ISSAC is a yearly international symposium that provides an opportunity to learn of new developments and to present original research results in all areas of symbolic mathematical computation.

To support this goal Three Tutorial Courses on important topics in symbolic and algebraic computation will be held by leading experts on

at the following times:

D. Duval H.J. Stetter M. Bronstein

7:30 - 10:30 11:00 - 14:00 15:00 - 18:00

preceeding the symposium proper.

The 3-hour courses are aimed at students and researchers in mathematics and computer science, as well as scientists in application areas who want to get a thorough introduction to a topic of current interest in symbolic computation. They are presented by leading experts in the field. Each participant will receive a set of printed course notes.

Fees:

1 Tutorial 2 Tutorials 3 Tutorials

DM 80 (students DM 60) DM 150 (students DM 100) DM 200 (students DM 130)

Abstracts of the Tutorial Courses:

Around Symbolic Integration
Manuel Bronstein
INRIA
email: Manuel.Bronstein@sophia.inria.fr
http://www.inria.fr/safir/WHOSWHO/Manuel.Bronstein/bronstein-fr.html

This tutorial is an introduction to algorithms for computing symbolic antiderivatives. Our goal is to describe the main lines of the Risch algorithm with recent enhancements to real integrands. Topics covered: integration of rational functions, differential fields and Liouville's Theorem, integration of transcendental elementary functions (log, exp, tan and arctan cases), the Risch differential equation, integration of algebraic functions. The algorithmic aspects will be stressed, while the mathematical background will be kept to a minimum.

Towards ``soft'' Typing in Computer Algebra Systems
Dominique Duval
Université de Limoges
email: dominique.duval@unilim.fr
http://www.unilim.fr/~laco/

The aim of this tutorial is to illustrate how ``soft'' (or ``approximate'') type specifications can be used in Computer Algebra as a frame for exact computations.

Recent results prove that a specification can be defined in a finite number of steps by an ``approximation'' method. The initial specification may be restricted to the main features, at the cost of some errors in less significant details. These errors may be corrected later during the approximation process, ending up with an exact type specification. These results rely on sketch theory.

First, sketch theory is presented by means of examples of type specifications: either usual types, like booleans and natural numbers, or less usual ones, like algebraic numbers.

Then ``soft'' specifications are introduced, together with the main features of the "approximation" process, on examples involving error handling, partiality, overloading, subsorts, global variables.

Sketch theory was introduced by C. Ehresmann in the sixties, and the work presented here is done in collaboration with J.-C. Reynaud, C. Lair, H. Kirchner, among others.

Interaction between Numerical Analysis and Computer Algebra
Hans J. Stetter
Technical University Vienna
email: stetter@uranus.tuwien.ac.at

The concepts and algorithms of classical polynomial algebra assume exact data and exact computation; this restricts their computer implementation to coefficients from finite fields or the rationals (with finite extensions) and the operations to integer or rational arithmetic. On the other hand, many desirable results (like zeros of polynomial systems) are not rational for rational data so that they can only be computed approximately in any case; furthermore, in tasks modelling real-life problems, some data are usually known only with a limited (often low) accuracy. The tutorial will show how these facts can be accomodated in computer algebra.

To deal properly with approximate data and approximate computation, we introduce a rudimentary topology derived from that of the complex number field to which we will restrict our considerations. This will require a reconsideration of some classical concepts of computer algebra which depend discontinuously on their data (e.g. Gr"obner bases). Furthermore, we will pay attention to the stability of our algorithms w.r.t. small intermediate perturbations. A stable algorithm for the approximate computation of results which are meaningful for data with limited accuracy can directly be executed in floating-point arithmetic without harm.

We will explicitly develop this principal approach (which parallels the well-known successful approach of numerical linear algebra) in connection with the task of computing the zeros of multivariate systems of polynomial equations with complex coefficients. Attendants of the tutorial should have some basic knowledge in computer algebra and in (numerical) linear algebra.

For further information contact the tutorial chair:

Laureano Gonzalez-Vega,
Departamento de Matematicas, Estadistica y Computacion,
Facultad de Ciencias, Universidad de Cantabria,
Avenida de los Castros s/n, Santander 39071, Cantabria, Spain
email: gvega@matesco.unican.es