Algebraic methods for counting Euclidean embeddings of rigid graphs (2009)
Emiris, Ioannis Z., Tsigaridas, Elias P., Varvitsiotis, Antonios
The study of (minimally) rigid graphs is motivated by numerous applications, mostly in robotics and bioinformatics. A major open problem concerns the number of embeddings of such graphs, up to rigid...
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...
SYNAPS: A LIBRARY FOR DEDICATED APPLICATIONS IN SYMBOLIC NUMERIC COMPUTING (2009)
Bernard Mourrain, Jean-pascal Pavone, Philippe Trebuchet, Elias P. Tsigaridas, Julien Wintz
Abstract. 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...
Bounds on eigenvalues and singular values of interval matrices (2009)
Hladik, Milan, Daney, David, Tsigaridas, Elias P.
We study bounds on eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce as-sharp-as-possible bounds. We consider two cases: general (unsymmetric) and...
Bounds on eigenvalues and singular values of interval matrices (2009)
Hladik, Milan, Daney, David, Tsigaridas, Elias P.
We study bounds on eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce as-sharp-as-possible bounds. We consider two cases: general (unsymmetric) and...
Univariate Algebraic Kernel and Application to Arrangements (2009)
Lazard, Sylvain, Peñaranda, Luis, Tsigaridas, Elias P.
Solving polynomials and performing operations with real algebraic numbers are critical issues in geometric computing, in particular when dealing with curved objects. Moreover, the real roots need to...
Univariate Algebraic Kernel and Application to Arrangements (2009)
Lazard, Sylvain, Peñaranda, Luis, Tsigaridas, Elias P.
Solving polynomials and performing operations with real algebraic numbers are critical issues in geometric computing, in particular when dealing with curved objects. Moreover, the real roots need to...
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 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...
A filtering method for the interval eigenvalue problem (2009)
Hladik, Milan, Daney, David, Tsigaridas, Elias P.
We consider the general problem of computing intervals that contain the real eigenvalues of interval matrices. Given an outer estimation of the real eigenvalue set of an interval matrix, we propose a...
A filtering method for the interval eigenvalue problem (2009)
Hladik, Milan, Daney, David, Tsigaridas, Elias P.
We consider the general problem of computing intervals that contain the real eigenvalues of interval matrices. Given an outer estimation of the real eigenvalue set of an interval matrix, we propose a...
On the topology of planar algebraic curves (2009)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and...
Univariate Algebraic Kernel and Application to Arrangements (2009)
Lazard, Sylvain, Mariano Penaranda, Luis, Tsigaridas, Elias P.
Abstract. We present a cgal-based univariate algebraic kernel, which provides certi
On the topology of planar algebraic curves (2009)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and...
Univariate Algebraic Kernel and Application to Arrangements (2009)
Lazard, Sylvain, Mariano Penaranda, Luis, Tsigaridas, Elias P.
Abstract. We present a cgal-based univariate algebraic kernel, which provides certi
ALGEBRAIC AND NUMERICAL ALGORITHMS 1 (2008)
Ioannis Z. Emiris, Elias P. Tsigaridas
Arithmetic manipulation with matrices and polynomials is a common subject for algebraic (or symbolic) and numerical computing. Typical computational problems in these areas include the solution of a...
Thème Sym, Elias P. Tsigaridas, Ioannis Z. Emiris, Projet Geometrica
apport de recherche SN 0249-6399 ISRN INRIA/RR--6059--FR+ENG
Thème Sym, Elias P. Tsigaridas, Ioannis Z. Emiris, Projet Geometrica
apport de recherche SN 0249-6399 ISRN INRIA/RR--????--FR+ENG
Comparing real algebraic numbers of small (2008)
Ioannis Z. Emiris, Elias P. Tsigaridas
Abstract. We study polynomials of degree up to 4 over the rationals or a computable real subfield. Our motivation comes from the need to evaluate predicates in nonlinear computational geometry...
Real algebraic numbers and polynomial systems of small degree ⋆ (2008)
Ioannis Z. Emiris, Elias P. Tsigaridas
We present exact and complete algorithms based on precomputed Sturm-Habicht sequences, discriminants and invariants, that classify, isolate with rational points and compare the real roots of...
Computations with one and two real algebraic numbers (2008)
Ioannis Z. Emiris, Elias P. Tsigaridas
We present algorithmic and complexity results concerning computations with one and two real algebraic numbers, as well as real solving of univariate polynomials and bivariate polynomial systems with...
Abstract The Predicates for the Voronoi Diagram of Ellipses ∗ (2008)
Ioannis Z. Emiris, Elias P. Tsigaridas, George M. Tzoumas
This paper examines the computation of the Voronoi diagram of a set of ellipses in the Euclidean plane. We propose the first complete algorithms, under the exact computation paradigm, for the...
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
An Algorithm for the Real Interval Eigenvalue Problem (2008)
Hladik, Milan, Daney, David, Tsigaridas, Elias P.
In this paper we present an algorithm for approximating the range of the real eigenvalues of interval matrices. Such matrices could be used to model real-life problems, where data sets suffer from...
An Algorithm for the Real Interval Eigenvalue Problem (2008)
Hladik, Milan, Daney, David, Tsigaridas, Elias P.
In this paper we present an algorithm for approximating the range of the real eigenvalues of interval matrices. Such matrices could be used to model real-life problems, where data sets suffer from...
On The Topology of Planar Algebraic Curves (2008)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We introduce a method to compute the topology of planar algebraic curves. The curve may not be in generic position and may have vertical asymptotes. The algebraic tools are rational univariate...
On The Topology of Planar Algebraic Curves (2008)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We introduce a method to compute the topology of planar algebraic curves. The curve may not be in generic position and may have vertical asymptotes. The algebraic tools are rational univariate...
A CGAL-based Univariate Algebraic Kernel and Application to Arrangements (2008)
Lazard, Sylvain, Mariano Penaranda, Luis, Tsigaridas, Elias P.
Solving univariate polynomials and operations with real algebraic numbers are critical in geometric computing with curved objects. Moreover, the real roots need to be computed in a certified way in...
A CGAL-based Univariate Algebraic Kernel and Application to Arrangements (2008)
Lazard, Sylvain, Mariano Penaranda, Luis, Tsigaridas, Elias P.
Solving univariate polynomials and operations with real algebraic numbers are critical in geometric computing with curved objects. Moreover, the real roots need to be computed in a certified way in...
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...
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...
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...
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...
Ioannis Z. Emiris, George M. Tzoumas, Elias P. Tsigaridas
We present a C++ open-source implementation of an incremental algorithm for the computation of the Voronoi diagram of ellipses in the Euclidean plane. This is the first complete implementation, under...
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)...
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)...
Tsigaridas. Real Algebraic Numbers: Complexity Analysis and Experimentation (2006)
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...
Algebraic Algorithms and Applications to Geometry (2006)
Abstract. Real algebraic numbers are the real numbers that are real roots of univariate polynomials with integer coefficients. We study exact algorithms, from a theoretical and an implementation...
Ioannis Z. Emiris, Elias P. Tsigaridas, Ioannis Z. Emiris, Elias P. Tsigaridas
Project co-funded by the European Commission within FP6 (2002–2006) under contract nr. IST-006413 Robust operations on small polynomial systems
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...
On the complexity of real root isolation using Continued Fractions (2006)
Elias P. Tsigaridas, Ioannis Z. Emiris
We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algebraic numbers. One...
Tsigaridas. Minkowski decomposition of convex lattice polygons (2005)
Ioannis Z. Emiris, Elias P. Tsigaridas
Summary. A relatively recent area of study in geometric modelling concerns toric Bézier patches. In this line of work, several questions reduce to testing whether a given convex lattice polygon can...
Real solving of bivariate polynomial systems (2005)
Ioannis Z. Emiris, Elias P. Tsigaridas
Abstract. We propose exact, complete and efficient methods for 2 problems: First, the real solving of systems of two bivariate rational polynomials of arbitrary degree. This means isolating all...
Computations with real algebraic numbers of degree up to 4 (2004)
Elias P. Tsigaridas, Ioannis Z. Emiris
up to 4
Comparison Of Fourth-Degree Algebraic Numbers And Applications To Geometric Predicates (2000)
Ioannis Z. Emiris, Ioannis Z. Emiris, Elias P. Tsigaridas, Elias P. Tsigaridas
We present algorithms for the exact comparison of the real roots of two polynomials of degree 4. The algorithm precomputes Sturm sequences and isolating intervals for the representation of the roots...