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

  • Lars Hörnfeldt
7. Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 72)


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.


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  1. 1.
    Frick, I 1977 "The Computer Algebra System SHEEP, what it can and cannot do in General Relativity".Google Scholar
  2. 2.
    Frick, I 1977 "SHEEP, users guide", preprint. Inst. of Theor. Physics, Univ. of Stockholm.Google Scholar
  3. 3.
    Hörnfeldt, L 1976 NIGSAM:11 "A Tensor Compiler".Google Scholar
  4. 4.
    Hörnfeldt, L 1977 NIGSAM:12 "Indicial and componentwise tensor calculus with computer"Google Scholar
  5. 5.
    Hörnfeldt, L 1978 ManualGoogle Scholar
  6. 6.
    Bogen R. and Pavelle R. "Indicial Tensor Manipulation on MACSYMA" Lett. Math. Phys. 1977Google Scholar
  7. 7.
    Pereira, M J. Math. Phys., Vol. 15, No. 3, March 1974Google Scholar
  8. 8.
    Schouten, J A "Ricci-Calculus" Springer-VerlagGoogle Scholar
  9. 9.
    Anderson, J. N.Y. Private communicationGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Lars Hörnfeldt
    • 1
  1. 1.Institute of Theoretical PhysicsUniversity of StockholmStockholmSweden

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