Elimination and nonlinear equations of Rees algebra (2009)
Busé, Laurent, Chardin, Marc, Simis, Aron
A new approach is established to computing the image of a rational map, whereby the use of approximation complexes is complemented with a detailed analysis of the torsion of the symmetric algebra in...
Noether's forms for the study of non-composite rational functions and their spectrum (2009)
Busé, Laurent, Chèze, Guillaume, Najib, Salah
In this paper, the spectrum and the decomposability of a multivariate rational function are studied by means of the effective Noether's irreducibility theorem given by Ruppert. With this approach,...
EXPLICIT FACTORS OF SOME ITERATED RESULTANTS AND DISCRIMINANTS (2009)
Laurent Busé, Bernard Mourrain, Dedicated Professor, Jean-pierre Jouanolou
Abstract. 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...
A computational study of ruled surfaces (2009)
Busé, Laurent, Elkadi, Mohamed, Galligo, André
We study rational ruled surfaces and $\mu$-bases which were recently considered in a series of articles by Chen and coworkers. We give short and conceptual proofs with geometric insights and...
A computational study of ruled surfaces (2009)
Busé, Laurent, Elkadi, Mohamed, Galligo, André
We study rational ruled surfaces and $\mu$-bases which were recently considered in a series of articles by Chen and coworkers. We give short and conceptual proofs with geometric insights and...
Torsion of the symmetric algebra and implicitization (2009)
Busé, Laurent, Chardin, Marc, Jouanolou, Jean-Pierre
Recently, a method to compute the implicit equation of a parametrized hypersurface has been developed by the authors. We address here some questions related to this method. First, we prove that the...
Torsion of the symmetric algebra and implicitization (2009)
Busé, Laurent, Chardin, Marc, Jouanolou, Jean-Pierre
Recently, a method to compute the implicit equation of a parametrized hypersurface has been developed by the authors. We address here some questions related to this method. First, we prove that the...
Explicit factors of some iterated resultants and discriminants (2009)
Busé, Laurent, Mourrain, Bernard
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...
Explicit factors of some iterated resultants and discriminants (2009)
Busé, Laurent, Mourrain, Bernard
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...
On the equations of the moving curve ideal of a rational algebraic plane curve (2009)
Given a parametrization of a rational plane algebraic curve C, some explicit adjoint pencils on C are described in terms of determinants. Moreover, some generators of the Rees algebra associated to...
On the equations of the moving curve ideal of a rational algebraic plane curve (2009)
Given a parametrization of a rational plane algebraic curve C, some explicit adjoint pencils on C are described in terms of determinants. Moreover, some generators of the Rees algebra associated to...
Noether's forms for the study of non-composite rational functions and their spectrum (2009)
Busé, Laurent, Chèze, Guillaume, Najib, Salah
In this paper, the spectrum and the decomposability of a multivariate rational function are studied by means of the effective Noether's irreducibility theorem given by Ruppert. With this approach,...
Noether's forms for the study of non-composite rational functions and their spectrum (2009)
Busé, Laurent, Chèze, Guillaume, Najib, Salah
In this paper, the spectrum and the decomposability of a multivariate rational function are studied by means of the effective Noether's irreducibility theorem given by Ruppert. With this approach,...
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...
Elimination and nonlinear equations of Rees algebra (2009)
Busé, Laurent, Chardin, Marc, Simis, Aron
A new approach is established to computing the image of a rational map, whereby the use of approximation complexes is complemented with a detailed analysis of the torsion of the symmetric algebra in...
Elimination and nonlinear equations of Rees algebra (2009)
Busé, Laurent, Chardin, Marc, Simis, Aron
A new approach is established to computing the image of a rational map, whereby the use of approximation complexes is complemented with a detailed analysis of the torsion of the symmetric algebra in...
On the total order of reducibility of a pencil of algebraic plane curves (2008)
Busé, Laurent, Chèze, Guillaume
In this paper, the problem of bounding the number of reducible curves in a pencil of algebraic plane curves is addressed. Unlike most of the previous related works, each reducible curve of the pencil...
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...
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in Busé and Jouanolou...
We present a subresultant-based algorithm for deciding if the parametrization of a toric hypersurface is invertible or not, and for computing the inverse of the parametrization in the case where it...
Intersection and self-intersection of surfaces by means of Bezoutian matrices (2008)
Busé, Laurent, Elkadi, Mohamed, Galligo, André
The computation of intersection and self-intersection loci of parameterized surfaces is an important task in Computer Aided Geometric Design. Computer algebra tools need to be developed further for...
Intersection and self-intersection of surfaces by means of Bezoutian matrices (2008)
Busé, Laurent, Elkadi, Mohamed, Galligo, André
The computation of intersection and self-intersection loci of parameterized surfaces is an important task in Computer Aided Geometric Design. Computer algebra tools need to be developed further for...
Division Algorithms for Bernstein Polynomials (2008)
Three division algorithms are presented for univariate Bernstein polynomials: an algorithm for finding the quotient and remainder of two univariate polynomials, an algorithm for calculating the GCD...
Division Algorithms for Bernstein Polynomials (2008)
Three division algorithms are presented for univariate Bernstein polynomials: an algorithm for finding the quotient and remainder of two univariate polynomials, an algorithm for calculating the GCD...
On the total order of reducibility of a pencil of algebraic plane curves (2008)
Busé, Laurent, Chèze, Guillaume
In this paper, the problem of bounding the number of reducible curves in a pencil of algebraic plane curves is addressed. Unlike most of the previous related works, each reducible curve of the pencil...
On the total order of reducibility of a pencil of algebraic plane curves (2008)
Busé, Laurent, Chèze, Guillaume
In this paper, the problem of bounding the number of reducible curves in a pencil of algebraic plane curves is addressed. Unlike most of the previous related works, each reducible curve of the pencil...
On the equations of the moving curve ideal (2007)
Given a parametrization of a plane algebraic curve C, some explicit adjoint linear systems on C are described in terms of determinants. Moreover, some generators of the Rees algebra associated to...
On the equations of the moving curve ideal of a rational algebraic plane curve (2007)
Given a parametrization of a rational plane algebraic curve C, some explicit adjoint pencils on C are described in terms of determinants. Moreover, some generators of the Rees algebra associated to...
On the equations of the moving curve ideal (2007)
Given a parametrization of a plane algebraic curve C, some explicit adjoint linear systems on C are described in terms of determinants. Moreover, some generators of the Rees algebra associated to...
Implicitization of Bihomogeneous Parametrizations of Algebraic Surfaces via Linear Syzygies (2007)
We show that the implicit equation of a surface in 3-dimensional projective space parametrized by bi-homogeneous polynomials of bi-degree (d,d), for a given positive integer d, can be represented and...
Explicit factors of some iterated resultants and discriminants (2007)
Busé, Laurent, Mourrain, Bernard
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...
Explicit factors of some iterated resultants and discriminants (2007)
Busé, Laurent, Mourrain, Bernard
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...
Implicitization of Bihomogeneous Parametrizations of Algebraic Surfaces via Linear Syzygies (2007)
We show that the implicit equation of a surface in 3-dimensional projective space parametrized by bi-homogeneous polynomials of bi-degree (d,d), for a given positive integer d, can be represented and...
Implicitization of Bihomogeneous Parametrizations of Algebraic Surfaces via Linear Syzygies (2007)
We show that the implicit equation of a surface in 3-dimensional projective space parametrized by bi-homogeneous polynomials of bi-degree (d,d), for a given positive integer d, can be represented and...
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...
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...
Proposition de Stage Master 2ième année (2007)
Calcul des points singuliers du courbe plane rationnelle
Explicit factors of some iterated resultants and discriminants (2006)
Busé, Laurent, Mourrain, Bernard
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...
Busé, Laurent, Chardin, Marc, Jouanolou, Jean-Pierre
Recently, a method to compute the implicit equation of a parameterized hypersurface has been developed by the authors. We address here some questions related to this method : optimality of a degree...
Busé, Laurent, Chardin, Marc, Jouanolou, Jean-Pierre
Recently, a method to compute the implicit equation of a parameterized hypersurface has been developed by the authors. We address here some questions related to this method : optimality of a degree...
Intersection and self-intersection of surfaces by means of Bezoutian matrices (2006)
Busé, Laurent, Elkadi, Mohamed, Galligo, André
The computation of intersection and self-intersection loci of parameterized surfaces is an important task in Computer Aided Geometric Design. Computer algebra tools need to be developed further for...
Intersection and self-intersection of surfaces by means of Bezoutian matrices (2006)
Busé, Laurent, Elkadi, Mohamed, Galligo, André
The computation of intersection and self-intersection loci of parameterized surfaces is an important task in Computer Aided Geometric Design. Computer algebra tools need to be developed further for...
Étude du résultant sur une variété algébrique (2006)
Dans ce travail de thèse une étude théorique et pratique du résultant résiduel est proposée. Ce résultant résiduel fournit une condition nécessaire et suffisante pour qu'un système...
Elimination theory in codimension one and applications (2006)
In these notes, we present a general framework to compute the codimension one part of the elimination ideal of a system of homogeneous polynomials. It is based on the computation of the so-called...
Intersection and self-intersection of surfaces by means of Bezoutian matrices (2006)
Busé, Laurent, Elkadi, Mohamed, Galligo, André
The computation of intersection and self-intersection loci of parameterized surfaces is an important task in Computer Aided Geometric Design. Computer algebra tools need to be developed further for...
Busé, Laurent, Chardin, Marc, Jouanolou, Jean-Pierre
Recently, a method to compute the implicit equation of a parameterized hypersurface has been developed by the authors. We address here some questions related to this method : optimality of a degree...
A matrix-based approach to properness and inversion problems for rational surfaces (2006)
Busé, Laurent, D'Andrea, Carlos
We present a matrix-based approach for deciding if the parameterization of an algebraic space surface is invertible or not, and for computing the inverse of the parametrization if it exists
A matrix-based approach to properness and inversion problems for rational surfaces (2006)
Busé, Laurent, D'Andrea, Carlos
We present a matrix-based approach for deciding if the parameterization of an algebraic space surface is invertible or not, and for computing the inverse of the parametrization if it exists
A matrix-based approach to properness and inversion problems for rational surfaces (2006)
Busé, Laurent, D'Andrea, Carlos
We present a matrix-based approach for deciding if the parameterization of an algebraic space surface is invertible or not, and for computing the inverse of the parametrization if it exists
Elimination theory in codimension one and applications (2006)
In these notes, we present a general framework to compute the codimension one part of the elimination ideal of a system of homogeneous polynomials. It is based on the computation of the so-called...
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...
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...
In this paper we introduce an intermediate representation of surfaces that we call semi-implicit. We give a general definition in the language of projective complex algebraic geometry, and we begin...
Implicitizing rational hypersurfaces using approximation complexes (2005)
We describe an algorithm for implicitizing rational hypersurfaces with at most a finite number of base points, based on a technique already described by Busé and Jouanolou, where implicit equations...
In this paper we introduce an intermediate representation of surfaces that we call semi-implicit. We give a general definition in the language of projective complex algebraic geometry, and we begin...
Implicitizing rational hypersurfaces using approximation complexes (2005)
We describe an algorithm for implicitizing rational hypersurfaces with at most a finite number of base points, based on a technique already described by Busé and Jouanolou, where implicit equations...
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...
In this paper we introduce an intermediate representation of surfaces that we call semi-implicit. We give a general definition in the language of projective complex algebraic geometry, and we begin...
Implicitizing rational hypersurfaces using approximation complexes (2005)
We describe an algorithm for implicitizing rational hypersurfaces with at most a finite number of base points, based on a technique already described by Busé and Jouanolou, where implicit equations...
Resultant-based method for plane curves intersection problems (2005)
Laurent Busé, Houssam Khalil, Bernard Mourrain
problems
Using semi-implicit representation of algebraic surfaces (2004)
In a previous work we introduced a new general representation of algebraic surfaces, that we called semi-implicit, which encapsulates both usual and less known surfaces. Here we specialize this...
Using semi-implicit representation of algebraic surfaces (2004)
In a previous work we introduced a new general representation of algebraic surfaces, that we called semi-implicit, which encapsulates both usual and less known surfaces. Here we specialize this...
Resultants of determinantal varieties (2004)
In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct...
On the irreducibility of multivariate subresultants (2004)
Busé, Laurent, D'Andrea, Carlos
Let $P_1,\ldots,P_n$ be generic homogeneous polynomials in $n$ variables of degrees $d_1,\ldots,d_n$ respectively. We prove that if $\nu$ is an integer satisfying ${\sum_{i=1}^n d_i}-n+1-\min\{d_i\}
Inversion of parameterized hypersurfaces by means of subresultants (2004)
Busé, Laurent, D'Andrea, Carlos
We present a subresultant-based algorithm for deciding if the parametrization of a toric hypersurface is invertible or not, and for computing the inverse of the parametrization in the case where it...
Resultants of determinantal varieties (2004)
In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct...
On the irreducibility of multivariate subresultants (2004)
Busé, Laurent, D'Andrea, Carlos
Let $P_1,\ldots,P_n$ be generic homogeneous polynomials in $n$ variables of degrees $d_1,\ldots,d_n$ respectively. We prove that if $\nu$ is an integer satisfying ${\sum_{i=1}^n d_i}-n+1-\min\{d_i\}
Inversion of parameterized hypersurfaces by means of subresultants (2004)
Busé, Laurent, D'Andrea, Carlos
We present a subresultant-based algorithm for deciding if the parametrization of a toric hypersurface is invertible or not, and for computing the inverse of the parametrization in the case where it...
Géométrie différentielle et applications (2004)
Ces notes de cours traitent principalement des outils de la géométrie différentielle pour les courbes et surfaces algébriques pour la modélisation des formes.
Géométrie différentielle et applications (2004)
Ces notes de cours traitent principalement des outils de la géométrie différentielle pour les courbes et surfaces algébriques pour la modélisation des formes.
Géométrie différentielle et applications (2004)
Ces notes de cours traitent principalement des outils de la géométrie différentielle pour les courbes et surfaces algébriques pour la modélisation des formes.
Using semi-implicit representation of algebraic surfaces (2004)
In a previous work we introduced a new general representation of algebraic surfaces, that we called semi-implicit, which encapsulates both usual and less known surfaces. Here we specialize this...
Resultants of determinantal varieties (2004)
In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct...
On the irreducibility of multivariate subresultants (2004)
Busé, Laurent, D'Andrea, Carlos
Let $P_1,\ldots,P_n$ be generic homogeneous polynomials in $n$ variables of degrees $d_1,\ldots,d_n$ respectively. We prove that if $\nu$ is an integer satisfying ${\sum_{i=1}^n d_i}-n+1-\min\{d_i\}
Inversion of parameterized hypersurfaces by means of subresultants (2004)
Busé, Laurent, D'Andrea, Carlos
We present a subresultant-based algorithm for deciding if the parametrization of a toric hypersurface is invertible or not, and for computing the inverse of the parametrization in the case where it...
Using Semi-Implicit Representation of Algebraic Surfaces (2004)
Laurent Bus Inria, Laurent Busé
In [3] we introduced a new general representation of algebraic surfaces, that we called semi-implicit, which encapsulates both usual and less known surfaces. Here we specialize this notion in order...
On the irreducibility of multivariate subresultants (2003)
Busé, Laurent, D'Andrea, Carlos
Let $P_1,...,P_n$ be generic homogeneous polynomials in $n$ variables of degrees $d_1,...,d_n$ respectively. We prove that if $\nu$ is an integer satisfying ${\sum_{i=1}^n d_i}-n+1-\min\{d_i\}
Computing resultant matrices with Macaulay2 and Maple (2003)
We present implementations in both computer systems Macaulay2 and Maple for computing resultant matrices. We give a brief overview of classical resultants, sparse resultants, residual resultants and...
Computing resultant matrices with Macaulay2 and Maple (2003)
We present implementations in both computer systems Macaulay2 and Maple for computing resultant matrices. We give a brief overview of classical resultants, sparse resultants, residual resultants and...
A resultant approach to detect intersecting curves in the projective space (2003)
Given two curves in the projective space, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant...
A resultant approach to detect intersecting curves in the projective space (2003)
Given two curves in the projective space, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant...
Implicitization of surfaces in the projective space in the presence of base points (2003)
Busé, Laurent, Cox, David, D'Andrea, Carlos
We show that the method of moving quadrics for implicitizing surfaces in $\PP^3$ applies in certain cases where base points are present. However, if the ideal defined by the parametrization is...
On the closed image of a rational map and the implicitization problem (2003)
Busé, Laurent, Jouanolou, Jean-Pierre
In this paper, we investigate some topics around the closed image $S$ of a rational map $\lambda$ given by some homogeneous elements $f_1,\ldots,f_n$ of the same degree in a graded algebra $A$. We...
Using projection operators in computer aided geometric design (2003)
Busé, Laurent, Elkadi, Mohamed, Mourrain, Bernard
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,...
Implicitization of surfaces in the projective space in the presence of base points (2003)
Busé, Laurent, Cox, David, D'Andrea, Carlos
We show that the method of moving quadrics for implicitizing surfaces in $\PP^3$ applies in certain cases where base points are present. However, if the ideal defined by the parametrization is...
On the closed image of a rational map and the implicitization problem (2003)
Busé, Laurent, Jouanolou, Jean-Pierre
In this paper, we investigate some topics around the closed image $S$ of a rational map $\lambda$ given by some homogeneous elements $f_1,\ldots,f_n$ of the same degree in a graded algebra $A$. We...
Using projection operators in computer aided geometric design (2003)
Busé, Laurent, Elkadi, Mohamed, Mourrain, Bernard
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,...
Computing resultant matrices with Macaulay2 and Maple (2003)
We present implementations in both computer systems Macaulay2 and Maple for computing resultant matrices. We give a brief overview of classical resultants, sparse resultants, residual resultants and...
A resultant approach to detect intersecting curves in the projective space (2003)
Given two curves in the projective space, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant...
Implicitization of surfaces in the projective space in the presence of base points (2003)
Busé, Laurent, Cox, David, D'Andrea, Carlos
We show that the method of moving quadrics for implicitizing surfaces in $\PP^3$ applies in certain cases where base points are present. However, if the ideal defined by the parametrization is...
On the closed image of a rational map and the implicitization problem (2003)
Busé, Laurent, Jouanolou, Jean-Pierre
In this paper, we investigate some topics around the closed image $S$ of a rational map $\lambda$ given by some homogeneous elements $f_1,\ldots,f_n$ of the same degree in a graded algebra $A$. We...
Using projection operators in computer aided geometric design (2003)
Busé, Laurent, Elkadi, Mohamed, Mourrain, Bernard
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,...
Syzygies of points in a projective space (2002)
Von Bothmer, Hans-Christian, Busé, Laurent, Fu, Baohua
We study different aspects of syzygies of points in a projective space
Syzygies of points in a projective space (2002)
Von Bothmer, Hans-Christian, Busé, Laurent, Fu, Baohua
We study different aspects of syzygies of points in a projective space
Syzygies of points in a projective space (2002)
Von Bothmer, Hans-Christian, Busé, Laurent, Fu, Baohua
We study different aspects of syzygies of points in a projective space
Étude du résultant sur une variété algébrique (2001)
Dans ce travail de thèse une étude théorique et pratique durésultant résiduel est proposée. Ce résultant résiduelfournit une condition nécessaire et suffisante pour qu'un systèmealgébrique...
Étude du résultant sur une variété algébrique (2001)
Dans ce travail de thèse une étude théorique et pratique du résultant résiduel est proposée. Ce résultant résiduel fournit une condition nécessaire et suffisante pour qu'un système...
Residual resultant over the projective plane and the implicitization problem (2001)
In this article, we first generalize the recent notion of residual resultant of a complete intersection to the case of a local complete intersection of codimension 2 in the projective plane, which is...
Resultant over the residual of a complete intersection (2001)
Busé, Laurent, Elkadi, Mohamed, Mourrain, Bernard
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...
Residual resultant over the projective plane and the implicitization problem (2001)
In this article, we first generalize the recent notion of residual resultant of a complete intersection to the case of a local complete intersection of codimension 2 in the projective plane, which is...
Resultant over the residual of a complete intersection (2001)
Busé, Laurent, Elkadi, Mohamed, Mourrain, Bernard
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...
Étude du résultant sur une variété algébrique (2001)
Dans ce travail de thèse une étude théorique et pratique du résultant résiduel est proposée. Ce résultant résiduel fournit une condition nécessaire et suffisante pour qu'un système...
Residual resultant over the projective plane and the implicitization problem (2001)
In this article, we first generalize the recent notion of residual resultant of a complete intersection to the case of a local complete intersection of codimension 2 in the projective plane, which is...
Resultant over the residual of a complete intersection (2001)
Busé, Laurent, Elkadi, Mohamed, Mourrain, Bernard
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...
Étude du résultant sur une variété algébrique (2001)
Dans ce travail de thèse une étude théorique et pratique du résultant résiduel est proposée. Ce résultant résiduel fournit une condition nécessaire et suffisante pour qu'un système...
Generalized resultants over unirational algebraic varieties (2000)
Busé, Laurent, Elkadi, Mohamed, Mourrain, Bernard
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...
Generalized resultants over unirational algebraic varieties (2000)
Busé, Laurent, Elkadi, Mohamed, Mourrain, Bernard
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...
Generalized resultants over unirational algebraic varieties (2000)
Busé, Laurent, Elkadi, Mohamed, Mourrain, Bernard
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...