Algebraic computing in general relativity : lecture notes from the First Brazilian School on Computer Algebra

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書誌事項

Algebraic computing in general relativity : lecture notes from the First Brazilian School on Computer Algebra

M.A.H. MacCallum ... [et al.]

（Lecture notes from the First Brazilian School on Computer Algebra, v. 2）

Clarendon Press , Oxford University Press, 1994

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注記

Includes bibliographical references and indexes

内容説明・目次

内容説明

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.

目次

  • 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.

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