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Group-Theoretic Approach For Symbolic Tensor Manipulation

Author

Listed:
  • L. R. U. MANSSUR

    (Laboratório Nacional de Computação Científica, Av. Getúlio Vargas, 333 Petrópolis, RJ, Brazil. Cep 25651-070, Brazil)

  • R. PORTUGAL

    (Laboratório Nacional de Computação Científica, Av. Getúlio Vargas, 333 Petrópolis, RJ, Brazil. Cep 25651-070, Brazil)

  • B. F. SVAITER

    (Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina, 110 Rio de Janeiro, RJ, Brazil. Cep 22460-320, Brazil)

Abstract

We describe how Computational Group Theory provides tools for manipulating indexed objects (tensors, spinors, and so on) in explicit index notation. In particular, we present algorithms that put tensors with free and dummy indices obeying permutation symmetries into the canonical form. The method is based on algorithms for determining canonical double coset representatives of subgroups of the symmetric group. The complexity of the algorithms is polynomial on the number of indices in practical applications and allows one to address the simplification of tensor expressions with hundreds of indices, going beyond what is needed in practical applications.

Suggested Citation

  • L. R. U. Manssur & R. Portugal & B. F. Svaiter, 2002. "Group-Theoretic Approach For Symbolic Tensor Manipulation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(07), pages 859-879.
    • Handle: RePEc:wsi:ijmpcx:v:13:y:2002:i:07:n:s0129183102004571
    DOI: 10.1142/S0129183102004571
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