The first rational Chebyshev knots (2009)
Koseleff, Pierre-Vincent, Pecker, Daniel, Rouillier, Fabrice
A Chebyshev knot ${\cal C}(a,b,c,\phi)$ is a knot which has a parametrization of the form $ x(t)=T_a(t); y(t)=T_b(t) ; z(t)= T_c(t + \phi), $ where $a,b,c$ are integers, $T_n(t)$ is the Chebyshev...
On the Topology of Planar Algebraic Curves (2009)
Jinsan Cheng, Sylvain Lazard, Luis Peñar, Marc Pouget, Fabrice Rouillier, Elias Tsigaridas
We introduce a method to compute the topology of planar algebraic curves. The curve may not be in generic position and may have vertical asymptotes. The algebraic tools are rational univariate...
The first rational Chebyshev knots (2009)
Koseleff, Pierre-Vincent, Pecker, Daniel, Rouillier, Fabrice
A Chebyshev knot ${\cal C}(a,b,c,\phi)$ is a knot which has a parametrization of the form $ x(t)=T_a(t); \ y(t)=T_b(t) ; \ z(t)= T_c(t + \phi), $ where $a,b,c$ are integers, $T_n(t)$ is the Chebyshev...
The first rational Chebyshev knots (2009)
Koseleff, Pierre-Vincent, Pecker, Daniel, Rouillier, Fabrice
A Chebyshev knot ${\cal C}(a,b,c,\phi)$ is a knot which has a parametrization of the form $ x(t)=T_a(t); \ y(t)=T_b(t) ; \ z(t)= T_c(t + \phi), $ where $a,b,c$ are integers, $T_n(t)$ is the Chebyshev...
On the topology of planar algebraic curves (2009)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and...
On the topology of planar algebraic curves (2009)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and...
Ridges and Umbilics of Polynomial Parametric Surfaces (2008)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
On The Topology of Planar Algebraic Curves (2008)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We introduce a method to compute the topology of planar algebraic curves. The curve may not be in generic position and may have vertical asymptotes. The algebraic tools are rational univariate...
Ridges and Umbilics of Polynomial Parametric Surfaces (2008)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
On The Topology of Planar Algebraic Curves (2008)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We introduce a method to compute the topology of planar algebraic curves. The curve may not be in generic position and may have vertical asymptotes. The algebraic tools are rational univariate...
On the topology of planar algebraic curves (2008)
Jinsan Cheng, Sylvain Lazard, Luis Peñar, Marc Pouget, Fabrice Rouillier, Elias Tsigaridas
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and...
Simultaneous Inequalities, Generic Case (2007)
Fabrice Rouillier Deliverable, Fabrice Rouillier
The simultaneous inequalities algorithm (see [2]) implements a method for computing all the possible sign conditions realized by a set of polynomials when they are evaluated on the real roots of a...
Guillaume Hanrot, Fabrice Rouillier, Paul Zimmermann
Well-defined semantics for floating-point computations: the MPFR library
Comments on "A blind signal separation method for multiuser communications" (2007)
Gu, Nong, Xiang, Yong, Rouillier, Fabrice, Cao, Zhiqiang
This correspondence first shows that the global convergence analysis of the method proposed in the above paper is incomplete. Then we provide a counter example to show that the sufficient condition...
Solving parametric polynomial systems (2007)
Daniel Lazard, Fabrice Rouillier
We present a new algorithm for solving basic parametric constructible or semi-algebraic
Comments on "A blind signal separation method for multiuser communications" (2007)
Gu, Nong, Xiang, Yong, Rouillier, Fabrice, Cao, Zhiqiang
This correspondence first shows that the global convergence analysis of the method proposed in the above paper is incomplete. Then we provide a counter example to show that the sufficient condition...
On solving the direct kinematics problem for parallel robots (2006)
Faugère, Jean-Charles, Merlet, Jean-Pierre, Rouillier, Fabrice
In this paper, we propose efficient methods for solving the direct kinematics problem (DKP) for parallel manipulators. By solving, we mean computing all the real solutions in a certified way, without...
On solving the direct kinematics problem for parallel robots (2006)
Faugère, Jean-Charles, Merlet, Jean-Pierre, Rouillier, Fabrice
In this paper, we propose efficient methods for solving the direct kinematics problem (DKP) for parallel manipulators. By solving, we mean computing all the real solutions in a certified way, without...
On solving the direct kinematics problem for parallel robots (2006)
Faugère, Jean-Charles, Merlet, Jean-Pierre, Rouillier, Fabrice
In this paper, we propose efficient methods for solving the direct kinematics problem (DKP) for parallel manipulators. By solving, we mean computing all the real solutions in a certified way, without...
On dertermining mixing parameter of CC-CMA algorithm by solving semi-algebraic sets (2006)
Gu, Nong, Lazard, Daniel, Rouillier, Fabrice, Xiang, Yong
The global convergence of a recently proposed constant modulus (CM) and cross-correlation (CC)-based algorithm (CC-CMA) is studied in this paper. We first show the original analysis of global...
On dertermining mixing parameter of CC-CMA algorithm by solving semi-algebraic sets (2006)
Gu, Nong, Lazard, Daniel, Rouillier, Fabrice, Xiang, Yong
The global convergence of a recently proposed constant modulus (CM) and cross-correlation (CC)-based algorithm (CC-CMA) is studied in this paper. We first show the original analysis of global...
On solving the direct kinematics problem for parallel robots (2006)
Faugère, Jean-Charles, Merlet, Jean-Pierre, Rouillier, Fabrice
In this paper, we propose efficient methods for solving the direct kinematics problem (DKP) for parallel manipulators. By solving, we mean computing all the real solutions in a certified way, without...
The implicit structure of ridges of a smooth parametric surface (2006)
Cazals, Frederic, Jean-Charles, Faugere, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve such that at each of its points, the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of {\em...
The implicit structure of ridges of a smooth parametric surface (2006)
Cazals, Frédéric, Jean-Charles, Faugere, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve such that at each of its points, the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of {\em...
The implicit structure of ridges of a smooth parametric surface (2006)
Cazals, Frédéric, Jean-Charles, Faugere, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve such that at each of its points, the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of {\em...
On solving the direct kinematics problem for parallel robots (2006)
Faugère, Jean-Charles, Merlet, Jean-Pierre, Rouillier, Fabrice
In this paper, we propose efficient methods for solving the direct kinematics problem (DKP) for parallel manipulators. By solving, we mean computing all the real solutions in a certified way, without...
On dertermining mixing parameter of CC-CMA algorithm by solving semi-algebraic sets (2006)
Gu, Nong, Lazard, Daniel, Rouillier, Fabrice, Xiang, Yong
The global convergence of a recently proposed constant modulus (CM) and cross-correlation (CC)-based algorithm (CC-CMA) is studied in this paper. We first show the original analysis of global...
Topologically certified approximation of umbilics and ridges on polynomial parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
The implicit structure of ridges of a smooth parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
Topologically certified approximation of umbilics and ridges on polynomial parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
The implicit structure of ridges of a smooth parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
Topologically certified approximation of umbilics and ridges on polynomial parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
The implicit structure of ridges of a smooth parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
The implicit structure of ridges of a smooth parametric surface (2005)
Frédéric Cazals, Jean-charles Faugère, Marc Pouget, Fabrice Rouillier
Given a smooth surface, a blue (red) ridge is a curve such that at each of its points, the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of...
Solving Parametric Polynomial Systems (2004)
Lazard, Daniel, Rouillier, Fabrice
We present a new algorithm for solving basic parametric constructible or semi-algebraic systems like $\mathcal{C} = \{ x \in \Cp_1 ( x ) = 0, \ldots, p_s ( x ) = 0, f_1 ( x ) \neq 0, \ldots, f_l ( x...
Bernstein's basis and real root isolation (2004)
Mourrain, Bernard, Rouillier, Fabrice, Roy, Marie-Françoise
The Bernstein basis is widely used in Computer Aided Design. We explain how, combined with Descartes's rule, the Bernstein basis, provides as well an efficient method for real root isolation, using...
Solving Parametric Polynomial Systems (2004)
Lazard, Daniel, Rouillier, Fabrice
We present a new algorithm for solving basic parametric constructible or semi-algebraic systems like $\mathcal{C} = \{ x \in \Cp_1 ( x ) = 0, \ldots, p_s ( x ) = 0, f_1 ( x ) \neq 0, \ldots, f_l ( x...
Bernstein's basis and real root isolation (2004)
Mourrain, Bernard, Rouillier, Fabrice, Roy, Marie-Françoise
The Bernstein basis is widely used in Computer Aided Design. We explain how, combined with Descartes's rule, the Bernstein basis, provides as well an efficient method for real root isolation, using...
Solving Parametric Polynomial Systems (2004)
Lazard, Daniel, Rouillier, Fabrice
We present a new algorithm for solving basic parametric constructible or semi-algebraic systems like $\mathcal{C} = \{ x \in \Cp_1 ( x ) = 0, \ldots, p_s ( x ) = 0, f_1 ( x ) \neq 0, \ldots, f_l ( x...
Bernstein's basis and real root isolation (2004)
Mourrain, Bernard, Rouillier, Fabrice, Roy, Marie-Françoise
The Bernstein basis is widely used in Computer Aided Design. We explain how, combined with Descartes's rule, the Bernstein basis, provides as well an efficient method for real root isolation, using...
Using computer algebra tools to classify serial cuspidal manipulators (2002)
Corvez, Solen, Rouillier, Fabrice
In this paper we present a classification of 3-revolute-jointed manipulators based on the cuspidal behaviour. It was shown in a previous work that this ability to change posture without meeting a...
Motivations for an arbitrary precision interval arithmetic and the MPFI library. (2002)
Revol, Nathalie, Rouillier, Fabrice
(eng) This paper explains why an arbitrary precision interval arithmetic is needed: to provide accurate results, an interval computation requires small input intervals; this explains why bisection is...
Using computer algebra tools to classify serial cuspidal manipulators (2002)
Corvez, Solen, Rouillier, Fabrice
In this paper we present a classification of 3-revolute-jointed manipulators based on the cuspidal behaviour. It was shown in a previous work that this ability to change posture without meeting a...
Motivations for an arbitrary precision interval arithmetic and the MPFI library (2002)
Revol, Nathalie, Rouillier, Fabrice
This paper justifies why an arbitrary precision interval arithmetic is needed: to provide accurate results, interval computations require small input intervals; this explains why bisection is so...
Motivations for an arbitrary precision interval arithmetic and the MPFI library (2002)
Revol, Nathalie, Rouillier, Fabrice
This paper justifies why an arbitrary precision interval arithmetic is needed: to provide accurate results, interval computations require small input intervals; this explains why bisection is so...
Using computer algebra tools to classify serial cuspidal manipulators (2002)
Corvez, Solen, Rouillier, Fabrice
In this paper we present a classification of 3-revolute-jointed manipulators based on the cuspidal behaviour. It was shown in a previous work that this ability to change posture without meeting a...
Efficient Isolation of a Polynomial Real Roots (2001)
Rouillier, Fabrice, Zimmermann, Paul
This paper gives new results for the isolation of real roots of a univariate polynomial using Descartes' rule of signs, following work of Vincent, Uspensky, Collins and Akritas, Johnson, Krandick....
Efficient Isolation of a Polynomial Real Roots (2001)
Rouillier, Fabrice, Zimmermann, Paul
This paper gives new results for the isolation of real roots of a univariate polynomial using Descartes' rule of signs, following work of Vincent, Uspensky, Collins and Akritas, Johnson, Krandick....
Efficient Isolation of a Polynomial Real Roots (2001)
Rouillier, Fabrice, Zimmermann, Paul
This paper gives new results for the isolation of real roots of a univariate polynomial using Descartes' rule of signs, following work of Vincent, Uspensky, Collins and Akritas, Johnson, Krandick....
Real Solving for Positive Dimensional Systems (2000)
Finding one point on each semi-algebraically connected component of a real algebraic variety, or at least deciding if such a variety is empty or not, is a fundamental problem of computational real...
Real Solving for Positive Dimensional Systems (2000)
Finding one point on each semi-algebraically connected component of a real algebraic variety, or at least deciding if such a variety is empty or not, is a fundamental problem of computational real...
Large Multi-Modular RUR (2000)
Jean-Charles Faugère, Fabrice Rouillier
this report works only in the case of Radical ideals for the moment. The algorithms are implemented as servers that can be called directly from Aldor through a socket stream interface designed by J.C...
Quotient Multiplication Table (2000)
Contents 1 Introduction 2 2 Description 2 3 Example of Use 4 3.1 using the C++ library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Using the PoSSo-Server . ....
Implementation of Infinitesimal Arithmetic (2000)
Many algorithms in Real Algebraic Geometry are using deformations of hypersurfaces or systems of multivariate polynomials (see [1] for example). The deliverable 3.2.1.3.1 provides a rst...
FGLM, Multimodular version (2000)
Jean-Charles Faugere, Fabrice Rouillier
this report, we describe some possible strategies for the computations and we illustrate the report using some basic implementations. We give two version of the algorithm: a probabilistic algorithm...
Testing Emptiness of Real Hypersurfaces, Real Algebraic Sets and Semi-Algebraic Sets (2000)
Fabrice Rouillier, Marie-Françoise Roy, Mohab Safey
Contents 1 Introduction 2 2 Testing the emptiness on a hypersurface dened by a single equation 2 2.1 Theoretically good algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
Solving Zero-dimensional Polynomial Systems through the Rational Univariate Representation (1998)
This paper is devoted to the {\it resolution} of zero-dimensional systems in $K[X_1,\ldots X_n]$, where $K$ is a field of characteristic zero (or strictly positive under some conditions). We give a...
Solving Zero-dimensional Polynomial Systems through the Rational Univariate Representation (1998)
This paper is devoted to the {\it resolution} of zero-dimensional systems in $K[X_1,\ldots X_n]$, where $K$ is a field of characteristic zero (or strictly positive under some conditions). We give a...
Solving Zero-dimensional Polynomial Systems through the Rational Univariate Representation (1998)
This paper is devoted to the {\it resolution} of zero-dimensional systems in $K[X_1,\ldots X_n]$, where $K$ is a field of characteristic zero (or strictly positive under some conditions). We give a...
Real roots counting for some robotics problems (1995)
We propose two algorithms to compute the number of real roots of zerodimensional systems, using effective algebraic methods. To compare their behaviour on practical examples, we apply these methods...
Real roots counting for some robotics problems (1995)
We propose two algorithms to compute the number of real roots of zerodimensional systems, using effective algebraic methods. To compare their behaviour on practical examples, we apply these methods...
Real roots counting for some robotics problems (1995)
We propose two algorithms to compute the number of real roots of zerodimensional systems, using effective algebraic methods. To compare their behaviour on practical examples, we apply these methods...