Number of documents

119

Fabrice Rouillier

Fabrice Rouillier 

Research Director
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.

Journal articles25 documents

  • Yacine Bouzidi, Alban Quadrat, Fabrice Rouillier. Certified Non-conservative Tests for the Structural Stability of Discrete Multidimensional Systems. Multidimensional Systems and Signal Processing, Springer Verlag, 2018. ⟨hal-01951765⟩
  • Ranjan Jha, Damien Chablat, Luc Baron, Fabrice Rouillier, Guillaume Moroz. Workspace, Joint space and Singularities of a family of Delta-Like Robot. Mechanism and Machine Theory, Elsevier, 2018, 127, pp.73-95. ⟨10.1016/j.mechmachtheory.2018.05.004⟩. ⟨hal-01796066⟩
  • Pierre-Vincent Koseleff, Daniel Pecker, Fabrice Rouillier, Cuong Tran. Computing Chebyshev knot diagrams. Journal of Symbolic Computation, Elsevier, 2018, 86, pp.21. ⟨10.1016/j.jsc.2017.04.001⟩. ⟨hal-01232181v2⟩
  • Sylvain Lazard, Marc Pouget, Fabrice Rouillier. Bivariate triangular decompositions in the presence of asymptotes. Journal of Symbolic Computation, Elsevier, 2017, 82, pp.123 - 133. ⟨10.1016/j.jsc.2017.01.004⟩. ⟨hal-01468796⟩
  • Elisha Falbel, Antonin Guilloux, Pierre-Vincent Koseleff, Fabrice Rouillier, Morwen Thistlethwaite. Character Varieties For SL(3,C): The Figure Eight Knot. Experimental Mathematics, Taylor & Francis, 2016, 25 (2), pp.17. ⟨10.1080/10586458.2015.1068249⟩. ⟨hal-01362208⟩
  • Yacine Bouzidi, Sylvain Lazard, Guillaume Moroz, Marc Pouget, Fabrice Rouillier, et al.. Solving bivariate systems using Rational Univariate Representations. Journal of Complexity, Elsevier, 2016, 37, pp.34--75. ⟨10.1016/j.jco.2016.07.002⟩. ⟨hal-01342211v2⟩
  • Yacine Bouzidi, Sylvain Lazard, Marc Pouget, Fabrice Rouillier. Separating linear forms and Rational Univariate Representations of bivariate systems. Journal of Symbolic Computation, Elsevier, 2015, 68, pp.84-119. ⟨10.1016/j.jsc.2014.08.009⟩. ⟨hal-00977671⟩
  • Elisha Falbel, Pierre-Vincent Koseleff, Fabrice Rouillier. Representations of fundamental groups of 3-manifolds into PGL(3,C): Exact computations in low complexity. Geometriae Dedicata, Springer Verlag, 2015, 177 (1), pp.52. ⟨10.1007/s10711-014-9987-x⟩. ⟨hal-00908843⟩
  • Nicolas Bergeron, Antonin Guilloux, Elisha Falbel, Pierre-Vincent Koseleff, Fabrice Rouillier. Local rigidity for SL (3,C) representations of 3-manifolds groups. Experimental Mathematics, Taylor & Francis, 2013, 22 (4), pp.10. ⟨10.1080/10586458.2013.832441⟩. ⟨hal-00803837⟩
  • Montserrat Manubens, Guillaume Moroz, Damien Chablat, Philippe Wenger, Fabrice Rouillier. Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators. Journal of Mechanisms and Robotics, American Society of Mechanical Engineers, 2012, pp.1-10. ⟨hal-00690975⟩
  • Guillaume Moroz, Fabrice Rouillier, Damien Chablat, Philippe Wenger. On the determination of cusp points of 3-R\underline{P}R parallel manipulators. Mechanism and Machine Theory, Elsevier, 2010, 45 (11), pp.1555-1567. ⟨10.1016/j.mechmachtheory.2010.06.016⟩. ⟨hal-00545502⟩
  • Jinsan Cheng, Sylvain Lazard, Luis Peñaranda, Marc Pouget, Fabrice Rouillier, et al.. On the topology of real algebraic plane curves. Mathematics in Computer Science, Springer, 2010, 4 (1), pp.113-137. ⟨10.1007/s11786-010-0044-3⟩. ⟨inria-00517175⟩
  • Pierre-Vincent Koseleff, Daniel Pecker, Fabrice Rouillier. The first rational Chebyshev knots. Journal of Symbolic Computation, Elsevier, 2010, 45 (12), pp.1341-1358. ⟨http://www.sciencedirect.com/science/article/pii/S0747717110000945⟩. ⟨10.1016/j.jsc.2010.06.014⟩. ⟨hal-00429510⟩
  • Gu Nong, Xiang Yong, Fabrice Rouillier, Zhiqiang Cao. Comments on A blind Signal Separation Method for Multiuser Communications. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2007, 55 (5), pp.2355-2356. ⟨10.1109/tsp.2007.892716⟩. ⟨hal-01148706⟩
  • Richard Cameron, Jean-Charles Faugère, Fabrice Rouillier, Fabien Seyfert. 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, Wiley, 2007, 17 (1), pp.4--12. ⟨10.1002/mmce.20190⟩. ⟨hal-00663777⟩
  • Gu Nong, Daniel Lazard, Fabrice Rouillier, Xiang Yong. Using computer algebra to certify the global convergence of a numerical optimization process. Mathematics in Computer Science, Springer, 2007, 1 (2), pp.291-304. ⟨10.1007/s11786-007-0021-7⟩. ⟨hal-01148502⟩
  • Daniel Lazard, Fabrice Rouillier. Solving parametric polynomial systems. Journal of Symbolic Computation, Elsevier, 2007, 42 (6), pp.636-667. ⟨10.1016/j.jsc.2007.01.007⟩. ⟨hal-01148721⟩
  • Frédéric Cazals, Jean-Charles Faugère, Marc Pouget, Fabrice Rouillier. The implicit structure of ridges of a smooth parametric surface. Computer Aided Geometric Design, Elsevier, 2006, 23 (7), pp.582-598. ⟨10.1016/j.cagd.2006.04.002⟩. ⟨inria-00097581⟩
  • Nathalie Revol, Fabrice Rouillier. Motivations for an arbitrary precision interval arithmetic and the MPFI library. Reliable Computing, Springer Verlag, 2005, 11 (4), pp.275-290. ⟨10.1007/s11155-005-6891-y⟩. ⟨inria-00544998⟩
  • Fabrice Rouillier, Paul Zimmermann. Efficient isolation of polynomial's real roots. Journal of Computational and Applied Mathematics, Elsevier, 2004, 162 (1), pp.33-50. ⟨10.1016/j.cam.2003.08.015⟩. ⟨inria-00099941⟩
  • Philippe Aubry, Fabrice Rouillier, Mohab Safey El Din. Real solving for positive dimensional systems. Journal of Symbolic Computation, Elsevier, 2002, 34 (6), pp.543-560. ⟨10.1006/jsco.2002.0563⟩. ⟨inria-00100982⟩
  • Fabrice Rouillier, Marie-Françoise Roy, Mohab Safey El Din. Finding at least one point in each connected component of a real algebraic set defined by a single equation. Journal of Complexity, Elsevier, 2000, 16 (4), pp.716-750. ⟨10.1006/jcom.2000.0563⟩. ⟨inria-00099275⟩
  • Fabrice Rouillier. Solving Zero-Dimensional Systems through the Rational Univariate Representation. Applicable Algebra in Engineering, Communication and Computing, Springer Verlag, 1999, 9 (5), pp.433-461. ⟨10.1007/s002000050114⟩. ⟨inria-00098872⟩
  • Jean-Charles Faugère, Francois Moreau de Saint Martin, Fabrice Rouillier. Design of regular nonseparable bidimensional wavelets using Grobner basis techniques. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 1998, 46 (4), pp.845-856. ⟨10.1109/78.668541⟩. ⟨inria-00098579⟩
  • Fabrice Rouillier. Des formules de Bareiss à la réduction des formes quadratiques. Notes aux comptes rendus de l'académie des sciences, 1995, 320, pp.1273-1278. ⟨hal-01434771⟩

Conference papers56 documents

  • Guillaume Rance, Yacine Bouzidi, Alban Quadrat, Arnaud Quadrat, Fabrice Rouillier. 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. ⟨hal-01667368⟩
  • Alexander Kobel, Fabrice Rouillier, Michael Sagraloff. 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⟩. ⟨hal-01363955⟩
  • Jan Draisma, Giorgio Ottaviani, Fabrice Rouillier. Foreword of MEGA 2015. MEGA'2015 (Special Issue), Jun 2016, Trento, Italy. ⟨hal-01351031⟩
  • Yacine Bouzidi, Fabrice Rouillier. 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. ⟨hal-01366202⟩
  • Ranjan Jha, Damien Chablat, Fabrice Rouillier, Guillaume Moroz. 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. ⟨hal-01309190⟩
  • Pierre-Vincent Koseleff, Fabrice Rouillier, Cuong Tran. On the sign of a trigonometric expression. ISSAC ' 15, Jul 2015, Bath, United Kingdom. ⟨10.1145/2755996.2756664⟩. ⟨hal-01200820⟩
  • Youcef Bouzidi, Alban Quadrat, Fabrice Rouillier. 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 ⟩. ⟨hal-01259968⟩
  • Ranjan Jha, Damien Chablat, Fabrice Rouillier, Guillaume Moroz. Workspace and Singularity analysis of a Delta like family robot. 4th IFTOMM International Symposium on Robotics and Mechatronics, Jun 2015, Poitiers, France. ⟨hal-01142465⟩
  • Ranjan Jha, Damien Chablat, Fabrice Rouillier, Guillaume Moroz. 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. ⟨hal-01142989⟩
  • Yacine Bouzidi, Sylvain Lazard, Guillaume Moroz, Marc Pouget, Fabrice Rouillier. Improved algorithm for computing separating linear forms for bivariate systems. ISSAC - 39th International Symposium on Symbolic and Algebraic Computation, Jul 2014, Kobe, Japan. ⟨hal-00992634⟩
  • Damien Chablat, Ranjan Jha, Fabrice Rouillier, Guillaume Moroz. 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. ⟨hal-01006614⟩
  • Daouda Niang Diatta, Fabrice Rouillier, Marie-Françoise Roy. 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⟩. ⟨hal-00935728v2⟩
  • Yacine Bouzidi, Sylvain Lazard, Marc Pouget, Fabrice Rouillier. 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. ⟨hal-00809430⟩
  • Yacine Bouzidi, Sylvain Lazard, Marc Pouget, Fabrice Rouillier. Separating Linear Forms for Bivariate Systems. ISSAC - 38th International Symposium on Symbolic and Algebraic Computation, Jun 2013, Boston, United States. pp.117-124. ⟨hal-00809425⟩
  • P-V. Koseleff, D. Pecker, Fabrice Rouillier. Computing Chebyshev knots diagrams. MEGA 11, 2011, Unknown, Unknown Region. ⟨hal-01434749⟩
  • Yacine Bouzidi, Sylvain Lazard, Marc Pouget, Fabrice Rouillier. New bivariate system solver and topology of algebraic curves. 27th European Workshop on Computational Geometry - EuroCG 2011, Mar 2011, Morschach, Switzerland. ⟨inria-00580431⟩
  • Fabrice Rouillier. 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⟩. ⟨hal-01110516⟩
  • Fabrice Rouillier, Rong Xiao. On Using Triangular Decomposition for Solving Parametric Polynomial Systems. MACIS'09, Dec 2009, Fukuoka, Japan. pp.1--1. ⟨hal-01298886⟩
  • Jinsan Cheng, Sylvain Lazard, Luis Peñaranda, Marc Pouget, Fabrice Rouillier, et al.. 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⟩. ⟨inria-00425383⟩
  • Jinsan Cheng, Sylvain Lazard, Luis Peñaranda, Marc Pouget, Fabrice Rouillier, et al.. On The Topology of Planar Algebraic Curves. 24th European Workshop on Computational Geometry - EuroCG 2008, Mar 2008, Nancy, France. pp.213--216. ⟨inria-00329754⟩
  • Jean-Charles Faugère, Guillaume Moroz, Fabrice Rouillier, Mohab Safey El Din. 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⟩. ⟨hal-01111711⟩
  • Guillaume Moroz, Fabrice Rouillier. 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. ⟨hal-01305663⟩
  • Nong Gu, Daniel Lazard, Fabrice Rouillier, Yong Xiang. 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. ⟨hal-01352508⟩
  • Jean-Charles Faugère, Fabrice Rouillier. 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. ⟨hal-01434754⟩
  • Frédéric Cazals, Jean-Charles Faugère, Marc Pouget, Fabrice Rouillier. Ridges and umbilics of polynomial parametric surfaces. Computational Methods for Algebraic Spline Surfaces II - COMPASS II, Sep 2005, Oslo, Norway. pp.1-1. ⟨hal-01434753⟩
  • Fabrice Rouillier, Jean-Charles Faugère. Polynomial System Solving for Industrial Problems. SIAM Conference on Mathematics for Industry, Oct 2005, Detroit, MI, United States. pp.1-5. ⟨hal-01486850⟩
  • Fabrice Rouillier. Exact Computations and Real Roots of Polynomial Systems. Algorithmic, Combinatorial and Applicable Real Algebraic Geometry, Apr 2004, Berkeley, CA, United States. ⟨hal-01497056⟩
  • Fabrice Rouillier. Real roots of parametric polynomial systems.. The Eighth International Workshop on Mathematics Mechanization, Jun 2004, Beijing, China. ⟨hal-01497052⟩
  • Colas Le Guernic, Fabrice Rouillier, Mohab Safey El Din. 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. ⟨hal-01434756⟩
  • Fabrice Rouillier. On the Rational Univariate Representation. International Conference on Polynomial System Solving, Nov 2004, Paris, France. pp.75--79. ⟨hal-01434755⟩
  • Fabrice Rouillier. Real roots of parametric systems of polynomial equalities and inequalities. Workshop on Real Computation and Complexity, 2004, Rennes, France. ⟨hal-01503542⟩
  • Daniel Lazard, Fabrice Rouillier. Solving Parametric Polynomial Systems. International Conference on Polynomial System Solving, Nov 2004, Paris, France. pp.53-55. ⟨hal-01520939⟩
  • Fabrice Rouillier. Efficient real solutions and robotics. 1st EMS - SMAI - SMF Joint Conference Applied Mathematics and Applications of Mathematics, Feb 2003, Nice, France. ⟨hal-01531942⟩
  • Gabriel Dos Reis, Bernard Mourrain, Philippe Trebuchet, Fabrice Rouillier. An environment for Symbolic and Numeric Computation. International Congress of Mathematical Software - ICMS'2002, 2002, Beijing, China. pp.239-249. ⟨inria-00100984⟩
  • Fabrice Rouillier. Computational problems related to positive polynomials. Workshop on positive polynomials, 2002, Oberwolfach, Germany. ⟨inria-00100983⟩
  • Nathalie Revol, Fabrice Rouillier. Motivations for an arbitrary precision interval arithmetic and the mpfi library. SIAM Workshop on Validated Computing 2002, 2002, Toronto, Canada. pp.155-161. ⟨inria-00100985⟩
  • Solen Corvez, Fabrice Rouillier. 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⟩. ⟨inria-00100987⟩
  • Fabrice Rouillier. Outils pour l'étude des zéros réels de systèmes algébriques. Colloque Mathématiques Effectives, 2002, Poitiers, France. ⟨inria-00100994⟩
  • Fabrice Rouillier. Real Solving and parallel robots. Workshop on Computations and Applications in RAAG 2002, 2002, Santander, Spain. ⟨inria-00100993⟩
  • Fabrice Rouillier. Outils pour l'Etude des Zéros Réels de Systèmes Algébriques. Journées de Géométrie Algorithmique - JGA'02, 2002, Obernai, France. ⟨inria-00100992⟩
  • Nathalie Revol, Fabrice Rouillier. A library for arbitrary precision interval arithmetic. 10th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (scan2002), 2002, Paris, France. ⟨hal-01434758⟩
  • Fabrice Rouillier. Calcul formel et calcul scientifique. Congrès national de mathématiques appliquées et industrielles (SMAI), May 2001, Club Med de Pompadour, Corrèze, France. pp.151-164. ⟨hal-01571753⟩
  • Fabrice Rouillier. 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. ⟨hal-01434759⟩
  • Fabrice Rouillier. Well-defined semantics for floating-point computations: the MPFR library. MuPAD Workshop 2000, 2000, Unknown, Unknown Region. ⟨hal-01434760⟩
  • Fabrice Rouillier, Mohab Safey El Din, Eric Schost. 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⟩. ⟨inria-00099276⟩
  • M. Kern, J.-C. Faugère, Fabrice Rouillier. Using Gröbner bases to compute higher order finite elements for ma\ss lumping. ICIAM'99, Edimburgh, 1999, Unknown, Unknown Region. ⟨hal-01434762⟩
  • Jean-Charles Faugère, Luc Rolland, Fabrice Rouillier. Using Computer algebra tools for off-line studies of parallel manipulators. International Conference on Applications of Computer Algebra (ACA'99), Jun 1999, Madrid, Spain. ⟨hal-01434763⟩
  • Jean-Charles Faugère, Fabrice Rouillier. Design of filter and filter banks using dedicated Computer Algebra Tools. International Conference on Applications of Computer Algebra (ACA'99), Jun 1999, Madrid, Spain. ⟨hal-01434764⟩
  • Fabrice Rouillier. Real Solving of Polynomial Systems and Applications. ICIAM'99 - Edhimburg, 1999, Unknown, Unknown Region. ⟨hal-01434761⟩
  • Michel Kern, Agany Oloui, Jean-Charles Faugère, Fabrice Rouillier. 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. ⟨inria-00110525⟩
  • Fabrice Rouillier. Application of Modules (RealSolving/FRISCO). MuPAD Workshop 1997, 1997, Unknown, Unknown Region. ⟨hal-01434768⟩
  • Fabrice Rouillier, M.F. Roy. Polynomial system solving in practice. FoCM'97, 1997, Unknown, Unknown Region. ⟨hal-01434770⟩
  • Fabrice Rouillier. Real roots counting for some robotics problems. Computational Kinematics'95, Sep 1995, Nice (France), pp.73-82. ⟨inria-00000936⟩
  • Fabrice Rouillier. Software for symbolic polynomial system solving: the PoSSo solver. ICIAM'95 - Hambourg, 1995, Unknown, Unknown Region. ⟨hal-01434772⟩
  • Fabrice Rouillier, G. Trujillo. PoSSo-RealSolving (Simultaneous Inequalities). Proceedings of the PoSSo-workshop on software, 1995, Unknown, Unknown Region. ⟨hal-01434773⟩
  • Fabrice Rouillier. PoSSo-RealSolving (zero-dimensional system of polynomials). Proceedings of the PoSSo-workshop on software, 1995, Unknown, Unknown Region. ⟨hal-01434774⟩

Books1 document

Book sections8 documents

  • Damien Chablat, Ranjan Jha, Fabrice Rouillier, Guillaume Moroz. 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. ⟨hal-00956325⟩
  • Guillaume Moroz, Damien Chablat, Philippe Wenger, Fabrice Rouillier. Cusp points in the parameter space of RPR-2PRR parallel manipulators. Pisla, D.; Ceccarelli, M.; Husty, M.; Corves, B. New Trends in Mechanism Science. Mechanisms and Machine Science, 5, Springer, pp.29-37, 2010, Mechanisms and Machine Science, ⟨10.1007/978-90-481-9689-0_4⟩. ⟨hal-00545445⟩
  • Frédéric Cazals, Jean-Charles Faugère, Marc Pouget, Fabrice Rouillier. 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⟩. ⟨inria-00329762⟩
  • Bernard Mourrain, Fabrice Rouillier, Marie-Françoise Roy. Bernstein's basis and real root isolation. Combinatorial and Computational Geometry, 52, Cambridge University Press, pp.459-478, 2005, MSRI Publications. ⟨hal-01486849⟩
  • Fabrice Rouillier. 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. ⟨hal-01434757⟩
  • Laureano Gonzalez-Vega, Fabrice Rouillier, Marie-Françoise Roy, Guadaluppe Trujillo. 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⟩. ⟨inria-00098571⟩
  • Fabrice Rouillier. Real Root Counting For some Robotics problems. Merlet, J.P. Solid Mechanics & its Applications, 9 p, 1998. ⟨inria-00098444⟩
  • Laureano Gonzalez-Vega, Fabrice Rouillier, Marie-Françoise Roy. 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⟩. ⟨inria-00098570⟩

Directions of work or proceedings1 document

  • Jan Draisma, Giorgio Ottaviani, Fabrice Rouillier. Special Issue : MEGA 2015. France. 79 (1), Elsevier, pp.196, 2017. ⟨hal-01412060⟩

Habilitation à diriger des recherches1 document

  • Fabrice Rouillier. Algorithmes pour l'étude des solutions réelles des systèmes polynomiaux. Calcul formel [cs.SC]. Université Pierre & Marie Curie - Paris 6, 2007. ⟨tel-01435142⟩

Other publications2 documents

Preprints, Working Papers, ...3 documents

  • Daouda Niang Diatta, Sény Diatta, Fabrice Rouillier, Marie-Françoise Roy, Michael Sagraloff. Bounds for polynomials on algebraic numbers and application to curve topology. 2018. ⟨hal-01891417⟩
  • Pierre-Vincent Koseleff, Fabrice Rouillier, Cuong Tran. On the sign of a trigonometric expression. 2015. ⟨hal-01108656⟩
  • Pierre-Vincent Koseleff, Daniel Pecker, Fabrice Rouillier. Computing Chebyshev knot diagrams. 2010. ⟨hal-00451221v2⟩

Reports22 documents

  • Yacine Bouzidi, Alban Quadrat, Fabrice Rouillier. Certified Non-conservative Tests for the Structural Stability of Multidimensional Systems. [Research Report] RR-9085, INRIA Lille - Nord Europe; INRIA Paris. 2017, pp.31. ⟨hal-01571230⟩
  • Sylvain Lazard, Marc Pouget, Fabrice Rouillier. Bivariate Triangular Decompositions in the Presence of Asymptotes. [Research Report] INRIA. 2015. ⟨hal-01200802⟩
  • Yacine Bouzidi, Sylvain Lazard, Guillaume Moroz, Marc Pouget, Fabrice Rouillier, et al.. Improved algorithms for solving bivariate systems via Rational Univariate Representations. [Research Report] Inria. 2015. ⟨hal-01114767v2⟩
  • Yacine Bouzidi, Sylvain Lazard, Marc Pouget, Fabrice Rouillier. Rational Univariate Representations of Bivariate Systems and Applications. [Research Report] RR-8262, INRIA. 2013, pp.26. ⟨hal-00802698v2⟩
  • Yacine Bouzidi, Sylvain Lazard, Marc Pouget, Fabrice Rouillier. Separating linear forms for bivariate systems. [Research Report] RR-8261, INRIA. 2013, pp.20. ⟨hal-00802693v2⟩
  • Nong Gu, Daniel Lazard, Fabrice Rouillier, Yong Xiang. On dertermining mixing parameter of CC-CMA algorithm by solving semi-algebraic sets. [Research Report] RR-5830, INRIA. 2006, pp.27. ⟨inria-00070195⟩
  • Jean-Charles Faugère, Jean-Pierre Merlet, Fabrice Rouillier. On solving the direct kinematics problem for parallel robots. [Research Report] RR-5923, INRIA. 2006. ⟨inria-00072366v2⟩
  • Frédéric Cazals, Jean-Charles Faugère, Marc Pouget, Fabrice Rouillier. Topologically certified approximation of umbilics and ridges on polynomial parametric surface. [Research Report] RR-5674, INRIA. 2005, pp.36. ⟨inria-00071225⟩
  • Frédéric Cazals, Jean-Charles Faugère, Marc Pouget, Fabrice Rouillier. The implicit structure of ridges of a smooth parametric surface. [Research Report] RR-5608, INRIA. 2005, pp.30. ⟨inria-00071237⟩
  • Daniel Lazard, Fabrice Rouillier. Solving Parametric Polynomial Systems. [Research Report] RR-5322, INRIA. 2004, pp.23. ⟨inria-00070678⟩
  • Bernard Mourrain, Fabrice Rouillier, Marie-Françoise Roy. Bernstein's basis and real root isolation. [Research Report] RR-5149, INRIA. 2004. ⟨inria-00071434⟩
  • Nathalie Revol, Fabrice Rouillier. Motivations for an arbitrary precision interval arithmetic and the MPFI library. [Research Report] RR-4498, LIP RR-2002-27, INRIA, LIP. 2002. ⟨inria-00072090⟩
  • Solen Corvez, Fabrice Rouillier. Using computer algebra tools to classify serial cuspidal manipulators. [Research Report] RR-4653, INRIA. 2002. ⟨inria-00071932⟩
  • Fabrice Rouillier, Paul Zimmermann. Efficient Isolation of a Polynomial Real Roots. [Research Report] RR-4113, INRIA. 2001. ⟨inria-00072518⟩
  • Luc Rolland, Fabrice Rouillier. Simulation géométrique de trajectoire avec erreurs de données de CAO. [Contrat] A00-R-265 || rolland00a, 2000, 25 p. ⟨inria-00099159⟩
  • Luc Rolland, Fabrice Rouillier. Simulation de trajectoire avec erreurs de mesures et modélisation de commande. [Contrat] A00-R-266 || rolland00b, 2000, 33 p. ⟨inria-00099160⟩
  • Fabrice Rouillier, Marie-Françoise Roy, Mohab Safey El Din. Finding at least one point in each connected component of a real algebraic set defined by a single equation. [Intern report] A00-R-017 || rouillier00a, 2000, 42 p. ⟨inria-00107845⟩
  • Philippe Aubry, Fabrice Rouillier, M. Safey El Din. Real Solving for Positive Dimensional Systems. [Research Report] RR-3992, INRIA. 2000, pp.20. ⟨inria-00072654⟩
  • Luc Rolland, Fabrice Rouillier. Simulation géométrique de trajectoire avec erreurs de mesures. [Contrat] 99-R-426 || rolland99c, 1999, 39 p. ⟨inria-00098915⟩
  • Fabrice Rouillier. FRISCO Tools for the isolation of the Real Roots of dense univariate polynomials with integer coefficients. [Contract] 98-R-072 || rouillier98b, 1998, 10 p. ⟨inria-00098567⟩
  • Fabrice Rouillier, M.F Roy, M. Safey. Testing emptyness of Real Hypersurfaces. [Contract] 98-R-073 || rouillier98c, 1998, 10 p. ⟨inria-00098568⟩
  • Fabrice Rouillier. Solving Zero-dimensional Polynomial Systems through the Rational Univariate Representation. [Research Report] RR-3426, INRIA. 1998, pp.23. ⟨inria-00073264⟩