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 …

We present an algorithm for meshing surfaces that is a simple adaptation of a greedy
“farthest point” technique proposed by Chew. Given a surface S, it progressively adds points …

The Hausdorff distance between two sets of curves is a measure for the similarity of these
objects and therefore an interesting feature in shape recognition. If the curves are algebraic …

The systematic development of efficient algorithms has become a key technology for all
kinds of ambitious and innovative computer applications. With major parts of algorithmic …

In this paper, we present a new method for computing the topology of curves defined as the
intersection of two implicit surfaces. The main ingredients are projection tools, based on …

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 …

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 …

The ability of feedforward neural networks to identify the number of real roots of univariate
polynomials is investigated. Furthermore, their ability to determine whether a system of …

Ion-exchange displacement chromatography has been adapted to centrifugal partition
chromatography. The use of an ionic liquid, benzalkonium chloride, as a strong anion …

Based on precomputed Sturm–Habicht sequences, discriminants and invariants, we classify,
isolate with rational points, and compare the real roots of polynomials of degree up to 4. In …