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.

SHEEP: A computer algebra system for general relativity: An overview of SHEEP; Using SHEEP and CLASSI; Using CLASSI to classify metrics; The internals of SHEEP; Packages for special occasions; STENSOR; REDUCE: in general relativity and Poincare gauge theory: Geometrical preliminaries; Calculations on coordinate bases; Anholonomic frames; The exterior calculus package EXCALC; The Poincare gauge theory; MAPLE: applications to general relativity: Introduction; Computation of the connection and the curvature; The Petrov classification of the Weyl tensor; Computer algebra aided integration of field equations with the NP package; Bibliography; Index.