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...
Strong bihomogeneous Bézout theorem and degree bounds for algebraic optimization (2008)
Let (f1,..., fs) be a polynomial family in Q[X1,..., Xn] (with s ≤ n − 1) of degree bounded by D, generating a radical ideal, and defining a smooth algebraic variety V ⊂ C n. Consider a generic...
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...
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...
Strong bi-homogeneous B\'{e}zout theorem and its use in effective real algebraic geometry (2006)
Din, Mohab Safey El, Trebuchet, Philippe
Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebraic variety V....
Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry (2006)
Safey El Din, Mohab, Trebuchet, Philippe
Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebraic variety V....
Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry (2006)
Safey El Din, Mohab, Trebuchet, Philippe
Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebraic variety V....
Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry (2006)
Safey El Din, Mohab, Trebuchet, Philippe
Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebraic variety V....
Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry (2006)
Safey El Din, Mohab, Trebuchet, Philippe
Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebraic variety V....
Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry (2006)
Safey El Din, Mohab, Trebuchet, Philippe
Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebraic variety V....
Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry (2006)
Safey El Din, Mohab, Trebuchet, Philippe
Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebraic variety V....
Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry (2006)
Safey El Din, Mohab, Trebuchet, Philippe
Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebraic variety V....
Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry (2006)
Safey El Din, Mohab, Trebuchet, Philippe
Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebraic variety V....
Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry (2006)
Safey El Din, Mohab, Trebuchet, Philippe
Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebraic variety V....
On circular cylinders by four or five points in space (2003)
Olivier Devillers, Bernard Mourrain, Franco P. Preparata, Philippe Trebuchet
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...
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...
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...
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...