1. Introduction

The motivation behind GiNaC derives from the observation that most present day computer algebra systems (CAS) are linguistically and semantically impoverished. Although they are quite powerful tools for learning math and solving particular problems they lack modern linguistic structures that allow for the creation of large-scale projects. GiNaC is an attempt to overcome this situation by extending a well established and standardized computer language (C++) by some fundamental symbolic capabilities, thus allowing for integrated systems that embed symbolic manipulations together with more established areas of computer science (like computation-intense numeric applications, graphical interfaces, etc.) under one roof.

The particular problem that led to the writing of the GiNaC framework is still a very active field of research, namely the calculation of higher order corrections to elementary particle interactions. There, theoretical physicists are interested in matching present day theories against experiments taking place at particle accelerators. The computations involved are so complex they call for a combined symbolical and numerical approach. This turned out to be quite difficult to accomplish with the present day CAS we have worked with so far and so we tried to fill the gap by writing GiNaC. But of course its applications are in no way restricted to theoretical physics.

This tutorial is intended for the novice user who is new to GiNaC but already has some background in C++ programming. However, since a hand-made documentation like this one is difficult to keep in sync with the development, the actual documentation is inside the sources in the form of comments. That documentation may be parsed by one of the many Javadoc-like documentation systems. If you fail at generating it you may access it from the GiNaC home page. It is an invaluable resource not only for the advanced user who wishes to extend the system (or chase bugs) but for everybody who wants to comprehend the inner workings of GiNaC. This little tutorial on the other hand only covers the basic things that are unlikely to change in the near future.