Algebraic curves and surfaces are an old topic of geometric and algebraic investigation.
They have found applications for instance in ancient and modern architectural designs, in …

The subject of this book is the solution of polynomial equations, that is, systems of
(generally) non-linear algebraic equations. This study is at the heart of several areas of …

With a software library included, this book provides an elementary introduction to polynomial
elimination in practice. The library Epsilon, implemented in Maple and Java, contains more …

In this paper, we investigate some topics around the closed image S of a rational map λ
given by some homogeneous elements f1,…, fn of the same degree in a graded algebra A …

The concept of a μ-basis was introduced in the case of parametrized curves in 1998 and
generalized to the case of rational ruled surfaces in 2001. The μ-basis can be used to …

We unveil in concrete terms the general machinery of the syzygy-based algorithms for the
implicitization of rational surfaces in terms of the monomials in the polynomials defining the …

We describe an algorithm for implicitizing rational hypersurfaces with at most a finite number
of base points, based on a technique described in Busé, Laurent, Jouanolou, Jean-Pierre …

The surface/surface intersection technique serves as one of the most fundamental functions
in modern Computer Aided Design (CAD) systems. Despite the long research history and …

We introduce and study a new implicit representation of rational Bézier curves and surfaces
in the 3-dimensional space. Given such a curve or surface, this representation consists of a …

A rational parametrization of an algebraic curve (resp. surface) establishes a rational
correspondence of this curve (resp. surface) with the affine or projective line (resp. affine or …