Algebraic Computing in General Relativity: Lecture Notes from the First Brazilian School on Computer Algebra Vol. 2

Based on lectures given at a summer school on computer algebra, the book provides a didactic description of the facilities available in three computor algebra systems - MAPLE, REDUCE and SHEEP - for performing calculations in the algebra-intensive field of general relativity. With MAPLE and REDUCE, two widespread great-purpose systems, the reader is shown how to use currently available packages to perform calculations with respect to tetrads, co-ordinate systems, and Poincare` gauge theory. The section on SHEEP and Stensor, being the first published book on these systems, explains how to use these systems to tackle a wide range of calculations with respect to tackle a wide range of calculations in general relativity, including the manipulation of indicial formulae. For the researcher in general relativity, the book therefore promises a wide overview of the facilities available in computer algebra to lessen the burden of the lengthy, error-prone calculations involved in their research.