The Voronoi diagram of three arbitrary lines in R 3 (2009)
Hazel Everett, Christian Gillot, Daniel Lazard, Sylvain Lazard, Marc Pouget
In this paper we study the Voronoi diagram of lines in R 3. The Voronoi diagram of three lines in general position was studied in [14]. In this paper we complete this work by presenting a complete...
The Voronoi diagram of three arbitrary lines in R3 (2009)
Everett, Hazel, Gillot, Christian, Lazard, Daniel, Lazard, Sylvain, Pouget, Marc
In this paper we study the Voronoi diagram of lines in R3 . The Voronoi diagram of three lines in general position was studied in [8]. In this paper we complete this work by presenting a complete...
The Voronoi diagram of three arbitrary lines in R3 (2009)
Everett, Hazel, Gillot, Christian, Lazard, Daniel, Lazard, Sylvain, Pouget, Marc
In this paper we study the Voronoi diagram of lines in R3 . The Voronoi diagram of three lines in general position was studied in [8]. In this paper we complete this work by presenting a complete...
The Voronoi diagram of three lines (2009)
Everett, Hazel, Lazard, Daniel, Lazard, Sylvain, Safey El Din, Mohab
We give a complete description of the Voronoi diagram, in $\R^3$, of three lines in general position, that is, that are pairwise skew and not all parallel to a common plane. In particular, we show...
The Voronoi diagram of three lines (2009)
Everett, Hazel, Lazard, Daniel, Lazard, Sylvain, Safey El Din, Mohab
We give a complete description of the Voronoi diagram, in $\R^3$, of three lines in general position, that is, that are pairwise skew and not all parallel to a common plane. In particular, we show...
Chapter 1 TOWARDS THE ROBUST INTERSECTION OF IMPLICIT QUADRICS (2008)
Laurent Dupont, Sylvain Lazard, Sylvain Petitjean, Daniel Lazard
Abstract We are interested in efficiently and robustly computing a parametric form of the intersection of two implicit quadrics with rational coefficients. Our method is similar in spirit to the...
Near-Optimal Parameterization of the Intersection of Quadrics: I.~The Generic Algorithm (2008)
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
We present an exact and efficient algorithm for computing a proper parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
We present here the first classification of pencils of quadrics based on the type of their intersection in real projective space and we show how this classification can be used to compute efficiently...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
We conclude, in this third part, the presentation of an algorithm for computing an exact and proper parameterization of the intersection of two quadrics. The coordinate functions of the...
Near-Optimal Parameterization of the Intersection of Quadrics: I.~The Generic Algorithm (2008)
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
We present an exact and efficient algorithm for computing a proper parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
We present here the first classification of pencils of quadrics based on the type of their intersection in real projective space and we show how this classification can be used to compute efficiently...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
We conclude, in this third part, the presentation of an algorithm for computing an exact and proper parameterization of the intersection of two quadrics. The coordinate functions of the...
Notes Informelles de Calcul Formel IX (2007)
Symmetric Polynomials And, Marc Giusti, Greco Calcul, Formel No, Daniel Lazard, Annick Valibouze
this paper a general transformation of polynomials, and show that the classical deep relationships between the problems : (T ) transforming equations by a morphism (R) elementary elimination theory...
The Voronoi Diagram of Three Lines (2007)
Everett, Hazel, Lazard, Daniel, Lazard, Sylvain, Safey El Din, Mohab
We give a complete description of the Voronoi diagram, in $\R^3$, of three lines in general position, that is, that are pairwise skew and not all parallel to a common plane. In particular, we show...
The Voronoi Diagram of Three Lines (2007)
Everett, Hazel, Lazard, Daniel, Lazard, Sylvain, Safey El Din, Mohab
We give a complete description of the Voronoi diagram, in $\R^3$, of three lines in general position, that is, that are pairwise skew and not all parallel to a common plane. In particular, we show...
Representation for the radical of a finitely generated differential ideal (2007)
Boulier, François, Lazard, Daniel, Ollivier, François, Petitot, Michel
We give an algorithm which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals. The computed representation provides an algorithm for...
The Voronoi Diagram of Three Lines (2007)
Everett, Hazel, Lazard, Daniel, Lazard, Sylvain, Safey El Din, Mohab
We give a complete description of the Voronoi diagram, in $\R^3$, of three lines in general position, that is, that are pairwise skew and not all parallel to a common plane. In particular, we show...
The Voronoi Diagram of Three Lines (2007)
Everett, Hazel, Lazard, Daniel, Lazard, Sylvain, Safey El Din, Mohab
We give a complete description of the Voronoi diagram, in $\R^3$, of three lines in general position, that is, that are pairwise skew and not all parallel to a common plane. In particular, we show...
The Voronoi Diagram of Three Lines (2007)
Everett, Hazel, Lazard, Daniel, Lazard, Sylvain, Safey El Din, Mohab
We give a complete description of the Voronoi diagram of three lines in $\R^3$. In particular, we show that the topology of the Voronoi diagram is invariant for three lines in general position, that...
The Voronoi Diagram of Three Lines (2007)
Everett, Hazel, Lazard, Daniel, Lazard, Sylvain, Safey El Din, Mohab
We give a complete description of the Voronoi diagram of three lines in $\R^3$. In particular, we show that the topology of the Voronoi diagram is invariant for three lines in general position, that...
It is shown that the discriminant of a discriminant has the same irreducible factors as the product of seven polynomials which are defined as the GCD of the generators of an elimination ideal. Under...
Solving parametric polynomial systems (2007)
Daniel Lazard, Fabrice Rouillier
We present a new algorithm for solving basic parametric constructible or semi-algebraic
It is shown that the discriminant of a discriminant has the same irreducible factors as the product of seven polynomials which are defined as the GCD of the generators of an elimination ideal. Under...
On dertermining mixing parameter of CC-CMA algorithm by solving semi-algebraic sets (2006)
Gu, Nong, Lazard, Daniel, Rouillier, Fabrice, Xiang, Yong
The global convergence of a recently proposed constant modulus (CM) and cross-correlation (CC)-based algorithm (CC-CMA) is studied in this paper. We first show the original analysis of global...
On dertermining mixing parameter of CC-CMA algorithm by solving semi-algebraic sets (2006)
Gu, Nong, Lazard, Daniel, Rouillier, Fabrice, Xiang, Yong
The global convergence of a recently proposed constant modulus (CM) and cross-correlation (CC)-based algorithm (CC-CMA) is studied in this paper. We first show the original analysis of global...
On dertermining mixing parameter of CC-CMA algorithm by solving semi-algebraic sets (2006)
Gu, Nong, Lazard, Daniel, Rouillier, Fabrice, Xiang, Yong
The global convergence of a recently proposed constant modulus (CM) and cross-correlation (CC)-based algorithm (CC-CMA) is studied in this paper. We first show the original analysis of global...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
In Part II [3] of this paper, we have shown, using a classification of pencils of quadrics over the reals, how to determine quickly and efficiently the real type of the intersection of two given...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all...
Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm (2005)
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
We present the first efficient algorithm for computing an exact parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
In Part II [3] of this paper, we have shown, using a classification of pencils of quadrics over the reals, how to determine quickly and efficiently the real type of the intersection of two given...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all...
Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm (2005)
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
We present the first efficient algorithm for computing an exact parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational...
Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm (2005)
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
We present the first efficient algorithm for computing an exact parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
In Part II [3] of this paper, we have shown, using a classification of pencils of quadrics over the reals, how to determine quickly and efficiently the real type of the intersection of two given...
Complexity of Zero-dimensional Gröbner Bases (2005)
In this paper, it is shown that the Gröbner basis (for any monomial ordering) of a zero-dimensional ideal may be computed within a bit complexity which is essentially polynomial in $D^n$ where $n$...
Sharper Complexity Bounds for Zero-dimensional Gröbner Bases and Polynomial System Solving (2005)
In this paper, we improve the bound of complexity of the algorithms on polynomial ideals having complexities polynomial in $d^n$ where $d$ is the maximal degree of input polynomials and $n$ the...
Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm (2005)
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
We present the first efficient algorithm for computing an exact parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
In Part II [3] of this paper, we have shown, using a classification of pencils of quadrics over the reals, how to determine quickly and efficiently the real type of the intersection of two given...
Complexity of Zero-dimensional Gröbner Bases (2005)
In this paper, it is shown that the Gröbner basis (for any monomial ordering) of a zero-dimensional ideal may be computed within a bit complexity which is essentially polynomial in $D^n$ where $n$...
Sharper Complexity Bounds for Zero-dimensional Gröbner Bases and Polynomial System Solving (2005)
In this paper, we improve the bound of complexity of the algorithms on polynomial ideals having complexities polynomial in $d^n$ where $d$ is the maximal degree of input polynomials and $n$ the...
Complexity of Zero-dimensional Gröbner Bases (2005)
In this paper, it is shown that the Gröbner basis (for any monomial ordering) of a zero-dimensional ideal may be computed within a bit complexity which is essentially polynomial in $D^n$ where $n$...
Sharper Complexity Bounds for Zero-dimensional Gröbner Bases and Polynomial System Solving (2005)
In this paper, we improve the bound of complexity of the algorithms on polynomial ideals having complexities polynomial in $d^n$ where $d$ is the maximal degree of input polynomials and $n$ the...
Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm (2005)
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
We present the first efficient algorithm for computing an exact parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all...
Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain
In Part II [3] of this paper, we have shown, using a classification of pencils of quadrics over the reals, how to determine quickly and efficiently the real type of the intersection of two given...
Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean, Thème Sym, Laurent Dupont, ...
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Laurent Dupont, Sylvain Lazard, Daniel Lazard, Sylvain Petitjean
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Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean, Thème Sym, Laurent Dupont, ...
apport de recherche
Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean, Thème Sym, Laurent Dupont, ...
apport de recherche
Solving Parametric Polynomial Systems (2004)
Lazard, Daniel, Rouillier, Fabrice
We present a new algorithm for solving basic parametric constructible or semi-algebraic systems like $\mathcal{C} = \{ x \in \Cp_1 ( x ) = 0, \ldots, p_s ( x ) = 0, f_1 ( x ) \neq 0, \ldots, f_l ( x...
Solving Parametric Polynomial Systems (2004)
Lazard, Daniel, Rouillier, Fabrice
We present a new algorithm for solving basic parametric constructible or semi-algebraic systems like $\mathcal{C} = \{ x \in \Cp_1 ( x ) = 0, \ldots, p_s ( x ) = 0, f_1 ( x ) \neq 0, \ldots, f_l ( x...
Solving Parametric Polynomial Systems (2004)
Lazard, Daniel, Rouillier, Fabrice
We present a new algorithm for solving basic parametric constructible or semi-algebraic systems like $\mathcal{C} = \{ x \in \Cp_1 ( x ) = 0, \ldots, p_s ( x ) = 0, f_1 ( x ) \neq 0, \ldots, f_l ( x...
Near-Optimal Parameterization of the Intersection of Quadrics (2003)
Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean
In this paper, we present the rst exact, robust and practical method for computing an explicit representation of the intersection of two arbitrary quadrics whose coecients are rational. Combining...
Near-Optimal Parameterization of the Intersection of Quadrics (2003)
Laurent Dupont, Daniel Lazard, Sylvain Lazard
In this paper, we present the first exact, robust and practical method for computing an explicit representation of the intersection of two arbitrary quadrics whose coe#cients are rational. Combining...
Towards The Robust Intersection Of Implicit Quadrics (2001)
Laurent Dupont, Sylvain Lazard, Sylvain Petitjean, Daniel Lazard
We are interested in eciently and robustly computing a parametric form of the intersection of two implicit quadrics with rational coe- cients. Our method is similar in spirit to the general method...
Computing representations for radicals of finitely generated differential ideals (1999)
Boulier, François, Lazard, Daniel, Ollivier, François, Petitot, Michel
This paper deals with systems of polynomial differential equations, ordinary or with partial derivatives. The embedding theory is the differential algebra of Ritt and Kolchin. We describe an...
Computing representations for radicals of finitely generated differential ideals (1999)
Boulier, François, Lazard, Daniel, Ollivier, François, Petitot, Michel
This paper deals with systems of polynomial differential equations, ordinary or with partial derivatives. The embedding theory is the differential algebra of Ritt and Kolchin. We describe an...
On the Theories of Triangular Sets (1999)
Philippe Aubry, Daniel Lazard, Moreno Maza
Different notions of triangular sets are presented. The relationship between these notions are studied. The main result is that four different existing notions of good triangular sets are equivalent....
Representation for the radical of a finitely generated differential ideal (1995)
Boulier, François, Lazard, Daniel, Ollivier, François, Petitot, Michel
We give an algorithm which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals. The computed representation provides an algorithm for...
Representation for the radical of a finitely generated differential ideal (1995)
Boulier, François, Lazard, Daniel, Ollivier, François, Petitot, Michel
We give an algorithm which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals. The computed representation provides an algorithm for...
Algebraic Transformations Of Polynomial Equations, Symmetric Polynomials And Elimination (1993)
Marc Giusti, Ecole Polytechnique, Palaiseau Cedex, Daniel Lazard, Annick Valibouze
This paper is an extended abstract presenting some results of a paper in preparation. We refer to the preliminary version [GLV] for details.
Computing subfields : Reverse of the primitive element problem (1993)
Daniel Lazard Annick, Daniel Lazard, Annick Valibouze
We describe an algorithm which computes all subfields of an effectively given finite algebraic extension. Although the base field can be arbitrary, we focus our attention on the rationals. This...
Computing subfields: Reverse of the primitive element problem (1993)
Daniel Lazard, Annick Valibouze
We describe an algorithm which computes all subfields of an effectively given finite algebraic extension. Although the base field can be arbitrary, we focus our attention on the rationals. This...
Symmetric Polynomials And Elimination (1987)
Marc Giusti, Greco Calcul, Formel No, Daniel Lazard, Annick Valibouze
this paper a general transformation of polynomials, and show that the classical deep relationships between the problems : (T ) transforming equations by a morphism (R) elementary elimination theory...