ALGORITHMS FOR COMPUTER ALGEBRA CALCULATIONS IN SPACETIME .1. THE CALCULATION OF CURVATURE

We examine the relative performance of algorithms for the calculation of curvature in spacetime. The classical coordinate component method i s compared to two distinct versions of the Newman-Penrose tetrad appro ach for a variety of spacetimes, and distinct coordinates and tetrads for a given spacetime. Within the system GRTensorII, we find that ther e is no single preferred approach on the basis of speed. Rather, we fi nd that the fastest algorithm is the one that minimizes the amount of time spent on simplification. This means that arguments concerning the theoretical superiority of an algorithm need not translate into super ior performance when applied to a specific spacetime calculation. In a ll cases it is the simplification strategy which is of paramount impor tance. An appropriate simplification strategy can change an intractabl e problem into one which can be solved essentially instantaneously.