Computation of the connection and the curvature

Abstract One of the earliest general relativity calculations performed with the aid of computer algebra was the computation of the Christoffel symbols and the components of the curvature tensor, Weyl tensor, Ricci tensor and Einstein tensor from the components of a given covariant metric tensor 9ij in some coordinate system. These elementary calculations provide a good illustration of the importance of the choice of algorithms for computer algebra programs in general relativity, a consideration that often seems to have been overlooked. Programs for performing the above calculations were usually based on standard formulas given in general relativity or tensor calculus textbooks. An examination of these formulas reveals that there is a variety of ways of computing the curvature tensor for example.