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On the data structure straight-line program and its implementation in symbolic computation

Author

Listed:
  • Castaño, Bonifacio
  • Heintz, Joos
  • Llovet, Juan
  • Martínez, Raquel

Abstract

In this paper we describe a recent computer implementation (the PASCAL program TERA) of a well known Computer Algebra algorithm. The particularity of this implementation consists in the fact that it is based on a special abstract data type, namely that of a directed acyclic graph (DAG) which is of seldom use in Computer Algebra packages. This data type is particularly adapted to the algorithmic problem which we are considering in this paper: the computation of the of two multivariate polynomials. This task is solved by an algorithmic approach based on linear recurring sequences (see [F.R. Gantmacher, The Theory of Matrices, vol. 1/2, Chelsea, New York, 1959; R. Sendra, J. Llovet, Journal of Symbolic Computation 13 (1992) 25–39; J. Llovet, R. Sendra, J.A. Jaén, R. Martínez, Computer Science, 1992, pp. 159–165; R. Martínez, Procedimientos de Recurrencia Lineal en Algebra Computacional, PhD Thesis, Depto. de Matemáticas, Universidad de Alcalá de Henares, España, 1992; J. Llovet, R. Martínez, J.A. Jaén, Journal of Computational and Applied Mathematics 49 (1993) 145–152]). An experimental study shows that the time and memory space performance of the TERA program improves significantly upon that of traditional Computer Algebra Systems (MAPLE and MAGMA in our case).

Suggested Citation

  • Castaño, Bonifacio & Heintz, Joos & Llovet, Juan & Martínez, Raquel, 2000. "On the data structure straight-line program and its implementation in symbolic computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 51(5), pages 497-528.
    • Handle: RePEc:eee:matcom:v:51:y:2000:i:5:p:497-528
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    Cited by:

    1. Bruno, N. & Heintz, J. & Matera, G. & Wachenchauzer, R., 2002. "Functional programming concepts and straight-line programs in computer algebra," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 60(6), pages 423-473.

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