George Collins' discovery of Cylindrical Algebraic Decomposition (CAD) as a method for
Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major …

For several years now I have been teaching courses in computer algebra at the Universitat
Linz, the University of Delaware, and the Universidad de Alcala de Henares. In the summers …

We propose an efficient algorithm for computing triangular decompositions of algebraic
varieties. It is based on an incremental process and produces components in order of …

An efficient algorithm is presented for reconstructing a rational number from its residue
modulo a given integer. The algorithm is based on a double-digit version of Lehmer's …

Let F be a field and let f and g be polynomials in F [t] satisfying deg f> deg g. Recall that on
input of f and g the extended Euclidean algorithm computes a sequence of polynomials (si …

Le probleme de la factorisation d'opérateurs différentiels scalaires L=∑ ni= 0 ai (d/dx) i avec
les ai∈ Q (x), ou plus généralement de systemes différentiels linéaires homogenes Y= AY …

Shirayanagi and Sweedler proved that a large class of algorithms over the reals can be
modified slightly so that they also work correctly on fixed-precision oating-point numbers …

This paper presents an optimized method for factoring multivariate polynomials over
algebraic extension fields defined by an irreducible ascending set. The basic idea is to …

This study investigates the problem of computing the exact greatest common divisor of two
polynomials relative to an orthogonal basis, defined over the rational number field. The main …

We compare four fast methods for univariate polynomial GCD computation over an algebraic
number field. The first two are the modular method of Langemyr and McCallum (1987), and …