Computer Algebra Software for Scientific Applications

Abstract

Computer Algebra may be pursued within a wide range of sophistication. At the lowest level there is the casual user who applies some of the system facilities e.g. to evaluate an integral, to sum a series or to find the solution of a differential equation. For this kind of applications it is usually sufficient to read through the manual which is provided by the system developer. After a while it is realized that the machine might perform additional tasks for which there are no system functions available. So the user starts writing his own special purpose package. As the time goes on additional facilities are added which means that the size of the software keeps growing. That works fine for a while until a critical size of about one thousand lines of code is reached. It suddenly turns out that the time which has to be spent for debugging or adding a new feature has increased to an unacceptable amount. Even worse, that process resembles more and more a vicious circle where a simple change in one part of the program causes unexpected effects in completely different regions and a superficial repair often makes things even worse. While spending most of the time for implementing new algorithms for new tasks, somehow the survey over the organization of the package got lost. At that point the astute user will realize that he has reached a threshold where qualitatively new tools for further proceeding are needed. To provide these tools is the realm of software engineering.