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A sum-substitutor used as trigonometric simplifier

  • L. Hornfeldt
5. Applications I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 144)

Abstract

A program is presented that substitutes arbitrary sums. Among other applications, this sum-substitutor has been set up to exploit the relation:
$$sin^2 + \cos ^2 - 1 = 0$$
(1)
which it does more intelligently than previous programs, acheaving close to maximal reduction in size (see examples below).

The sumsubstitutor opens the new prospect of "Inverse evaluation" -that is recombina- tion of objects into higher, composed ones. This could greately compress otherwise unmanageably huge output swell from the ever larger machines. The program is a part of STENSOR [3,4,5,6,10] running on the algebraic systems MACSYMA [11] and SHEEP [1,2].

Keywords

Scalar Part Numeric Coefficient Minimal Form Large Machine Previous Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Frick, I 1977 "The Computer Algebra System SHEEP, what it can and cannot do in General Relativity". Preprint.Google Scholar
  2. 2.
    Frick, I 1977 "SHEEP, users guide", preprint. Inst. of Theor. Physics, Univ. of Stockholm.Google Scholar
  3. 3.
    Hornfeldt, L 1976 NIGSAM:11 "A Tensor Compiler".Google Scholar
  4. 4.
    Hornfeldt, L 1977 NIGSAM:12 "Indicial and componentwise tensor calculus with computer"Google Scholar
  5. 5.
    Hornfeldt, L 1977 "Tensor Calculus..." GR8 Proceedings.Google Scholar
  6. 6.
    Hornfeldt, L 1979 "A System for Tensor.. Substitution of Sums" Springer-Verlag, Lecture Notes in Computer Science, vol 72.Google Scholar
  7. 7.
    Stoutemyer, D. 1977 Macsyma users conference, Proceedings.Google Scholar
  8. 8.
    Bahr, K. Private communication (FORMAC).Google Scholar
  9. 9.
    Hearn, T. Private communication (REDUCE).Google Scholar
  10. 10.
    Hornfeldt, and R. Pavelle/Hornfeldt 1980 GR9 proceedings.Google Scholar
  11. 11.
    MACSYMA is the algebraic manipulation system of the Laboratory for Computer Science, Massachusetts Institute of Technology.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • L. Hornfeldt
    • 1
  1. 1.Institute of Theoretical PhysicsUniversity of StockholmStockholmSweden

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