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Rouillier, Fabrice

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Author ID: rouillier.fabrice Recent zbMATH articles by "Rouillier, Fabrice"
Published as: Rouillier, Fabrice; Rouillier, F.
Documents Indexed: 41 Publications since 1995

Publications by Year

Citations contained in zbMATH Open

33 Publications have been cited 424 times in 288 Documents Cited by Year
Solving zero-dimensional systems through the rational univariate representation. Zbl 0932.12008
Rouillier, Fabrice
98
1999
Efficient isolation of polynomial’s real roots. Zbl 1040.65041
Rouillier, Fabrice; Zimmermann, Paul
62
2004
Solving parametric polynomial systems. Zbl 1156.14044
Lazard, Daniel; Rouillier, Fabrice
38
2007
Motivations for an arbitrary precision interval arithmetic and the MPFI library. Zbl 1078.65543
Revol, Nathalie; Rouillier, Fabrice
28
2005
Real solving for positive dimensional systems. Zbl 1046.14031
Aubry, Philippe; Rouillier, Fabrice; Safey El Din, Mohab
20
2002
Finding at least one point in each connected component of a real algebraic set defined by a single equation. Zbl 1009.14010
Rouillier, F.; Roy, M.-F.; Safey El Din, M.
20
2000
Representations of fundamental groups of 3-manifolds into \(\mathrm{PGL}(3,\mathbb C)\): exact computations in low complexity. Zbl 1326.57041
Falbel, E.; Koseleff, P.-V.; Rouillier, F.
15
2015
Symbolic recipes for real solutions. Zbl 0994.12003
Gonzalez-Vega, Laureano; Rouillier, Fabrice; Roy, Marie-Françoise; Trujillo, Guadalupe
13
1999
The Bernstein-basis and real root isolation. Zbl 1094.14051
Mourrain, Bernard; Rouillier, Fabrice; Roy, Marie-Françoise
13
2005
On the topology of real algebraic plane curves. Zbl 1205.14038
Cheng, Jinsan; Lazard, Sylvain; Peñaranda, Luis; Pouget, Marc; Rouillier, Fabrice
13
2010
On the topology of planar algebraic curves. Zbl 1391.14060
Cheng, Jinsan; Lazard, Sylvain; Peñaranda, Luis; Pouget, Marc; Rouillier, Fabrice; Tsigaridas, Elias
10
2009
Symbolic recipes for polynomial system solving. Zbl 0966.13020
Gonzalez-Vega, Laureano; Rouillier, Fabrice; Roy, Marie-Françoise
9
1999
Computing real roots of real polynomials …and now for real! Zbl 1365.65142
Kobel, Alexander; Rouillier, Fabrice; Sagraloff, Michael
9
2016
Solving bivariate systems using rational univariate representations. Zbl 1351.65033
Bouzidi, Yacine; Lazard, Sylvain; Moroz, Guillaume; Pouget, Marc; Rouillier, Fabrice; Sagraloff, Michael
9
2016
Local rigidity for \(\mathrm{PGL}(3,\mathbb C)\)-representations of 3-manifold groups. Zbl 1297.57047
Bergeron, Nicolas; Falbel, Elisha; Guilloux, Antonin; Koseleff, Pierre-Vincent; Rouillier, Fabrice
8
2013
Character varieties for \(SL(3, \mathbb{C})\): the figure eight knot. Zbl 1353.57007
Falbel, E.; Guilloux, A.; Koseleff, P.-V.; Rouillier, F.; Thistlethwaite, M.
7
2016
Using computer algebra tools to classify serial manipulators. Zbl 1202.68489
Corvez, Solen; Rouillier, Fabrice
7
2004
Separating linear forms and rational univariate representations of bivariate systems. Zbl 1328.13041
Bouzidi, Yacine; Lazard, Sylvain; Pouget, Marc; Rouillier, Fabrice
6
2015
Rational univariate representations of bivariate systems and applications. Zbl 1360.68922
Bouzidi, Yacine; Lazard, Sylvain; Pouget, Marc; Rouillier, Fabrice
6
2013
On solving systems of bivariate polynomials. Zbl 1274.65156
Rouillier, Fabrice
5
2010
The first rational Chebyshev knots. Zbl 1202.57007
Koseleff, P.-V.; Pecker, D.; Rouillier, F.
4
2010
Solving the Birkhoff interpolation problem via the critical point method: An experimental study. Zbl 0985.68079
Rouillier, Fabrice; Safey El Din, Mohab; Schost, Éric
4
2001
The implicit structure of ridges of a smooth parametric surface. Zbl 1112.65013
Cazals, Frédéric; Faugère, Jean-Charles; Pouget, Marc; Rouillier, Fabrice
3
2006
Separating linear forms for bivariate systems. Zbl 1360.68923
Bouzidi, Yacine; Lazard, Sylvain; Pouget, Marc; Rouillier, Fabrice
3
2013
Improved algorithm for computing separating linear forms for bivariate systems. Zbl 1325.68267
Bouzidi, Yacine; Lazard, Sylvain; Moroz, Guillaume; Pouget, Marc; Rouillier, Fabrice
3
2014
An environment for symbolic and numeric computation. Zbl 1057.68140
Dos Reis, G.; Mourrain, B.; Trébuchet, Ph.; Rouillier, F.
2
2002
Ridges and umbilics of polynomial parametric surfaces. Zbl 1167.53004
Cazals, Frédéric; Faugère, Jean-Charles; Pouget, Marc; Rouillier, Fabrice
2
2008
On the computation of the topology of plane curves. Zbl 1325.68273
Diatta, Daouda Niang; Rouillier, Fabrice; Roy, Marie-Françoise
2
2014
Using computer algebra to certify the global convergence of a numerical optimization process. Zbl 1134.94314
Gu, Nong; Lazard, Daniel; Rouillier, Fabrice; Xiang, Yong
1
2007
On the sign of a trigonometric expression. Zbl 1345.68289
Koseleff, Pierre-Vincent; Rouillier, Fabrice; Tran, Cuong
1
2015
Real root counting for some robotics problems. Zbl 0900.70069
Rouillier, Fabrice
1
1995
On using triangular decomposition for solving parametric polynomial systems. Zbl 1184.68656
Rouillier, Fabrice; Xiao, Rong
1
2009
Certified non-conservative tests for the structural stability of discrete multidimensional systems. Zbl 1430.93179
Bouzidi, Yacine; Quadrat, Alban; Rouillier, Fabrice
1
2019
Certified non-conservative tests for the structural stability of discrete multidimensional systems. Zbl 1430.93179
Bouzidi, Yacine; Quadrat, Alban; Rouillier, Fabrice
1
2019
Computing real roots of real polynomials …and now for real! Zbl 1365.65142
Kobel, Alexander; Rouillier, Fabrice; Sagraloff, Michael
9
2016
Solving bivariate systems using rational univariate representations. Zbl 1351.65033
Bouzidi, Yacine; Lazard, Sylvain; Moroz, Guillaume; Pouget, Marc; Rouillier, Fabrice; Sagraloff, Michael
9
2016
Character varieties for \(SL(3, \mathbb{C})\): the figure eight knot. Zbl 1353.57007
Falbel, E.; Guilloux, A.; Koseleff, P.-V.; Rouillier, F.; Thistlethwaite, M.
7
2016
Representations of fundamental groups of 3-manifolds into \(\mathrm{PGL}(3,\mathbb C)\): exact computations in low complexity. Zbl 1326.57041
Falbel, E.; Koseleff, P.-V.; Rouillier, F.
15
2015
Separating linear forms and rational univariate representations of bivariate systems. Zbl 1328.13041
Bouzidi, Yacine; Lazard, Sylvain; Pouget, Marc; Rouillier, Fabrice
6
2015
On the sign of a trigonometric expression. Zbl 1345.68289
Koseleff, Pierre-Vincent; Rouillier, Fabrice; Tran, Cuong
1
2015
Improved algorithm for computing separating linear forms for bivariate systems. Zbl 1325.68267
Bouzidi, Yacine; Lazard, Sylvain; Moroz, Guillaume; Pouget, Marc; Rouillier, Fabrice
3
2014
On the computation of the topology of plane curves. Zbl 1325.68273
Diatta, Daouda Niang; Rouillier, Fabrice; Roy, Marie-Françoise
2
2014
Local rigidity for \(\mathrm{PGL}(3,\mathbb C)\)-representations of 3-manifold groups. Zbl 1297.57047
Bergeron, Nicolas; Falbel, Elisha; Guilloux, Antonin; Koseleff, Pierre-Vincent; Rouillier, Fabrice
8
2013
Rational univariate representations of bivariate systems and applications. Zbl 1360.68922
Bouzidi, Yacine; Lazard, Sylvain; Pouget, Marc; Rouillier, Fabrice
6
2013
Separating linear forms for bivariate systems. Zbl 1360.68923
Bouzidi, Yacine; Lazard, Sylvain; Pouget, Marc; Rouillier, Fabrice
3
2013
On the topology of real algebraic plane curves. Zbl 1205.14038
Cheng, Jinsan; Lazard, Sylvain; Peñaranda, Luis; Pouget, Marc; Rouillier, Fabrice
13
2010
On solving systems of bivariate polynomials. Zbl 1274.65156
Rouillier, Fabrice
5
2010
The first rational Chebyshev knots. Zbl 1202.57007
Koseleff, P.-V.; Pecker, D.; Rouillier, F.
4
2010
On the topology of planar algebraic curves. Zbl 1391.14060
Cheng, Jinsan; Lazard, Sylvain; Peñaranda, Luis; Pouget, Marc; Rouillier, Fabrice; Tsigaridas, Elias
10
2009
On using triangular decomposition for solving parametric polynomial systems. Zbl 1184.68656
Rouillier, Fabrice; Xiao, Rong
1
2009
Ridges and umbilics of polynomial parametric surfaces. Zbl 1167.53004
Cazals, Frédéric; Faugère, Jean-Charles; Pouget, Marc; Rouillier, Fabrice
2
2008
Solving parametric polynomial systems. Zbl 1156.14044
Lazard, Daniel; Rouillier, Fabrice
38
2007
Using computer algebra to certify the global convergence of a numerical optimization process. Zbl 1134.94314
Gu, Nong; Lazard, Daniel; Rouillier, Fabrice; Xiang, Yong
1
2007
The implicit structure of ridges of a smooth parametric surface. Zbl 1112.65013
Cazals, Frédéric; Faugère, Jean-Charles; Pouget, Marc; Rouillier, Fabrice
3
2006
Motivations for an arbitrary precision interval arithmetic and the MPFI library. Zbl 1078.65543
Revol, Nathalie; Rouillier, Fabrice
28
2005
The Bernstein-basis and real root isolation. Zbl 1094.14051
Mourrain, Bernard; Rouillier, Fabrice; Roy, Marie-Françoise
13
2005
Efficient isolation of polynomial’s real roots. Zbl 1040.65041
Rouillier, Fabrice; Zimmermann, Paul
62
2004
Using computer algebra tools to classify serial manipulators. Zbl 1202.68489
Corvez, Solen; Rouillier, Fabrice
7
2004
Real solving for positive dimensional systems. Zbl 1046.14031
Aubry, Philippe; Rouillier, Fabrice; Safey El Din, Mohab
20
2002
An environment for symbolic and numeric computation. Zbl 1057.68140
Dos Reis, G.; Mourrain, B.; Trébuchet, Ph.; Rouillier, F.
2
2002
Solving the Birkhoff interpolation problem via the critical point method: An experimental study. Zbl 0985.68079
Rouillier, Fabrice; Safey El Din, Mohab; Schost, Éric
4
2001
Finding at least one point in each connected component of a real algebraic set defined by a single equation. Zbl 1009.14010
Rouillier, F.; Roy, M.-F.; Safey El Din, M.
20
2000
Solving zero-dimensional systems through the rational univariate representation. Zbl 0932.12008
Rouillier, Fabrice
98
1999
Symbolic recipes for real solutions. Zbl 0994.12003
Gonzalez-Vega, Laureano; Rouillier, Fabrice; Roy, Marie-Françoise; Trujillo, Guadalupe
13
1999
Symbolic recipes for polynomial system solving. Zbl 0966.13020
Gonzalez-Vega, Laureano; Rouillier, Fabrice; Roy, Marie-Françoise
9
1999
Real root counting for some robotics problems. Zbl 0900.70069
Rouillier, Fabrice
1
1995
all top 5

Cited by 395 Authors

15 Rouillier, Fabrice
13 Safey El Din, Mohab
13 Schost, Éric
12 Sagraloff, Michael
12 Tsigaridas, Elias P.
9 Cheng, Jinsan
8 Falbel, Elisha
8 Lazard, Sylvain
7 Guilloux, Antonin
7 Koseleff, Pierre-Vincent
7 Pouget, Marc
7 Xia, Bican
6 Lazard, Daniel
6 Mourrain, Bernard
5 Bouzidi, Yacine
5 Díaz-Toca, Gema María
5 Emiris, Ioannis Z.
5 Giusti, Marc
5 Hauenstein, Jonathan D.
5 Jin, Kai
5 Moroz, Guillaume
5 Naldi, Simone
5 Wu, Wenyuan
5 Zickert, Christian K.
4 Bank, Bernd
4 Chen, Changbo
4 Chistov, Alexandre L.
4 Feng, Yong
4 Gao, Xiaoshan
4 Gonzalez-Vega, Laureano
4 Heintz, Joos
4 Henrion, Didier
4 Lichtblau, Daniel A.
4 Matera, Guillermo
4 Mehlhorn, Kurt
4 Niu, Wei
4 Pecker, Daniel
3 Alcazar, Juan Gerardo
3 Boussaada, Islam
3 Burr, Michael A.
3 Caravantes, Jorge
3 Cordero, Alicia
3 Görner, Matthias
3 Jeronimo, Gabriela
3 Kerber, Michael
3 Krandick, Werner
3 Lai, Yisheng
3 Lasserre, Jean-Bernard
3 Laurent, Monique
3 Moreno Maza, Marc
3 Niculescu, Silviu-Iulian
3 Pardo, Luis Miguel
3 Perrucci, Daniel
3 Platt, David John
3 Rostalski, Philipp
3 Roy, Marie-Françoise
3 Salvy, Bruno
3 Sottile, Frank
3 Szántó, Ágnes
3 Torregrosa Sanchez, Juan Ramón
3 Wang, Dongming
3 Wang, Renhong
3 Yap, Chee-Keng
3 Zhi, Lihong
2 Acosta, Miguel
2 Aubry, Philippe
2 Bates, Daniel J.
2 Bergeron, Nicolas
2 Botana, Francisco
2 Cafure, Antonio
2 Collins, George E.
2 de Oliveira Filho, Fernando Mário
2 Deraux, Martin
2 Dutertre, Nicolas
2 Eigenwillig, Arno
2 El Kahoui, M’hammed
2 Faugère, Jean-Charles
2 Fioravanti, Mario A.
2 Fortuna, Elisabetta
2 Galatolo, Stefano
2 Garoufalidis, Stavros
2 Gianni, Patrizia M.
2 Huang, Bo
2 Huang, Chengchao
2 Hubert, Evelyne
2 Imbach, Rémi
2 Kobel, Alexander
2 Lebrun, Jerome
2 Lecerf, Grégoire
2 Li, Zhibin
2 Mora, Teo
2 Mou, Chenqi
2 Nisoli, Isaia
2 Pan, Victor Yakovlevich
2 Parenti, Paola
2 Parker, John R.
2 Peñaranda, Luis Mariano
2 Petitjean, Sylvain
2 Possieri, Corrado
2 Poteaux, Adrien
...and 295 more Authors
all top 5

Cited in 86 Serials

73 Journal of Symbolic Computation
16 Computer Aided Geometric Design
12 Journal of Complexity
11 Theoretical Computer Science
10 Journal of Computational and Applied Mathematics
10 Mathematics in Computer Science
9 Journal of Systems Science and Complexity
6 Experimental Mathematics
6 Journal of Mathematical Sciences (New York)
5 Computers & Mathematics with Applications
5 Geometriae Dedicata
5 Discrete & Computational Geometry
5 Applicable Algebra in Engineering, Communication and Computing
4 Mathematics of Computation
4 Applied Mathematics and Computation
4 Computational Geometry
4 Geometry & Topology
4 Foundations of Computational Mathematics
3 Bulletin of Mathematical Biology
3 Mathematische Zeitschrift
2 Nonlinearity
2 Automatica
2 Computing
2 Journal of Pure and Applied Algebra
2 Mathematics and Computers in Simulation
2 Proceedings of the American Mathematical Society
2 Acta Applicandae Mathematicae
2 Journal of Global Optimization
2 Journal of Knot Theory and its Ramifications
2 Reliable Computing
2 Algebraic & Geometric Topology
2 Journal of Algebra and its Applications
2 Science China. Mathematics
1 Journal of the Franklin Institute
1 Journal of Mathematical Analysis and Applications
1 Chaos, Solitons and Fractals
1 Duke Mathematical Journal
1 Fuzzy Sets and Systems
1 Information Sciences
1 Journal of Differential Equations
1 Journal of Number Theory
1 Kybernetika
1 Michigan Mathematical Journal
1 Programming and Computer Software
1 Transactions of the American Mathematical Society
1 Chinese Annals of Mathematics. Series B
1 Graphs and Combinatorics
1 Algorithmica
1 Journal of Automated Reasoning
1 Journal of the American Mathematical Society
1 Science in China. Series A
1 Multidimensional Systems and Signal Processing
1 Differential Geometry and its Applications
1 MSCS. Mathematical Structures in Computer Science
1 Designs, Codes and Cryptography
1 Numerical Algorithms
1 Aequationes Mathematicae
1 Linear Algebra and its Applications
1 SIAM Journal on Optimization
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
1 Computational Complexity
1 Computational Optimization and Applications
1 Journal de Théorie des Nombres de Bordeaux
1 Economic Theory
1 Finite Fields and their Applications
1 Abstract and Applied Analysis
1 Mechanism and Machine Theory
1 Discrete Dynamics in Nature and Society
1 LMS Journal of Computation and Mathematics
1 Communications in Nonlinear Science and Numerical Simulation
1 International Journal of Applied Mathematics and Computer Science
1 Computational Geosciences
1 Journal of Applied Mathematics
1 SIAM Journal on Applied Dynamical Systems
1 Central European Journal of Mathematics
1 Journal of Intelligent and Fuzzy Systems
1 Journal of Zhejiang University. Science A
1 Discrete and Continuous Dynamical Systems. Series S
1 ACM Communications in Computer Algebra
1 São Paulo Journal of Mathematical Sciences
1 Physical Review A, Third Series
1 Science China. Information Sciences
1 S\(\vec{\text{e}}\)MA Journal
1 ISRN Computational Mathematics
1 European Journal of Mathematics
1 SIAM Journal on Applied Algebra and Geometry
all top 5

Cited in 42 Fields

116 Computer science (68-XX)
107 Numerical analysis (65-XX)
89 Algebraic geometry (14-XX)
75 Commutative algebra (13-XX)
35 Field theory and polynomials (12-XX)
22 Manifolds and cell complexes (57-XX)
21 Real functions (26-XX)
20 Number theory (11-XX)
18 Operations research, mathematical programming (90-XX)
10 Functions of a complex variable (30-XX)
10 Systems theory; control (93-XX)
9 Dynamical systems and ergodic theory (37-XX)
9 Biology and other natural sciences (92-XX)
6 Linear and multilinear algebra; matrix theory (15-XX)
6 Several complex variables and analytic spaces (32-XX)
6 Approximations and expansions (41-XX)
6 Information and communication theory, circuits (94-XX)
5 Combinatorics (05-XX)
5 Topological groups, Lie groups (22-XX)
5 Ordinary differential equations (34-XX)
5 Mechanics of particles and systems (70-XX)
4 History and biography (01-XX)
4 Group theory and generalizations (20-XX)
4 Special functions (33-XX)
4 Convex and discrete geometry (52-XX)
4 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 Partial differential equations (35-XX)
3 Geometry (51-XX)
3 Differential geometry (53-XX)
3 Quantum theory (81-XX)
2 Mathematical logic and foundations (03-XX)
2 Associative rings and algebras (16-XX)
2 Nonassociative rings and algebras (17-XX)
2 Calculus of variations and optimal control; optimization (49-XX)
2 Global analysis, analysis on manifolds (58-XX)
2 Statistics (62-XX)
1 \(K\)-theory (19-XX)
1 Difference and functional equations (39-XX)
1 Sequences, series, summability (40-XX)
1 Functional analysis (46-XX)
1 Algebraic topology (55-XX)
1 Geophysics (86-XX)

Citations by Year