the Computer and Information in Engineering Conference (IDETC/CIE), Aug 2016, Charlotte, NC, United States
Conference papers

### Foreword of MEGA 2015

MEGA'2015 (Special Issue), Jun 2016, Trento, Italy
Conference papers

### An algebraic method to check the singularity-free paths for parallel robots

International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, ASME, Aug 2015, Boston, United States
Conference papers

### Workspace and Singularity analysis of a Delta like family robot

4th IFTOMM International Symposium on Robotics and Mechatronics, Jun 2015, Poitiers, France
Conference papers

### On the sign of a trigonometric expression

ISSAC ' 15, Jul 2015, Bath, United Kingdom. ⟨10.1145/2755996.2756664⟩
Conference papers

### Computer algebra methods for testing the structural stability of multidimensional systems

IEEE 9th International Workshop on Multidimensional (nD) Systems, Sep 2015, Vila Real, Portugal. ⟨10.1109/nds.2015.7332633⟩
Conference papers

### Improved algorithm for computing separating linear forms for bivariate systems

ISSAC - 39th International Symposium on Symbolic and Algebraic Computation, Jul 2014, Kobe, Japan
Conference papers

### Workspace and joint space analysis of the 3-RPS parallel robot

ASME 2013 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Aug 2014, Buffalo, United States. pp.1-10
Conference papers

### On the computation of the topology of plane curves

International Symposium on Symbolic and Algebraic Computation, Kobe University, Jul 2014, Kobe, Japan. pp.130-137, ⟨10.1145/2608628.2608670⟩
Conference papers

### Separating Linear Forms for Bivariate Systems

ISSAC - 38th International Symposium on Symbolic and Algebraic Computation, Jun 2013, Boston, United States. pp.117-124
Conference papers

### Rational Univariate Representations of Bivariate Systems and Applications

ISSAC - 38th International Symposium on Symbolic and Algebraic Computation, Jun 2013, Boston, United States. pp.109-116
Conference papers

### Computing Chebyshev knots diagrams

MEGA 11, 2011, Unknown, Unknown Region
Conference papers

### New bivariate system solver and topology of algebraic curves

27th European Workshop on Computational Geometry - EuroCG 2011, Mar 2011, Morschach, Switzerland
Conference papers

### On Solving Systems of Bivariate Polynomials

Mathematical Software - ICMS 2010, Sep 2010, Kobe, Japan. pp.100-104, ⟨10.1007/978-3-642-15582-6_21⟩
Conference papers

### Cusp points in the parameter space of RPR-2PRR parallel manipulators

3rd European Conference on Mechanism Science : EUCOMES 2010, Sep 2010, Cluj-Napoca, Romania. pp.29-37, ⟨10.1007/978-90-481-9689-0_4⟩
Conference papers

### On the topology of planar algebraic curves

25th annual symposium on Computational geometry - SCG 2009, Jun 2009, Aarhus, Denmark. pp.361--370, ⟨10.1145/1542362.1542424⟩
Conference papers

### On Using Triangular Decomposition for Solving Parametric Polynomial Systems

MACIS'09, Dec 2009, Fukuoka, Japan. pp.1--1
Conference papers

### Explicit classification of the 9 first Haas parametric systems

ADG 2008 --- Seventh International Workshop on Automated Deduction in Geometry, 2008, Shanghai, China. pp.1-1
Conference papers

### On The Topology of Planar Algebraic Curves

24th European Workshop on Computational Geometry - EuroCG 2008, Mar 2008, Nancy, France. pp.213--216
Conference papers

### Classification of the perspective-three-point problem, discriminant variety and real solving polynomial systems of inequalities

ISSAC 2008 - 21st International Symposium on Symbolic and Algebraic Computation, Jul 2008, Hagenberg, Austria. pp.79-86, ⟨10.1145/1390768.1390782⟩
Conference papers

### Using Computer Algebra to Certify the Global Convergence of a Numerical Optimization Process

Mathematical Aspects of Computer and Information Sciences, Jul 2006, Beijing, China. pp.100-112
Conference papers

### Ridges and umbilics of polynomial parametric surfaces

Computational Methods for Algebraic Spline Surfaces II - COMPASS II, Sep 2005, Oslo, Norway. pp.1-1
Conference papers

### Polynomial System Solving for Industrial Problems

SIAM Conference on Mathematics for Industry, Oct 2005, Detroit, MI, United States. pp.1-5
Conference papers

### Outils de calcul formel performants pour la résolution de certains problèmes en robotique

Journées Nationales de Recherche en Robotique, Oct 2005, Lorient, France. pp.89-99
Conference papers

### On the Rational Univariate Representation

International Conference on Polynomial System Solving, Nov 2004, Paris, France. pp.75--79
Conference papers

### Real roots of parametric polynomial systems.

The Eighth International Workshop on Mathematics Mechanization, Jun 2004, Beijing, China
Conference papers

### Exact Computations and Real Roots of Polynomial Systems

Algorithmic, Combinatorial and Applicable Real Algebraic Geometry, Apr 2004, Berkeley, CA, United States
Conference papers

### Real roots of parametric systems of polynomial equalities and inequalities

Workshop on Real Computation and Complexity, 2004, Rennes, France
Conference papers

### Computing sampling points in a semi-algebraic set defined by non-strict inequalities, Application to Pattern-Matching Problems

EACA 2004 - Encuentro de Álgebra Computacional y Aplicaciones, Jul 2004, Santander, Spain
Conference papers

### Solving Parametric Polynomial Systems

International Conference on Polynomial System Solving, Nov 2004, Paris, France. pp.53-55
Conference papers

### Efficient real solutions and robotics

1st EMS - SMAI - SMF Joint Conference Applied Mathematics and Applications of Mathematics, Feb 2003, Nice, France
Conference papers

### Using computer algebra tools to classify serial manipulators

Fourth International Workshop on Automated Deduction in Geometry - ADG 2002, Sep 2002, Hagenberg, Austria. pp.31-43, ⟨10.1007/978-3-540-24616-9_3⟩
Conference papers

### A library for arbitrary precision interval arithmetic

10th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (scan2002), 2002, Paris, France
Conference papers

### Outils pour l'Etude des Zéros Réels de Systèmes Algébriques

Journées de Géométrie Algorithmique - JGA'02, 2002, Obernai, France
Conference papers

### Computational problems related to positive polynomials

Workshop on positive polynomials, 2002, Oberwolfach, Germany
Conference papers

### Real Solving and parallel robots

Workshop on Computations and Applications in RAAG 2002, 2002, Santander, Spain
Conference papers

### Motivations for an arbitrary precision interval arithmetic and the mpfi library

SIAM Workshop on Validated Computing 2002, 2002, Toronto, Canada. pp.155-161
Conference papers

### Outils pour l'étude des zéros réels de systèmes algébriques

Colloque Mathématiques Effectives, 2002, Poitiers, France
Conference papers

### An environment for Symbolic and Numeric Computation

International Congress of Mathematical Software - ICMS'2002, 2002, Beijing, China. pp.239-249
Conference papers

### Calcul formel et calcul scientifique

Congrès national de mathématiques appliquées et industrielles (SMAI), May 2001, Club Med de Pompadour, Corrèze, France. pp.151-164
Conference papers

### Efficient Agorithms Based on the Critical Point Method

DIMACS Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, Mar 2001, Rutgers, United States. pp.123-138
Conference papers

### Solving the Birkhoff interpolation problem via the critical point method: an experimental study

Third International Workshop on Automated Deduction in Geometry - ADG'2000, Sep 2000, Zurich, Switzerland. pp.26-40, ⟨10.1007/3-540-45410-1_3⟩
Conference papers

### Well-defined semantics for floating-point computations: the MPFR library

MuPAD Workshop 2000, 2000, Unknown, Unknown Region
Conference papers

### Using Gröbner bases to compute higher order finite elements for ma\ss lumping

ICIAM'99, Edimburgh, 1999, Unknown, Unknown Region
Conference papers

### Real Solving of Polynomial Systems and Applications

ICIAM'99 - Edhimburg, 1999, Unknown, Unknown Region
Conference papers

### Using Computer algebra tools for off-line studies of parallel manipulators

International Conference on Applications of Computer Algebra (ACA'99), Jun 1999, Madrid, Spain
Conference papers

### Design of filter and filter banks using dedicated Computer Algebra Tools

International Conference on Applications of Computer Algebra (ACA'99), Jun 1999, Madrid, Spain
Conference papers

### Using Groebner bases to compute higher order finite elements for mass lumping

Fourth International Congress on Industrial & Applied Mathematics - ICIAM'99, Jul 1999, Edinburgh, United Kingdom
Conference papers

### Application of Modules (RealSolving/FRISCO)

MuPAD Workshop 1997, 1997, Unknown, Unknown Region
Conference papers

### Polynomial system solving in practice

FoCM'97, 1997, Unknown, Unknown Region
Conference papers

### Software for symbolic polynomial system solving: the PoSSo solver

ICIAM'95 - Hambourg, 1995, Unknown, Unknown Region
Conference papers

### PoSSo-RealSolving (zero-dimensional system of polynomials)

Proceedings of the PoSSo-workshop on software, 1995, Unknown, Unknown Region
Conference papers

### Real roots counting for some robotics problems

Computational Kinematics'95, Sep 1995, Nice (France), pp.73-82
Conference papers

### PoSSo-RealSolving (Simultaneous Inequalities)

Proceedings of the PoSSo-workshop on software, 1995, Unknown, Unknown Region
Conference papers

### Special Issue : MEGA 2015

Elsevier, 79 (1), pp.196, 2017
Books

### Polynomial system solving

Academic Press, Inc., 44 (3), pp.1--221, 2009, 0747-7171. ⟨10.1016/j.jsc.2008.08.004⟩
Books

### Symbolic Methods for Solving Algebraic Systems of Equations and Applications for Testing the Structural Stability

Alban Quadrat; Eva Zerz. Algebraic and Symbolic Computation Methods in Dynamical Systems, Springer, pp.203-237, 2020, ⟨10.1007/978-3-030-38356-5_8⟩
Book sections

### Using Maple to analyse parallel robots

Jürgen Gerhard; Ilias Kotsireas. Maple in Mathematics Education and Research, Springer, Cham, pp.50-64, 2020, Maple in Mathematics Education and Research, 978-3-030-41257-9. ⟨10.1007/978-3-030-41258-6_4⟩
Book sections

### On the effective computation of stabilizing controllers of 2D systems

Jürgen Gerhard, Ilias Kotsireas. Maple in Mathematics Education and Research, Maple in Mathematics Education and Research, Springer, pp.30-49, 2020, 978-3-030-41257-9
Book sections

### Non-singular assembly mode changing trajectories in the workspace for the 3-RPS parallel robot

Jadran Lenarčič, Oussama Khatib. Advances in Robot Kinematics, Springer, pp.149 - 159, 2014, 978-3-319-06697-4
Book sections

### Ridges and Umbilics of Polynomial Parametric Surfaces

B. Juttler and R. Piene. Geometric Modeling and Algebraic Geometry, Springer, pp.141--159, 2008, 978-3-540-72184-0. ⟨10.1007/978-3-540-72185-7_8⟩
Book sections

### Bernstein's basis and real root isolation

Combinatorial and Computational Geometry, 52, Cambridge University Press, pp.459-478, 2005, MSRI Publications
Book sections

### Efficient algorithms based on critical points method

Algorithmic and Quantitative Real Algebraic Geometry, 60, American Mathematical Society, pp.123--138, 2003, Discrete Mathematics and Theoretical Computer Science
Book sections

### Real Root Counting For some Robotics problems

Merlet, J.P. Solid Mechanics & its Applications, 9 p, 1998
Book sections

### Symbolic Recipes for Polynomial System Solving

A.M. Cohen, H. Cuypers and H. Sterk. Some Tapas of Computer Algebra, 4, Springer, pp.34-65, 1998, Algorithms and Computation in Mathematics, 3-540-63480-0. ⟨10.1007/978-3-662-03891-8_2⟩
Book sections

### Symbolic Recipes for Real Solutions

Cohen, A.M.; Cuypers, H.; Sterk, H. Some Tapas of Computer Algebra, 4, Springer, pp.121-167, 1998, Algorithms and Computation in Mathematics, 3-540-63480-0. ⟨10.1007/978-3-662-03891-8_6⟩
Book sections

### Algorithmes pour l'étude des solutions réelles des systèmes polynomiaux

Calcul formel [cs.SC]. Université Pierre & Marie Curie - Paris 6, 2007
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