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Manuscript Title: ATENSOR - REDUCE program for tensor simplification.
Authors: V.A. Ilyin, A.P. Kryukov
Program title: ATENSOR
Catalogue identifier: ADDQ_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 96(1996)36
Programming language: Reduce.
Computer: HP9000/735.
Operating system: UNIX.
Word size: 32
Keywords: Tensor, Symmetry, Multiterm linear Identities, Dummy indices, Simplification, Permutation group, Reduce, Computer algebra.
Classification: 5.

Nature of problem:
Simplification of tensor expressions taking into account multiterm linear identities, symmetry relations and renaming dummy indices. This problem is important for the calculations in the gravity theory, differential geometry and other fields where indexed objects arise.

Solution method:
The group algebra technique for permutation group is applied to construct a canonical subspace and the effective algorithm for the corresponding projection.

Restrictions:
Computer operative memory is the severest restriction. Running time It depends on the problem. For example the expression contained contraction of Riemann tensor with antisymmetric tensor of second order epsilon mu nu * R mu nu lambda kappa - epsilon alpha beta * R lambda kappa beta alpha require about 82s CPU time on HP9000/735 with 8M for REDUCE.

References:
[1] V.A. Ilyin and A.P. Kryukov, in Proc. of the Int. Symp. of Symbolic. and Algebraic Computation (ISSAC'91), July 15-17, 1991, Bonn, Ed. by S. Watt, ACM Press (1991) 224.
[2] V.A. Ilyin and A.P. Kryukov, in "New Computing Techniques in Physics Research II", Proc. of AIHENP-92, Ed. by D. Perret-Gallix, World Scientific, Singapore (1992) 639-348.