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SHEEP: A computer algebra system for general relativity. (English) Zbl 0829.53057
MacCallum, M. A. H. (ed.) et al., Algebraic computing in general relativity. Lecture notes from the first Brazilian school on computer algebra, held in Rio de Janeiro, Brazil, July 24-August 11, 1989. Volume 2. Oxford: Oxford University Press. Oxford Science Publications. 1-172 (1994).
The lecture notes contain a detailed description of a computer algebra system for general relativity based on the package SHEEP (Frick 1977), whose 1982 year version is written in LISP.
Chapter 1 contains a historical overview, basic concepts of LISP, some calculations (coordinate frame) using the package CLASSI (Åman 1987) which extends SHEEP. In Chapters 2, 4 the operators and procedures of SHEEP and CLASSI are described. Chapter 3 describes the use of CLASSI for problems of classification and equivalence of metrics in general relativity. The given algorithms are based on Cartan’s structure equations and Newman-Penrose formalism. Results, examples and problems for the future development of the package are discussed. Chapter 5 is devoted to the packages MATTER (E. Sviestins), GFRAME and VFRAME (G. Joly 1986) for non-constant frames, which are based on SHEEP and best used in CLASSI, and provides a large number of tensor and user input. Chapter 6 is devoted to the package STENSOR (L. Hörnfeldt), which is based on SHEEP, for handling “indicial” tensor manipulations.
All chapters contain exercises and verbatim sessions.
For the entire collection see [Zbl 0816.00033].

53Z05 Applications of differential geometry to physics
83-08 Computational methods for problems pertaining to relativity and gravitational theory
68W30 Symbolic computation and algebraic computation