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

## 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. sin^{2}x+cos^{2}x−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.

## Preview

Unable to display preview. Download preview PDF.

## References

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