by Henk Nieland
The Research Institute for Applications of Computer Algebra RIACA was established in 1993 by the Mathematical Centre Foundation (to which CWI belongs), the Foundation Computer Algebra Nederland CAN - which is responsible for one of the twenty odd expertise centres founded in the late 1980s by the Dutch Research Council NWO - and the Gödel School GmbH for Symbolic Computation, Linz, Austria. RIACA functions as an international R&D centre for applications of computer algebra in science and technology.
Whereas the CAN foundation focuses on making available computing facilities, distributing software, providing information and support, consultancy, and education in The Netherlands, RIACA's first concern is to act as a research centre on an international scale. Contacts were established with several institutions (mainly in Europe), and one subgoal is to initiate cooperation on a larger scale within ERCIM. So far, attention focused on three projects: Human Interaction for Symbolic Computation (HISC), Computer Algebra and Geometrical Optics (CAGO), and a smaller `backup' project Algebra.
In HISC new research directions are explored to simplify the use of symbolic computation tools. In the long-term RIACA/CWI project ACELA a software environment is developed for writing interactive mathematical books. In particular work is underway on such a book on Lie algebras, offering full hypertext facilities and including some comprehension of the syntactical and semantical structure of the formulas. Research items in the project include:
Geometrical optics concerns the study of the behaviour of light rays before and after refraction or reflection at one or more surfaces, in particular the aberrations. There are several ways to study aberrations. In particular the method of eikonals and the closely related method of Lie transformations (a way of describing trajectories for any object, called `contact transformations' in the classical literature) can benefit from computer algebra support. Research in the CAGO project addressed, among other things, the following items:
A workshop on the subject attracted quite a number of opticians from practice.
Topics studied in the smaller Algebra project included:
return to the contents page