Bernard Mourrain

We propose new Las Vegas randomized algorithms for the solution of a multivariate generic or sparse polynomial system of equations. The algorithms use...

Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias

We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We...

Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias

We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We...

Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias

We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We...

On the Computation of Matrices of Traces and Radicals of Ideals (2009)

Janovitz-Freireich, Itnuit, Mourrain, Bernard, Ronayi, Lajos, Szanto, Agnes

Let $f_1,...,f_s \in \mathbb{K}[x_1,...,x_m]$ be a system of polynomials generating a zero-dimensional ideal $\I$, where $\mathbb{K}$ is an arbitrary algebraically closed field. We study the...

Subdivision methods for solving polynomial equations (2009)

Mourrain, Bernard, Pavone, Jean-Pascal

This paper presents a new algorithm for solving a system of polynomials, in a domain of $ ^n$. It can be seen as an improvement of the Interval Projected Polyhedron algorithm proposed by Sherbrooke...

Subdivision methods for solving polynomial equations (2009)

Mourrain, Bernard, Pavone, Jean-Pascal

This paper presents a new algorithm for solving a system of polynomials, in a domain of $ ^n$. It can be seen as an improvement of the Interval Projected Polyhedron algorithm proposed by Sherbrooke...

Explicit factors of some iterated resultants and discriminants (2009)

Explicit factors of some iterated resultants and discriminants (2009)

In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree...

A Sparse Flat Extension Theorem for Moment Matrices (2009)

In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree...

A Sparse Flat Extension Theorem for Moment Matrices (2009)

In this note we prove a generalization of the flat extension theorem of Curto and Fialkow for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its...

In this note we prove a generalization of the flat extension theorem of Curto and Fialkow for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its...

Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias

We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We...

Brachat, Jerome, Comon, Pierre, Mourrain, Bernard, Tsigaridas, Elias

We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We...

Continued Fraction Expansion of Real Roots of Polynomial Systems (2009)

Mantzaflaris, Angelos, Mourrain, Bernard, Tsigaridas, Elias P.

We present a new algorithm for isolating the real roots of a system of multivariate polynomials, given in the monomial basis. It is inspired by existing subdivision methods in the Bernstein basis; it...

Continued Fraction Expansion of Real Roots of Polynomial Systems (2009)

Mantzaflaris, Angelos, Mourrain, Bernard, Tsigaridas, Elias P.

We present a new algorithm for isolating the real roots of a system of multivariate polynomials, given in the monomial basis. It is inspired by existing subdivision methods in the Bernstein basis; it...

The DMM bound: multivariate (aggregate) separation bounds (2009)

Emiris, Ioannis Z., Mourrain, Bernard, Tsigaridas, Elias

In this paper we present aggregate separation bounds for polynomials systems. We call the bounds Davenport-Mahler-Mignotte (\dmm), and we prove that in most of the cases are close to optimal. The...

The DMM bound: multivariate (aggregate) separation bounds (2009)

Emiris, Ioannis Z., Mourrain, Bernard, Tsigaridas, Elias P.

In this paper we present aggregate separation bounds for polynomials systems. We call the bounds Davenport-Mahler-Mignotte (\dmm), and we prove that in most of the cases are close to optimal. The...

The DMM bound: multivariate (aggregate) separation bounds (2009)

Emiris, Ioannis Z., Mourrain, Bernard, Tsigaridas, Elias P.

In this paper we present aggregate separation bounds for polynomials systems. We call the bounds Davenport-Mahler-Mignotte (\dmm), and we prove that in most of the cases are close to optimal. The...

Curve/surface intersection problem by means of matrix representations (2009)

Luu Ba, Thang, Busé, Laurent, Mourrain, Bernard

In this paper, we introduce matrix representations of algebraic curves and surfaces for Computer Aided Geometric Design (CAGD). The idea of using matrix representations in CAGD is quite old. The...

Curve/surface intersection problem by means of matrix representations (2009)

Luu Ba, Thang, Busé, Laurent, Mourrain, Bernard

In this paper, we introduce matrix representations of algebraic curves and surfaces for Computer Aided Geometric Design (CAGD). The idea of using matrix representations in CAGD is quite old. The...

The Hilbert scheme of points and its link with border basis (2009)

Alonso, Mariemi, Brachat, Jérome, Mourrain, Bernard

In this paper, we give new explicit representations of the Hilbert scheme of $\mu$ points in $\PP^{r}$ as a projective subvariety of a Grassmanniann variety. This new explicit description of the...

Isotopic triangulation of a real algebraic surface (2009)

Alberti, Lionel, Mourrain, Bernard, Técourt, Jean-Pierre

We present a new algorithm for computing the topology of a real algebraic surface $S$ in a ball $B$, even in singular cases. We use algorithms for 2D and 3D algebraic curves and show how one can...

Isotopic triangulation of a real algebraic surface (2009)

Alberti, Lionel, Mourrain, Bernard, Técourt, Jean-Pierre

We present a new algorithm for computing the topology of a real algebraic surface $S$ in a ball $B$, even in singular cases. We use algorithms for 2D and 3D algebraic curves and show how one can...

A Sparse Flat Extension Theorem for Moment Matrices (2008)

A Sparse Flat Extension Theorem for Moment Matrices (2008)

In this note we prove a generalization of the flat extension theorem of Curto and Fialkow for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its...

A Sparse Flat Extension Theorem for Moment Matrices (2008)

In this note we prove a generalization of the flat extension theorem of Curto and Fialkow for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its...

Stable normal forms for polynomial system solving (2008)

In this note we prove a generalization of the flat extension theorem of Curto and Fialkow for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its...

Moment matrices, trace matrices and the radical of ideals (2008)

This paper describes and analyzes a method for computing border bases of a zero-dimensional ideal $I$. The criterion used in the computation involves specific commutation polynomials and leads to an...

Janovitz-Freireich, Itnuit, Szanto, Agnes, Mourrain, Bernard, Ronyai, Lajos

Let $f_1,...,f_s \in \mathbb{K}[x_1,...,x_m]$ be a system of polynomials generating a zero-dimensional ideal $\I$, where $\mathbb{K}$ is an arbitrary algebraically closed field. Assume that the...

Computing Approximate Radicals using (2008)

Itnuit Janovitz-freireich, Bernard Mourrain, Lajos Rónyai, Ágnes Szántó

Consider I ⊂ C[x1,..., xm], a zero dimensional complete intersection ideal, with I = (f1,..., fm). Assume that I has clusters of roots, each cluster of radius at most ε in the ∞-norm. We compute...

to appear inSIAM Journal on Matrix Analysis and Applications. SYMMETRIC TENSORS AND SYMMETRIC TENSOR RANK (2008)

Pierre Comon, Gene Golub, Lek-heng Lim, Bernard Mourrain

Abstract. A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric...

Shape Interrogation (2008)

Stefanie Hahmann, Er Belyaev, Laurent Busé, Gershon Elber, Bernard Mourrain, Christian Rössl

Summary. Shape interrogation methods are of increasing interest in geometric modeling as well as in computer graphics. Originating 20 years ago from CAD/CAM applications where ”class A ” surfaces...

ACS Algorithms for Complex Shapes with Certified Numerics and Topology (2008)

Dimitrios I, Ioannis Z. Emiris, Bernard Mourrain, Elias P. Tsigaridas, Elias P. Tsigaridas

Experimental implementation of more operations on algebraic numbers, possibly with the addition of numeric filters, and of robust operations on small polynomial systems

On the Computation of the Topology of a Non-Reduced Implicit Space Curve (2008)

Diatta, Daouda Niang, Mourrain, Bernard, Ruatta, Olivier

An algorithm is presented for the computation of the topology of a non-reduced space curve defined as the intersection of two implicit algebraic surfaces. It computes a Piecewise Linear Structure...

Symmetric tensors and symmetric tensor rank (2008)

Comon, Pierre, Golub, Gene, Lim, Lek-Heng, Mourrain, Bernard

A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a sum of symmetric outer...

On Circular Cylinders through Four or Five Points in Space (2008)

Olivier Devillers, Bernard Mourrain, Franco P. Preparata, Philippe Trebuchet

this paper is the analysis of circular cylinders through sets of points in three dimensions. This investigation has a number of motivations. Clearly, if a cylinder of radius R and direction t passes...

On the Computation of the Topology of a Non-Reduced Implicit Space Curve (2008)

On the Computation of the Topology of a Non-Reduced Implicit Space Curve (2008)

An algorithm is presented for the computation of the topology of a non-reduced space curve defined as the intersection of two implicit algebraic surfaces. It computes a Piecewise Linear Structure...

Symmetric tensors and symmetric tensor rank (2008)

An algorithm is presented for the computation of the topology of a non-reduced space curve defined as the intersection of two implicit algebraic surfaces. It computes a Piecewise Linear Structure...

Comon, Pierre, Golub, Gene, Lim, Lek-Heng, Mourrain, Bernard

A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer...

Symmetric tensors and symmetric tensor rank (2008)

Comon, Pierre, Golub, Gene, Lim, Lek-Heng, Mourrain, Bernard

A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer...

A polynomial based approach to extract the maxima of an antipodally symmetric spherical function and its application to extract fiber directions from the Orientation Distribution Function in Diffusion MRI (2008)

Ghosh, Aurorata, Tsigaridas, Elias, Descoteaux, Maxime, Comon, Pierre, Mourrain, Bernard, Deriche, Rachid

In this paper we extract the geometric characteristics from an antipodally symmetric spherical function (ASSF), which can be de- scribed equivalently in the spherical harmonic (SH) basis, in the...

A polynomial based approach to extract the maxima of an antipodally symmetric spherical function and its application to extract fiber directions from the Orientation Distribution Function in Diffusion MRI (2008)

Ghosh, Aurorata, Tsigaridas, Elias, Descoteaux, Maxime, Comon, Pierre, Mourrain, Bernard, Deriche, Rachid

In this paper we extract the geometric characteristics from an antipodally symmetric spherical function (ASSF), which can be de- scribed equivalently in the spherical harmonic (SH) basis, in the...

Experimental evaluation and cross-benchmarking of univariate real solvers (2008)

Emiris, Ioannis Z., Hemmer, Michael, Karavelas, Menelaos, Mourrain, Bernard, Tsigaridas, Elias P., Zafeirakopoulos, Zafeirakis

Real solving of univariate polynomials is a fundamental problem with several important applications. This paper focuses on the efficient and generic black-box implementations of state-of-the-art...

Experimental evaluation and cross-benchmarking of univariate real solvers (2008)

Emiris, Ioannis Z., Hemmer, Michael, Karavelas, Menelaos, Mourrain, Bernard, Tsigaridas, Elias P., Zafeirakopoulos, Zafeirakis

Real solving of univariate polynomials is a fundamental problem with several important applications. This paper focuses on the efficient and generic black-box implementations of state-of-the-art...

Stable normal forms for polynomial system solving (2008)

Stable normal forms for polynomial system solving (2008)

This paper describes and analyzes a method for computing border bases of a zero-dimensional ideal $I$. The criterion used in the computation involves specific commutation polynomials and leads to an...

Topology and arrangement computation of semi-algebraic planar curves (2008)

This paper describes and analyzes a method for computing border bases of a zero-dimensional ideal $I$. The criterion used in the computation involves specific commutation polynomials and leads to an...

Alberti, Lionel, Mourrain, Bernard, Wintz, Julien

We describe a new subdivision method to efficiently compute the topology and the arrangement of implicit planar curves. We emphasize that the output topology and arrangement are guaranteed to be...

Moment matrices, trace matrices and the radical of ideals (2008)

Janovitz-Freireich, Inuit, Szanto, Agnes, Mourrain, Bernard, Ronyai, Lajos

Let $f_1,\ldots,f_s \in \mathbb{K}[x_1,\ldots,x_m]$ be a system of polynomials generating a zero-dimensional ideal $\I$, where $\mathbb{K}$ is an arbitrary algebraically closed field. Assume that the...

Topology and arrangement computation of semi-algebraic planar curves (2008)

Alberti, Lionel, Mourrain, Bernard, Wintz, Julien

We describe a new subdivision method to efficiently compute the topology and the arrangement of implicit planar curves. We emphasize that the output topology and arrangement are guaranteed to be...

Moment matrices, trace matrices and the radical of ideals (2008)

Janovitz-Freireich, Inuit, Szanto, Agnes, Mourrain, Bernard, Ronyai, Lajos

Let $f_1,\ldots,f_s \in \mathbb{K}[x_1,\ldots,x_m]$ be a system of polynomials generating a zero-dimensional ideal $\I$, where $\mathbb{K}$ is an arbitrary algebraically closed field. Assume that the...

On the Computation of Matrices of Traces and Radicals of Ideals (2008)

Janovitz-Freireich, Itnuit, Mourrain, Bernard, Ronayi, Lajos, Szanto, Agnes

Let $f_1,\ldots,f_s \in \mathbb{K}[x_1,\ldots,x_m]$ be a system of polynomials generating a zero-dimensional ideal $\I$, where $\mathbb{K}$ is an arbitrary algebraically closed field. We study the...

On the Computation of Matrices of Traces and Radicals of Ideals (2008)

Janovitz-Freireich, Itnuit, Mourrain, Bernard, Ronayi, Lajos, Szanto, Agnes

Let $f_1,\ldots,f_s \in \mathbb{K}[x_1,\ldots,x_m]$ be a system of polynomials generating a zero-dimensional ideal $\I$, where $\mathbb{K}$ is an arbitrary algebraically closed field. We study the...

Experimental evaluation and cross-benchmarking of univariate real solvers (2008)

Emiris, Ioannis Z., Hemmer, Michael, Karavelas, Menelaos, Mourrain, Bernard, Tsigaridas, Elias P., Zafeirakopoulos, Zafeirakis

Real solving of univariate polynomials is a fundamental problem with several important applications. This paper focuses on the efficient and generic black-box implementations of state-of-the-art...

Experimental evaluation and cross-benchmarking of univariate real solvers (2008)

Emiris, Ioannis Z., Hemmer, Michael, Karavelas, Menelaos, Mourrain, Bernard, Tsigaridas, Elias P., Zafeirakopoulos, Zafeirakis

Real solving of univariate polynomials is a fundamental problem with several important applications. This paper focuses on the efficient and generic black-box implementations of state-of-the-art...

Shape Interrogation (2008)

Hahmann, Stefanie, Belyaev, Alexander, Buse, Laurent, Elber, Gershon, Mourrain, Bernard, Rössl, Christian

On the isotopic meshing of an algebraic implicit surface (2008)

On the isotopic meshing of an algebraic implicit surface (2008)

We present a new and complete algorithm for computing the topology of an algebraic surface given by a squarefree polynomial in Q[X, Y, Z]. Our algorithm involves only subresultant computations and...

We present a new and complete algorithm for computing the topology of an algebraic surface given by a squarefree polynomial in Q[X, Y, Z]. Our algorithm involves only subresultant computations and...

Contents (2007)

Generalized resultants over unirational algebraic (2007)

Laurent Bus, Mohamed Elkadi, Bernard Mourrain

varieties

Linear Algebra for Polynomial System Solving (2007)

Bernard Mourrain Composite, Bernard Mourrain

Contents 1 3.4.2.3.2 Quotient approximation 2 2 3.4.2.5.1 Iterative methods 2 3 3.4.2.7.1 Structured matrices 3 4 3.4.2.8.1 Overconstrained systems 4 5 Workplan 5 1 We report here on dierent methods...

Quelques Points D'intrt : (2007)

Unication Des Dioerentes, Craig Huneke, Ernst Kunz, Joseph Lipman, Marc Chardin, Centre De Math#matiques, ...

) 22 The origins of the theory of residues are in Cauchy's works and especially for multiresidues in Poincar#'s. A satisfactory theory based on duality was given by J. Leray [L] and the...

Article Submitted to Journal of Symbolic Computation (2007)

Bernard Mourrain, Olivier Ruatta

Relation between roots and coecients, interpolation and application to system solving

Solution of a polynomial system of equations via the eigenvector computation (2007)

We propose new techniques and algorithms for the solution of a polynomial system of equations by matrix methods. For such a system, we seek its specied root, at which a xed polynomial takes its...

INRIA, SAGA, (2007)

For a system of polynomial equations, we seek its speci-ed root, maximizing or minimizing the absolute value of a xed polynomial over all roots of the system. The latter requirement to a root,...

y (2007)

Closed-form blind channel identification with MSK inputs (2007)

of a specied root of a polynomial system of equations using eigenvectors

Pierre Comon, Olivier Grellier, Bernard Mourrain

Blind equalization of non minimumphase FIR channels requires prior identification, for stability reasons. We present a novel algorithm able to identify a channel in presence of an unknown MSK...

between (2007)

Olivier Faugeras, Bernard Mourrain

the geometry and algebra of the point and line correspondences

, Patrick Sol'e (2007)

Alexis Bonnecaze, Bernard Mourrain

Jacobi polynomials were introduced by Ozeki in analogy with Jacobi forms of lattices. They are useful for coset weight enumeration, and weight enumeration of children. We determine them in most...

predicates on circle arcs (2007)

Apport De Recherche, Olivier Devillers Alex, Olivier Devillers, Ra Fronville, Bernard Mourrain, Monique Teillaud, ...

The purpose of this paper is to present a new method to design exact geometric predicates in algorithms dealing with curved objects such as circular arcs. We focus on the comparison of the abscissae...

et calcul symbolique (2007)

Apport De Recherche, Mihail N. Vrahatis, Ioannis Z. Emiris, Ioannis Z. Emiris, Bernard Mourrain, Bernard Mourrain, ...

In this report, we implement the concept of topological degree to isolate and compute all zeros of systems of nonlinear algebraic equations when the only computable information required is the...

ISSN (2007)

Alexandra Fronville, Olivier Devillers, Olivier Devillers, Ra Fronville, Bernard Mourrain, Bernard Mourrain, ...

apport de recherche

About the rational map associated to a parallel robot (2007)

Bernard Mourrain, Bernard Mourrain, Projet Safir

programmation et génie logiciel apport de recherche 1994 About the rational map associated to a parallel robot

ISSN (2007)

Bernard Mourrain, Bernard Mourrain, Victor Y. Pan, Victor Y. Pan

apport de recherche

et calcul symbolique (2007)

Ioannis Z. Emiris, Ioannis Z. Emiris, Bernard Mourrain, Bernard Mourrain, Thème Génie Logiciel, Projet Safir

apport de recherche Polynomial system solving: the case of a six-atom molecule

Explicit factors of some iterated resultants and discriminants (2007)

Explicit factors of some iterated resultants and discriminants (2007)

In this paper, we analyze the result of applying iterative univariate resultant constructions to multivariate polynomials. We consider the input polynomials as generic polynomials of a given degree...

Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification (2007)

In this paper, we analyze the result of applying iterative univariate resultant constructions to multivariate polynomials. We consider the input polynomials as generic polynomials of a given degree...

Tu, Changhe, Wang, Wenping, Mourrain, Bernard, Wang, Jiaye

We present an efficient method for classifying the morphology of the intersection curve of two quadrics (QSIC) in PR3, 3D real projective space; here, the term morphology is used in a broad sense to...

Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification (2007)

Tu, Changhe, Wang, Wenping, Mourrain, Bernard, Wang, Jiaye

We present an efficient method for classifying the morphology of the intersection curve of two quadrics (QSIC) in PR3, 3D real projective space; here, the term morphology is used in a broad sense to...

Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification (2007)

Tu, Changhe, Wang, Wenping, Mourrain, Bernard, Wang, Jiaye

We present an efficient method for classifying the morphology of the intersection curve of two quadrics (QSIC) in PR3, 3D real projective space; here, the term morphology is used in a broad sense to...

Subdivision Methods for the Topology of 2d and 3d Implicit Curves (2007)

Liang, Chen, Mourrain, Bernard, Pavone, Jean-Pascal

In this paper, we describe a subdivision method for handling algebraic implicit curves in 2d and 3d. We use the representation of polynomials in the Bernstein basis associated with a given box, to...

Subdivision Methods for the Topology of 2d and 3d Implicit Curves (2007)

Liang, Chen, Mourrain, Bernard, Pavone, Jean-Pascal

In this paper, we describe a subdivision method for handling algebraic implicit curves in 2d and 3d. We use the representation of polynomials in the Bernstein basis associated with a given box, to...

Pythagore's Dilemma, Symbolic-Numeric Computation, and the Border Basis Method (2007)

Pythagore's Dilemma, Symbolic-Numeric Computation, and the Border Basis Method (2007)

In this tutorial paper, we first discuss the motivation of doing symbolic-numeric computation, with the aim of developing efficient and certified polynomial solvers. We give a quick overview of...

Regularity criteria for the topology of algebraic curves and surfaces (2007)

In this tutorial paper, we first discuss the motivation of doing symbolic-numeric computation, with the aim of developing efficient and certified polynomial solvers. We give a quick overview of...

Regularity criteria for the topology of algebraic curves and surfaces (2007)

In this paper, we consider the problem of analysing the shape of an object defined by polynomial equations in a domain. We describe regularity criteria which allow us to determine the topology of the...

Visualisation of implicit algebraic curves (2007)

In this paper, we consider the problem of analysing the shape of an object defined by polynomial equations in a domain. We describe regularity criteria which allow us to determine the topology of the...

Visualisation of implicit algebraic curves (2007)

We describe a new algorithm for the visualisation of implicit algebraic curves, which isolates the singular points, compute the topological degree around these points in order to check that the...

SYNAPS: A library for dedicated applications in symbolic numeric computing, (2007)

We describe a new algorithm for the visualisation of implicit algebraic curves, which isolates the singular points, compute the topological degree around these points in order to check that the...

Mourrain, Bernard, Pavone, Jean-Pascal, Trebuchet, Philippe, Tsigaridas, Elias P., Wintz, Julien

We present an overview of the open source library synaps. We describe some of the representative algorithms of the library and illustrate them on some explicit computations, such as solving...

SYNAPS: A library for dedicated applications in symbolic numeric computing, (2007)

Mourrain, Bernard, Pavone, Jean-Pascal, Trebuchet, Philippe, Tsigaridas, Elias P., Wintz, Julien

We present an overview of the open source library synaps. We describe some of the representative algorithms of the library and illustrate them on some explicit computations, such as solving...

A subdivision arrangement algorithm for semi-algebraic curves: an overview (2007)

Wintz, Julien, Mourrain, Bernard

We overview a new method for computing the arrangement of semi-algebraic curves. A subdivision approach is used to compute the topology of the algebraic objects and to segment the boundary of regions...

A subdivision arrangement algorithm for semi-algebraic curves: an overview (2007)

Wintz, Julien, Mourrain, Bernard

We overview a new method for computing the arrangement of semi-algebraic curves. A subdivision approach is used to compute the topology of the algebraic objects and to segment the boundary of regions...

Shape Interrogation (2007)

Hahmann, Stefanie, Belyaev, Alexander, Busé, Laurent, Elber, Gershon, Mourrain, Bernard, Roessl, C.

Shape interrogation methods are of increasing interest in geometric modeling as well as in computer graphics. Originating 20 years ago from CAD/CAM applications where "class A" surfaces are required...

Shape Interrogation (2007)

Hahmann, Stefanie, Belyaev, Alexander, Busé, Laurent, Elber, Gershon, Mourrain, Bernard, Roessl, C.

Shape interrogation methods are of increasing interest in geometric modeling as well as in computer graphics. Originating 20 years ago from CAD/CAM applications where "class A" surfaces are required...

Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification (2007)

Tu, Changhe, Wang, Wenping, Mourrain, Bernard, Wang, Jiaye

We present an efficient method for classifying the morphology of the intersection curve of two quadrics (QSIC) in PR3, 3D real projective space; here, the term morphology is used in a broad sense to...

Toeplitz and Toeplitz-block-Toeplitz matrices and their correlation with syzygies of polynomials. (2007)

Khalil, Houssam, Mourrain, Bernard, Schatzman, Michelle

In this paper, we re-investigate the resolution of Toeplitz systems $T\, u =g$, from a new point of view, by correlating the solution of such problems with syzygies of polynomials or moving lines. We...

Toeplitz and Toeplitz-block-Toeplitz matrices and their correlation with syzygies of polynomials. (2007)

Khalil, Houssam, Mourrain, Bernard, Schatzman, Michelle

In this paper, we re-investigate the resolution of Toeplitz systems $T\, u =g$, from a new point of view, by correlating the solution of such problems with syzygies of polynomials or moving lines. We...

Effective Computational Geometry for Curves and Surfaces (2007)

Jean-daniel Boissonnat, David Cohen-steiner, Bernard Mourrain, Günter Rote, Gert Vegter

Meshing is the process of computing, for a given surface, a representation consisting of pieces of simple surface patches, like triangles. This survey discusses all currently known surface (and...

Effective Computational Geometry for Curves and Surfaces (2007)

Jean-daniel Boissonnat, David Cohen-steiner, Bernard Mourrain, Günter Rote, Gert Vegter

Meshing is the process of computing, for a given surface, a representation consisting of pieces of simple surface patches, like triangles. This survey discusses all currently known surface (and...

Algebraic Issues in Computational Geometry (2007)

Mourrain, Bernard, Pion, Sylvain, Schmitt, Susanne, Técourt, Jean-Pierre, Tsigaridas, Elias, Wolpert, Nicola

Explicit factors of some iterated resultants and discriminants (2006)

Genericity and Rank Deficiency of High Order Symmetric Tensors (2006)

In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree...

Comon, Pierre, Mourrain, Bernard, Lim, Lek-Heng, Golub, Gene

Blind Identification of Under-Determined Mixtures (UDM) is involved in numerous applications, including Multi-Way factor Analysis (MWA) and Signal Processing. In the latter case, the use of...

Real Algebraic Numbers: Complexity Analysis and Experimentations (2006)

Emiris, Ioannis Z., Mourrain, Bernard, Tsigaridas, Elias P.

We present algorithmic, complexity and implementation results concerning real root isolation of a polynomial of degree $d$, with integer coefficients of bit size $\le\tau$, using Sturm (-Habicht)...

Des formes aux formules, ou comment les singularités nous aident à mieux calculer (2006)

Des formes aux formules, ou comment les singularités nous aident à mieux calculer (2006)

Lorsqu'on roule tranquillement sur l'autoroute, le principal problème est de ne pas rater la bonne sortie. Avant de traverser un carrefour, c'est de pouvoir vérifier que le croisement n'est pas...

Real Algebraic Numbers: Complexity Analysis and Experimentations (2006)

Lorsqu'on roule tranquillement sur l'autoroute, le principal problème est de ne pas rater la bonne sortie. Avant de traverser un carrefour, c'est de pouvoir vérifier que le croisement n'est pas...

Emiris, Ioannis Z., Mourrain, Bernard, Tsigaridas, Elias P.

We present algorithmic, complexity and implementation results concerning real root isolation of a polynomial of degree $d$, with integer coefficients of bit size $\le\tau$, using Sturm (-Habicht)...

Isotopic meshing of a real algebraic surface (2006)

Mourrain, Bernard, Técourt, Jean-Pierre

We present a new algorithm for computing the topology of a real algebraic surface $S$, even in singular cases. We use previous algorithms for 2D and 3D algebraic curves and show how properties of the...

Real Algebraic Numbers: Complexity Analysis and Experimentations (2006)

Emiris, Ioannis Z., Mourrain, Bernard, Tsigaridas, Elias P.

We present algorithmic, complexity and implementation results concerning real root isolation of a polynomial of degree $d$, with integer coefficients of bit size $\le\tau$, using Sturm (-Habicht)...

Isotopic meshing of a real algebraic surface (2006)

Mourrain, Bernard, Técourt, Jean-Pierre

We present a new algorithm for computing the topology of a real algebraic surface $S$, even in singular cases. We use previous algorithms for 2D and 3D algebraic curves and show how properties of the...

Symmetric tensors and symmetric tensor rank (2006)

Pierre Comon, Gene Golub, Lek-heng Lim, Bernard Mourrain

Abstract. A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric...

Tsigaridas. Real Algebraic Numbers: Complexity Analysis and Experimentation (2006)

Ioannis Z. Emiris, Bernard Mourrain, Elias P. Tsigaridas

Abstract. We present algorithmic, complexity and implementation results concerning real root isolation of a polynomial of degree d, with integer coefficients of bit size ≤ τ, using Sturm...

• “La Caixa ” bank Participants Name Affiliation Country e-mail (2006)

Martín Sombra, Ron Goldman, Laureano González-vega, Bernard Mourrain, ...

Algebraic Geometry and Geometric Modeling both deal with curves and surfaces generated by polynomial equations. AG investigates the theoretical properties of polynomial curves and surfaces; GM uses...

Subdivision methods for solving polynomial equations (2005)

Mourrain, Bernard, Pavone, Jean-Pascal

This paper presents a new algorithm for solving a system of polynomials, in a domain of $ ^n$. It can be seen as an improvement of the Interval Projected Polyhedron algorithm proposed by Sherbrooke...

Isotopic meshing of a real algebraic surface (2005)

Mourrain, Bernard, Técourt, Jean-Pierre

We present a new algorithm for computing the topology of a real algebraic surface $S$, even in singular cases. We use previous algorithms for 2D and 3D algebraic curves and show how properties of the...

Generalised normal forms and polynomial system solving (2005)

Resultant-based methods for plane curves intersection problems (2005)

This report describes a new method for computing the normal form of a polynomial modulo a zero-dimensional ideal $I$. We give a detailed description of the algorithm, a proof of its correctness, and...

Busé, Laurent, Khalil, Houssam, Mourrain, Bernard

We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special attention to the case of two bivariate polynomials...

Resultant-based methods for plane curves intersection problems (2005)

Busé, Laurent, Khalil, Houssam, Mourrain, Bernard

We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special attention to the case of two bivariate polynomials...

Generalised normal forms and polynomial system solving (2005)

Resultant-based methods for plane curves intersection problems (2005)

This report describes a new method for computing the normal form of a polynomial modulo a zero-dimensional ideal $I$. We give a detailed description of the algorithm, a proof of its correctness, and...

Busé, Laurent, Khalil, Houssam, Mourrain, Bernard

We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special attention to the case of two bivariate polynomials...

The Offset to an Algebraic Curve and an Application to Conics (2005)

Anton, François, Emiris, Ioannis Z., Mourrain, Bernard, Teillaud, Monique

Curve offsets are important objects in computer-aided design. We study the algebraic properties of the offset to an algebraic curve, thus obtaining a general formula for its degree. This is applied...

On the Computation of an Arrangement of Quadrics in 3D (2005)

Mourrain, Bernard, Técourt, Jean-Pierre, Teillaud, Monique

In this paper, we study a sweeping algorithm for computing the arrangement of a set of quadrics in $\RR^{3}$. We define a ``trapezoidal'' decomposition in the sweeping plane, and we study the...

The Offset to an Algebraic Curve and an Application to Conics (2005)

Anton, François, Emiris, Ioannis Z., Mourrain, Bernard, Teillaud, Monique

Curve offsets are important objects in computer-aided design. We study the algebraic properties of the offset to an algebraic curve, thus obtaining a general formula for its degree. This is applied...

On the Computation of an Arrangement of Quadrics in 3D (2005)

Mourrain, Bernard, Técourt, Jean-Pierre, Teillaud, Monique

In this paper, we study a sweeping algorithm for computing the arrangement of a set of quadrics in $\RR^{3}$. We define a ``trapezoidal'' decomposition in the sweeping plane, and we study the...

Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification (2005)

Changhe Tu, Wenping Wang, Bernard Mourrain, Jiaye Wang

this paper -- we enumerate all 35 di#erent morphologies of QSIC, and characterize each of these morphologies using a signature sequence that can exactly be computed using rational arithmetic. The...

Resultant-based method for plane curves intersection problems (2005)

Laurent Busé, Houssam Khalil, Bernard Mourrain

problems

Abstract (2005)

Bernard Mourrain, Equipe Calfor

solving

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...

Computing the topology of three-dimensional algebraic curves (2004)

Gatelier, Grégory, Labrouzy, Abder, Mourrain, Bernard, Técourt, Jean-Pierre

In this report, we present a new method for computing the topology of curves defined as the intersection of two implicit surfaces. The main ingredients are projection tools, based on resultant...

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...

Computing the topology of three-dimensional algebraic curves (2004)

Gatelier, Grégory, Labrouzy, Abder, Mourrain, Bernard, Técourt, Jean-Pierre

In this report, we present a new method for computing the topology of curves defined as the intersection of two implicit surfaces. The main ingredients are projection tools, based on resultant...

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...

Computing the Number of Real Roots of Polynomials through Neural Networks (2004)

Bernard Mourrain, Nicos G. Pavlidis, Dimitris K. Tasoulis, Michael N. Vrahatis, Projet Galaad, Inria Sophia Antipolis, ...

Introduction Numerous problems in robotics, computer vision, computational geometry and signal processing, involve the solution of polynomial systems of equations. Recently, Artificial Feedforward...

Using projection operators in computer aided geometric design (2003)

Using projection operators in computer aided geometric design (2003)

We give an overview of resultant theory and some of its applications in computer aided geometric design. First, we mention different formulations of resultants, including the projective resultant,...

Using projection operators in computer aided geometric design (2003)

We give an overview of resultant theory and some of its applications in computer aided geometric design. First, we mention different formulations of resultants, including the projective resultant,...

On circular cylinders by four or five points in space (2003)

We give an overview of resultant theory and some of its applications in computer aided geometric design. First, we mention different formulations of resultants, including the projective resultant,...

Olivier Devillers, Bernard Mourrain, Franco P. Preparata, Philippe Trebuchet

Using projection operators in Computer Aided Geometric Design (2003)

Laurent Buse, Mohamed Elkadi, Bernard Mourrain

We give an overview of resultant theory and some of its applications in computer aided geometric design. First, we mention di#erent formulations of resultants, including the projective resultant, the...

Circular Cylinders by Four or Five Points in Space (2002)

Devillers, Olivier, Mourrain, Bernard, Preparata, Franco, Trebuchet, Philippe

We are interested in computing effectively cylinders through 5 points, and in other problems involved in metrology. In particular, we consider the cylinders through 4 points with a fix radius and...

Circular Cylinders by Four or Five Points in Space (2002)

Devillers, Olivier, Mourrain, Bernard, Preparata, Franco, Trebuchet, Philippe

We are interested in computing effectively cylinders through 5 points, and in other problems involved in metrology. In particular, we consider the cylinders through 4 points with a fix radius and...

Circular Cylinders by Four or Five Points in Space (2002)

Devillers, Olivier, Mourrain, Bernard, Preparata, Franco, Trebuchet, Philippe

We are interested in computing effectively cylinders through 5 points, and in other problems involved in metrology. In particular, we consider the cylinders through 4 points with a fix radius and...

Algebraic methods and arithmetic filtering for exact predicates on circle arcs (2002)

Devillers, Olivier, Fronville, Alexandra, Mourrain, Bernard, Teillaud, Monique

The purpose of this paper is to present a new method to design exact geometric predicates in algorithms dealing with curved objects such as circular arcs. We focus on the comparison of the abscissae...

Algebraic methods and arithmetic filtering for exact predicates on circle arcs (2002)

Devillers, Olivier, Fronville, Alexandra, Mourrain, Bernard, Teillaud, Monique

The purpose of this paper is to present a new method to design exact geometric predicates in algorithms dealing with curved objects such as circular arcs. We focus on the comparison of the abscissae...

Analytical blind channel identification (2002)

Olivier Grellier, Pierre Comon, Senior Member, Bernard Mourrain

Abstract—In this paper, a novel analytical blind single-input single-output (SISO) identification algorithm is presented, based on the noncircular second-order statistics of the output. It is shown...

On circular Cylinders by Four or Five Points in Space (2001)

Devillers, Olivier, Mourrain, Bernard, Preparata, Franco P., Trebuchet, Philippe

We are interested in computing effectively cylinders through 5 points, and in other problems involved in metrology. In particular, we consider the cylinders through 4 points with a fix radius and...

Isolation of Real Roots and Computation of the Topological Degree (2001)

Mourrain, Bernard, Vrahatis, Michael N., Yakoubsohn, Jean-Claude

In this work, the isolation of real rootsbased on Bernstein polynomials, and the computation of the topological degree in two dimensions are considered and their complexity is analyzed. In...

On circular Cylinders by Four or Five Points in Space (2001)

Devillers, Olivier, Mourrain, Bernard, Preparata, Franco P., Trebuchet, Philippe

We are interested in computing effectively cylinders through 5 points, and in other problems involved in metrology. In particular, we consider the cylinders through 4 points with a fix radius and...

Resultant over the residual of a complete intersection (2001)

Resultant over the residual of a complete intersection (2001)

In this article, we study the residual resultant which is the necessary and sufficient condition for a polynomial system F to have a solution in the residual of a variety, defined here by a complete...

Isolation of Real Roots and Computation of the Topological Degree (2001)

In this article, we study the residual resultant which is the necessary and sufficient condition for a polynomial system F to have a solution in the residual of a variety, defined here by a complete...

Mourrain, Bernard, Vrahatis, Michael N., Yakoubsohn, Jean-Claude

In this work, the isolation of real rootsbased on Bernstein polynomials, and the computation of the topological degree in two dimensions are considered and their complexity is analyzed. In...

On circular Cylinders by Four or Five Points in Space (2001)

Devillers, Olivier, Mourrain, Bernard, Preparata, Franco P., Trebuchet, Philippe

We are interested in computing effectively cylinders through 5 points, and in other problems involved in metrology. In particular, we consider the cylinders through 4 points with a fix radius and...

Resultant over the residual of a complete intersection (2001)

Using scene constraints during the calibration procedure (2001)

In this article, we study the residual resultant which is the necessary and sufficient condition for a polynomial system F to have a solution in the residual of a variety, defined here by a complete...

Didier Bondyfalat, Thodore Papadopoulo, Bernard Mourrain

This paper focuses on the problem of calibration from a single view and a map of a scene. This situation arises quite often when modelling urban scenes, e.g. for augmented reality purposes. We show...

A symbolicnumeric silhouette algorithm (2001)

Hirohisa Hirukawa, Bernard Mourrain, Yves Papegay

We have revisited the silhouette algorithm developed by Canny, and designed its new symbolic-numeric version. The symbolic-numeric silhouette algorithm do not require the symbolic computation of the...

On Circular Cylinders by Four or Five Points in Space (2001)

Unit Inria, Sophia Antipolis, Olivier Devillers, Olivier Devillers, Bernard Mourrain, Bernard Mourrain, ...

We are interested in computing eoeectively cylinders through 5 points, and in other problems involved in metrology. In particular, we consider the cylinders through 4 points with a x radius and with...

Generalized Resultants Over Unirational Algebraic Varieties (2001)

Laurent Buse, Mohamed Elkadi, Bernard Mourrain

this paper, we propose a new method, based on Bezoutian matrices, for computing a nontrivial multiple of the resultant over a projective variety X, which is described on an open subset by a...

Resultant Matrices in ALP: LU Decomposition for Sparse Matrices (2001)

Alexandro Artola, Z. Emiris, Dr. Bernard Mourrain

There are several linear algebra packages available from many research institutions. However, there is no generic LU decomposition package specialized for sparse matrices available. This paper...

A framework for Symbolic and Numeric Computations (2000)

Mourrain, Bernard, Prieto, Hélène

The need to combine symbolic and numeric computations is ubiquitous is many problems such as the forward and inverse kinematics of robots, motion planning, the analysis of the geometric structure of...

Generalized resultants over unirational algebraic varieties (2000)

Generalized resultants over unirational algebraic varieties (2000)

In this paper, we propose a new method, based on Bezoutian matrices, for computing a nontrivial multiple of the resultant over a projective variety X, which is described on an open subset by a...

A framework for Symbolic and Numeric Computations (2000)

In this paper, we propose a new method, based on Bezoutian matrices, for computing a nontrivial multiple of the resultant over a projective variety X, which is described on an open subset by a...

Mourrain, Bernard, Prieto, Hélène

The need to combine symbolic and numeric computations is ubiquitous is many problems such as the forward and inverse kinematics of robots, motion planning, the analysis of the geometric structure of...

Generalized resultants over unirational algebraic varieties (2000)

Multivariate polynomials, duality and structured matrices (2000)

In this paper, we propose a new method, based on Bezoutian matrices, for computing a nontrivial multiple of the resultant over a projective variety X, which is described on an open subset by a...

Multivariate polynomials, duality and structured matrices (2000)

We rst review the basic properties of the well known classes of Toeplitz, Hankel, Vandermonde, and other related structured matrices and reexamine their correlation to operations with univariate...

Algebraic Methods and Arithmetic Filtering for Exact Predicates on Circle Arcs (1999)

We rst review the basic properties of the well known classes of Toeplitz, Hankel, Vandermonde, and other related structured matrices and reexamine their correlation to operations with univariate...

Devillers, Olivier, Fronville, Alexandra, Mourrain, Bernard, Teillaud, Monique

The purpose of this paper is to present a new method to design exact geometric predicates in algorithms dealing with curved objects such as circular arcs. We focus on the comparison of the abscissae...

Sign Methods for Counting and Computing Real Roots of Algebraic Systems (1999)

Emiris, Ioannis Z., Mourrain, Bernard, Vrahatis, Mihail N.

In this report, we implement the concept of topological degree to isolate and compute all zeros of systems of nonlinear algebraic equations when the only computable information required is the...

Algebraic Methods and Arithmetic Filtering for Exact Predicates on Circle Arcs (1999)

Devillers, Olivier, Fronville, Alexandra, Mourrain, Bernard, Teillaud, Monique

The purpose of this paper is to present a new method to design exact geometric predicates in algorithms dealing with curved objects such as circular arcs. We focus on the comparison of the abscissae...

Sign Methods for Counting and Computing Real Roots of Algebraic Systems (1999)

Emiris, Ioannis Z., Mourrain, Bernard, Vrahatis, Mihail N.

In this report, we implement the concept of topological degree to isolate and compute all zeros of systems of nonlinear algebraic equations when the only computable information required is the...

Algebraic Methods and Arithmetic Filtering for Exact Predicates on Circle Arcs (1999)

Devillers, Olivier, Fronville, Alexandra, Mourrain, Bernard, Teillaud, Monique

The purpose of this paper is to present a new method to design exact geometric predicates in algorithms dealing with curved objects such as circular arcs. We focus on the comparison of the abscissae...

Sign Methods for Counting and Computing Real Roots of Algebraic Systems (1999)

Emiris, Ioannis Z., Mourrain, Bernard, Vrahatis, Mihail N.

In this report, we implement the concept of topological degree to isolate and compute all zeros of systems of nonlinear algebraic equations when the only computable information required is the...

14:45- 15:15 Design and implementation of the FRISCO framework (1999)

Robert M. Corless, Mark W. Giesbrecht, David J. Jeffrey, Xianping Liu, Stephen M. Watt, Pete Huerter, ...

Proceedings of the FRISCO Workshop

Sign Methods for Counting and Computing Real Roots of Algebraic Systems (1999)

Unit Inria, Sophia Antipolis, Ioannis Z. Emiris, Ioannis Z. Emiris, Bernard Mourrain, Bernard Mourrain, ...

In this report, we implement the concept of topological degree to isolate and compute all zeros of systems of nonlinear algebraic equations when the only computable information required is the...

Matrices in Elimination Theory (1999)

A New Algorithm for the Geometric Decomposition of a Variety (1999)

The last decade has witnessed the rebirth of resultant methods as a powerful computational tool for variable elimination and polynomial system solving. In particular, the advent of sparse elimination...

Mohamed Elkadi, Bernard Mourrain

In this article, we present a new method for computing the decomposition of a variety into irreducible components. It is based on a property of Bezoutian matrices, which allows us to compute a...

Some Applications of Bezoutians in Effective Algebraic Geometry (1998)

Multivariate Polynomials, Duality and Structured Matrices (1998)

In this report, we investigate some problems of effectivity, related to algebraic residue theory. We show how matrix techniques based on Bezoutian formulations, enable us to derive new algorithms for...

Mourrain, Bernard, Pan, Victor Y.

We re-investigate the well known classes of Toeplitz, Hankel, Vandermonde, and other related structured matrices, by re-examining their correlations to operations with univariate polynomials. Then we...

Some Applications of Bezoutians in Effective Algebraic Geometry (1998)

Multivariate Polynomials, Duality and Structured Matrices (1998)

In this report, we investigate some problems of effectivity, related to algebraic residue theory. We show how matrix techniques based on Bezoutian formulations, enable us to derive new algorithms for...

Mourrain, Bernard, Pan, Victor Y.

We re-investigate the well known classes of Toeplitz, Hankel, Vandermonde, and other related structured matrices, by re-examining their correlations to operations with univariate polynomials. Then we...

Some Applications of Bezoutians in Effective Algebraic Geometry (1998)

Multivariate Polynomials, Duality and Structured Matrices (1998)

In this report, we investigate some problems of effectivity, related to algebraic residue theory. We show how matrix techniques based on Bezoutian formulations, enable us to derive new algorithms for...

Mourrain, Bernard, Pan, Victor Y.

We re-investigate the well known classes of Toeplitz, Hankel, Vandermonde, and other related structured matrices, by re-examining their correlations to operations with univariate polynomials. Then we...

Some applications of bezoutians in eoeective algebraic geometry. Rapport de Recherche 3572 (1998)

Unit Inria, Sophia Antipolis, Mohamed Elkadi, Mohamed Elkadi, Bernard Mourrain, Bernard Mourrain

apport de recherche

An application of automatic theorem proving in computer vision (1998)

Didier Bondyfalat, Bernard Mourrain

Abstract. Getting accurate construction of tridimensional CAD models is a eld of great importance: with the increasing complexity of the models that modeling tools can manage nowadays, it becomes...

An application of automatic theorem proving in computer vision (1998)

Didier Bondyfalat, Bernard Mourrain

Abstract. Getting accurate construction of tridimensional CAD models is a eld of great importance: with the increasing complexity of the models that modeling tools can manage nowadays, it becomes...

Matrices in Elimination Theory (1998)

Lifting/Descending Processes for Polynomial Zeros (1998)

The last decade has witnessed the rebirth of resultant methods as a powerful computational tool for variable elimination and polynomial system solving. In particular, the advent of sparse elimination...

Controlled Iterative Methods for Solving Polynomial Systems (1998)

The recently proposed Chebyshev-like lifting map for the zeros of a univariate polynomial was motivated by its applications to splitting a univariate polynomial p(x) numerically into factors, which...

Multivariate Polynomials, Duality, and Structured Matrices (1998)

For a system of polynomial equations, we seek its specified root, maximizing or minimizing the absolute value of a fixed polynomial over all roots of the system. The latter requirement to a root,...

Some applications of Bezoutians in Effective Algebraic Geometry (1998)

We first review the basic properties of the well known classes of Toeplitz, Hankel, Vandermonde, and other related structured matrices and re-examine their correlations to operations with univariate...

Bernard Mourrain, Mohamed Elkadi, Mohamed Elkadi, Bernard Mourrain Y, Thème Génie Logiciel, Projet Saga, ...

In this report, we investigate some problems of effectivity, related to algebraic residue theory. We show how matrix techniques based on Bezoutian formulations, enable us to derive new algorithms for...

Asymptotic Acceleration of Solving Multivariate Polynomial Systems of Equations (1998)

Type II Codes over Z 4 (1997)

We propose new Las Vegas randomized algorithms for the solution of a multivariate generic or sparse polynomial system of equations. The algorithms use O ((ffi+4 n )3 n D 2 log b) arithmetic...

Alexis Bonnecaze, Patrick Solé, Christine Bachoc, Bernard Mourrain

Type II Z 4 -codes are introduced as self-dual codes over the integers modulo 4 containing the all-one vector and with euclidean weights multiple of 8: Their weight enumerators are characterized by...

Computer Algebra Methods for Studying and Computing Molecular Conformations (1997)

Ioannis Emiris And, Ioannis Z. Emiris, Bernard Mourrain

A relatively new branch of computational biology has been emerging as an eoeort to supplement traditional techniques of large scale search in drug design by structure-based methods, in order to...

Multidimensional Structured Matrices and Polynomial Systems (1997)

Bernard Mourrain, Bernard Mourrain Inria, Victor Y. Pan

We apply and extend some well-known and some recent techniques from algebraic residue theory in order to relate to each other two major subjects of algebraic and numerical computing, that is,...

Solving Special Polynomial Systems By Using Structured Matrices and Algebraic Residues (1997)

Computer Algebra Methods for Studying and Computing Molecular Conformations (1997)

We apply and extend some well-known and some recent techniques from algebraic residue theory in order to relate to each other two major subjects of algebraic and numerical computing, that is,...

Polynomial System Solving: the Case of a Six-Atom Molecule (1996)

A relatively new branch of computational biology has been emerging as an effort to supplement traditional techniques of large scale search in drug design by structure-based methods, in order to...

Emiris, Ioannis Z., Mourrain, Bernard

A relatively new branch of computational biology and chemistry has been emerging as an effort to apply successful paradigms and algorithms from geometry and robot kinematics to predicting the...

Approche effective des résidus algébriques (1996)

Polynomial System Solving: the Case of a Six-Atom Molecule (1996)

Dans ce rapport, nous nous intéressons aux propriétés du dual des polynômes et leurs connections avec la théorie algébrique des résidus. En particulier, nous voulons éclaircir le rôle que...

Emiris, Ioannis Z., Mourrain, Bernard

A relatively new branch of computational biology and chemistry has been emerging as an effort to apply successful paradigms and algorithms from geometry and robot kinematics to predicting the...

Approche effective des résidus algébriques (1996)

Polynomial System Solving: the Case of a Six-Atom Molecule (1996)

Dans ce rapport, nous nous intéressons aux propriétés du dual des polynômes et leurs connections avec la théorie algébrique des résidus. En particulier, nous voulons éclaircir le rôle que...

Emiris, Ioannis Z., Mourrain, Bernard

A relatively new branch of computational biology and chemistry has been emerging as an effort to apply successful paradigms and algorithms from geometry and robot kinematics to predicting the...

Approche effective des résidus algébriques (1996)

Isolated points, duality and residues (1996)

Dans ce rapport, nous nous intéressons aux propriétés du dual des polynômes et leurs connections avec la théorie algébrique des résidus. En particulier, nous voulons éclaircir le rôle que...

Isolated points, duality and residues (1996)

In this paper, we are interested in the use of duality in effective computations on polynomials. We represent the elements of the dual of the algebra R of polynomials over the field K as formal...

Isolated points, duality and residues (1996)

In this paper, we are interested in the use of duality in effective computations on polynomials. We represent the elements of the dual of the algebra R of polynomials over the field K as formal...

Workshop on Symbolic-Numeric Algebra for Polynomials SNAP 96 15-17th July 1996 INRIA Sophia-Antipolis, France (1996)

In this paper, we are interested in the use of duality in effective computations on polynomials. We represent the elements of the dual of the algebra R of polynomials over the field K as formal...

I.Z. Emiris, Bernard Mourrain

Let a and b be two polynomials having numerical coeOEcients. We consider the question: when are a and b relatively prime? Since the coeOEcients of a and b are approximant the question is the same as:...

Polynomial System Solving: The Case of a Six-Atom Molecule (1996)

Ioannis Z. Emiris, Ioannis Z. Emiris, Bernard Mourrain, Bernard Mourrain

: A relatively new branch of computational biology and chemistry has been emerging as an eoeort to apply successful paradigms and algorithms from geometry and robot kinematics to predicting the...

Workshop on Symbolic-Numeric Algebra for Polynomials (1996)

B. Mourrain, S. Watt, Ioannis Z. Emiris, Bernard Mourrain

This meeting is intended as a timely workshop to discuss the emerging understanding of problems involving polynomials with inexactly-known coe cients. Such polynomial problems arise, for example,...

On the Geometry and Algebra of the Point and Line Correspondences between $N$ Images (1995)

Faugeras, Olivier, Mourrain, Bernard

We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the Grassmann-Cayley...

On the Geometry and Algebra of the Point and Line Correspondences between $N$ Images (1995)

Faugeras, Olivier, Mourrain, Bernard

We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the Grassmann-Cayley...

On the Geometry and Algebra of the Point and Line Correspondences between $N$ Images (1995)

Faugeras, Olivier, Mourrain, Bernard

We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the Grassmann-Cayley...

On the geometry and algebra of the point and line correspondences between N images (1995)

Olivier Faugeras, Olivier Faugeras, Bernard Mourrain, Bernard Mourrain, Projet Robotvis Safir

: We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the GrassmannCayley...

Visualization of Mathematical Surfaces: the IZIC Server Approach (1995)

On the geometry and algebra of the point and line correspondences between N images (1995)

This paper presents IZIC, a stand-alone high-quality 3D graphic tool driven by a command language. IZIC is an interactive version of ZICLIB, a 3D graphic...

Olivier Faugeras, Bernard Mourrain

We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the GrassmannCayley...

Visualization of Mathematical Surfaces: the IZIC Server Approach (1994)

Visualization of Mathematical Surfaces: the IZIC Server Approach (1994)

This paper presents IZIC, a stand-alone high-quality 3D graphic tool driven by a command

New Aspects of Geometrical Calculus With Invariants (1994)

This paper presents IZIC, a stand-alone high-quality 3D graphic tool driven by a command language. IZIC is an interactive version of ZICLIB, a 3D graphic library allowing efficient curve and surface...

B. Mourrain, Bernard Mourrain

In this paper, we show how to treat projective configurations of points in an invariant way. By this, we mean that we do not want to take any basis, but compute directly with these geometric objects...

About the rational map (1993)

About the rational map (1993)

In this paper, we consider the direct kinematic problem of a parallel robot (called the Stewart platform or left hand) from a mathematical point of view. We do not try to give real time and numerical...

About the rational map (1993)

In this paper, we consider the direct kinematic problem of a parallel robot (called the Stewart platform or left hand) from a mathematical point of view. We do not try to give real time and numerical...

About the Rational Map Associated to a Parallel Robot (1993)

In this paper, we consider the direct kinematic problem of a parallel robot (called the Stewart platform or left hand) from a mathematical point of view. We do not try to give real time and numerical...

Bernard Mourrain, Bernard Mourrain, Projet Safir

: In this paper, we consider the direct kinematic problem of a parallel robot (called the Stewart platform or left hand) from a mathematical point of view. We do not try to give real time and...

IZIC: a Portable Language-Driven Tool for Mathematical Surfaces Visualization (1993)