The use of algebraic computing in general relativity

Abstract

In the past ten years various computer systems have been developed able to perform algebraic calculations. Unfortunately, the fact that there are ready to use, mostly easily attainable, computer languages and programs for manipulation of non-numerical algebraic data is often overlooked by potential users. Several investigations in general relativity have been performed using such systems in the past few years, and in many cases the calculations were of such a length that it would have been prohibitive to complete them without help from a computer. In the first part of the paper we discuss the type of calculations that can be performed by algebraic systems, and several of these relativistic calculations are very briefly reviewed by way of example. In the second and main part of the paper we present a comparative review of most of the leading algebraic systems. To make the comparison more concrete we have taken two calculations from relativity and programed them, as closely as possible, in the same way for all these systems. It is not necessary for a future user who wants to do the same kind of calculations for other metrics to learn the complete syntax of one of these languages. He can make a slight modification to one of our programs, which we are prepared to distribute.