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Overview of Computer Algebra in Relativity

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Relativity and Scientific Computing

Summary

Over the last few years, the use of computer algebra has become increasingly widespread in many areas of science, mathematics, and engineering. These two lectures are intended to give an idea of the range of computer algebra tools available to the relativist and the kind of problems to which they can be applied. The first lecture deals with the main general-purpose systems in use today, while the second covers systems and packages more specific to general relativity. In each case, the features and design philosophies are highlighted and the areas of application indicated.

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References

  1. Symbolic Mathematical Computation Information Center, Kent State University, Kent, Ohio, 44242 USA. WWW home page http://symbolicnet.mcs.kent.edu/

    Google Scholar 

  2. Computer Algebra Nederland, Kruislaan 419, 1098 VA Amsterdam, The Netherlands. WWW home page http://www.can.nl/cain.html

    Google Scholar 

  3. Macsyma Inc, 20 Academy Street, Arlington, MA 02174–6436, USA. WWW home page http://www.macsyma.com/

    Google Scholar 

  4. A.C. Hearn, RAND, 1700 Main Street, P.O. Box 2138, Santa Monica CA 90407–2138, USA. WWW home pages http://www.zib-berlin.de/Symbolik/reduce/ and http://www.rrz.uni-koeln.de/REDUCE/

    Google Scholar 

  5. Wolfram Research Inc, 100 Trade Center Drive, Champaign, IL 61820–7237, USA. WWW home page http://www.wri.com/

    Google Scholar 

  6. NAG Ltd, Wilkinson House, Jordan Hill Road, Oxford, OX2 8DR, UK. WWW home page http://www.nag.co.uk/symbolic/AX.html/

    Google Scholar 

  7. Waterloo Maple Software, 450 Phillip Street, Waterloo, Ontario, Canada N2L 5J2. WWW home page http://www.maplesoft.on.ca/

    Google Scholar 

  8. Buchberger, B., Loos, R. (1983): Algebraic simplification. In Buchberger, B.,Collins, G.E., Loos, R. (eds): Computer Algebra: Symbolic and Algebraic Computation (2nd edition), pp. 11–44. Springer, Wien

    Google Scholar 

  9. Frick, I. (1977): The computer algebra system SHEEP, what it can and cannot do in general relativity. University of Stockholm Institute of Theoretical Physics Report 77–14. Available from http://www.maths.qmw.ac.uk/hyperspace/

    Google Scholar 

  10. MacCallum, M.A.H., Skea, J.E.F. (1994): SHEEP: A computer algebra system for general relativity. In [28], 1–172

    Google Scholar 

  11. Skea, J.E.F. (1987): RSHEEP User guide. QMW, London

    Google Scholar 

  12. Harper, J.F., Dyer, C.C. (1994): Tensor algebra with REDTEN: A user manual. University of Toronto, Toronto. Available from http://www.scar.utoronto.ca/~harper/redten.html

    Google Scholar 

  13. Zhytnikov, V.V. (1994): GRG version 3.1. Computer algebra system for differential geometry, gravitation and field theory. National Central University, Chung-Li, Taiwan

    Google Scholar 

  14. Tertychniy, S.I., Obukhova, I.G. (1995): Computer algebra system for calculations in gravitation theory. In Francaviglia, M. (ed.): Abstracts of GR14, the 14th international conference on general relativity and gravitation ,p. A.184. SIGRAV-GR14, Turin

    Google Scholar 

  15. Soleng, H.H. (1995): Cartan: a Mathematica package for tensor computations. Electronic archive Los Alamos, gr-qc/9502035 (program files for Unix and documentation)

    Google Scholar 

  16. Castellví, P., Jaén, X., Llanta, E. (1994): TTC: Symbolic tensor and exterior calculus. Computers in Physics 8, 360–367. Available from ftp://pinet.aip.org/cip/cip_sourcecode/llanta.mj.94

    Article  ADS  Google Scholar 

  17. Parker, L., Christensen, S. (1994): Math Tensor: A system for doing tensor analysis by computer. Addison-Wesley, New York

    Google Scholar 

  18. Musgrave, P., Pollney, D., Lake, K. (1994): GRTensor II for Maple V release 3. Queen’s University, Kingston. Available from http://astro.queensu.ca/~grtensor/GRHome.html

    Google Scholar 

  19. Krasinski, A. (1993): The program ORTOCARTAN for algebraic calculations in relativity. Gen. Rel. Grav. 25, 165–177

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Kadlecsik, J. (1992): Tensor manipulation package for general relativity calculations. Preprint KFKI-1992–05/B+M, KFKI, Budapest. Available from ftp://ftp.kfki.hu/pub/local/riccir/

    Google Scholar 

  21. Klioner, S.A. (1995): EinS: a Mathematica package for tensorial calculations in astronomical applications of relativistic gravity theories. In Francaviglia, M. (ed.): Abstracts of GR14, the 14th international conference on general relativity and gravitation ,p. A.182. SIGRAV-GR14, Turin

    Google Scholar 

  22. Zizza, F. (1994): Differential forms package. Available from http://www.wri.com/MathSource under Applications/Mathematics/Pure

    Google Scholar 

  23. Lee, J. (1992): RICCI: a Mathematica package for doing tensor calculations in differential geometry. Available from http://www.wri.com/MathSource/ under Applications/Mathematics/Pure

    Google Scholar 

  24. Lang, J. (1993): Contributions to the study of general relativistic shear-free perfect fluids. An approach involving Cartan’s equivalence method, differential forms and symbolic computation. PhD thesis, University of Waterloo, Waterloo

    Google Scholar 

  25. Hornfeldt, L.(1988): STENSOR Reference manual and user guide. Preprint Stockholm University, Stockholm. Available from lh@vand.physto.se

    Google Scholar 

  26. McCrea, J.D. (1994): REDUCE in relativity and Poincaré gauge theory. In [28], 173–263 Available from http://www.maths.qmw.ac.uk/hyperspace/

    Google Scholar 

  27. Grebot, G., (1995): Automatic symmetry investigation in General Relativity: CLASSYM, an utility for CRACK. Preprint QMW, London. Available from ftp://euclid.maths.qmw.ac.uk/pub/classym/

    Google Scholar 

  28. Rebouças, M.J., Roque W.L. (eds.) (1994): Algebraic computing in general relativity (Proceedings of the first Brazilian school on computer algebra), vol. 2. Oxford University Press, Oxford

    Google Scholar 

  29. Hereman, W. (1995): Symbolic software for Lie symmetry analysis. In Ibragimov, N.N. (ed.): CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 3: New Trends in Theoretical Developments and Computational Methods ,pp. 367–413. CRC Press, Boca Raton, Florida

    Google Scholar 

  30. McLenaghan, R.G. (1994): MAPLE applications to general relativity. In [28], 265–354

    Google Scholar 

  31. Musgrave,P., Lake, K. (1994): The regularity of static spherically cylindrically and plane symmetric spacetimes at the origin. Gen. Rel. Grav. 26, 917–925

    Article  MathSciNet  ADS  Google Scholar 

  32. Carminati, J., McLenaghan, R.G. (1991): Algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space. J. Math. Phys. 32, 3135–3140

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. Roman, T.A. (1994): The inflating wormhole: a Mathematica animation. Computers in Physics 8, 480–487

    Article  ADS  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Algorithms and Scientific Computing, GMD - German National Research Center for Information Technology, St. Augustin, Germany

    David Hartley

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  1. David Hartley
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Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, D-50923, Köln, Germany

    Friedrich W. Hehl  & Roland A. Puntigam  & 

  2. Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Tübingen, Germany

    Hanns Ruder

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© 1996 Springer-Verlag Berlin Heidelberg

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Hartley, D. (1996). Overview of Computer Algebra in Relativity. In: Hehl, F.W., Puntigam, R.A., Ruder, H. (eds) Relativity and Scientific Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95732-1_9

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  • DOI: https://doi.org/10.1007/978-3-642-95732-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-95734-5

  • Online ISBN: 978-3-642-95732-1

  • eBook Packages: Springer Book Archive

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