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A system for automatic generation of tensor algorithms and indicial tensor calculus, including substitution of sums

  • 7. Systems
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Book cover Symbolic and Algebraic Computation (EUROSAM 1979)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 72))

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Abstract

SHEEP is an algebraic system written by I. Frick [1,2] that is specialized for manipulating components of tensors. On top of this language another system has been built treating a new data type "indicial formula" representing formulas containing tensors or spinors with symbolic (letter) indices. Such formulas can be used in two ways:

1. There are routines for manipulating indicial formulas, such as evaluation, differentiation, simplification using symmetries, substitution of products and sums, etc.

Also scalar sums can be efficiently substituted, e.g. sin2x+cos2x−1=>0

2. There is a compiler which for any indicial formula generates a corresponding program that actually performs the contractions etc. indicated in the formula. Thus the components of a tensor can be computed as soon as an indicial formula for its computation has been typed.

Terminology adopted from [6]

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References

  1. Frick, I 1977 "The Computer Algebra System SHEEP, what it can and cannot do in General Relativity".

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  2. Frick, I 1977 "SHEEP, users guide", preprint. Inst. of Theor. Physics, Univ. of Stockholm.

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  3. Hörnfeldt, L 1976 NIGSAM:11 "A Tensor Compiler".

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  4. Hörnfeldt, L 1977 NIGSAM:12 "Indicial and componentwise tensor calculus with computer"

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  5. Hörnfeldt, L 1978 Manual

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  6. Bogen R. and Pavelle R. "Indicial Tensor Manipulation on MACSYMA" Lett. Math. Phys. 1977

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  7. Pereira, M J. Math. Phys., Vol. 15, No. 3, March 1974

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  8. Schouten, J A "Ricci-Calculus" Springer-Verlag

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  9. Anderson, J. N.Y. Private communication

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Authors and Affiliations

  1. Institute of Theoretical Physics, University of Stockholm, Vanadisv. 9, S-113 46, Stockholm, Sweden

    Lars Hörnfeldt

Authors
  1. Lars Hörnfeldt
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Edward W. Ng

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© 1979 Springer-Verlag Berlin Heidelberg

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Hörnfeldt, L. (1979). A system for automatic generation of tensor algorithms and indicial tensor calculus, including substitution of sums. In: Ng, E.W. (eds) Symbolic and Algebraic Computation. EUROSAM 1979. Lecture Notes in Computer Science, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09519-5_80

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  • DOI: https://doi.org/10.1007/3-540-09519-5_80

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09519-4

  • Online ISBN: 978-3-540-35128-3

  • eBook Packages: Springer Book Archive

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