Optimal evaluation of algebraic expressions

  • Anthony C. Hearn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 229)


Algebraic computation systems produce results for either human or machine consumption. In the latter case, numerical evaluation of the resulting expressions is often the goal. In either case, it is important to produce results in an appropriately optimal form. In this paper, we consider some of the methods available for doing this. In particular, we shall see that several of our techniques mirror the methods used by human experts. In addition, we shall mention some new algorithms that promise to make the whole problem more tractable mathematically.


Human Expert Expanded Form Algebraic Computation Remainder Function Compiler Optimization 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. C. Hearn, “The Personal Algebra Machine”, Information Processing 80 (Proc. IFIP Congress 80), North-Holland, 1980, 621–628.Google Scholar
  2. [2]
    W. Leler and N. Soiffer, “An Interactive Graphical Interface for Symbolic Algebra Systems”, this proceedings.Google Scholar
  3. [3]
    B. L. Gates and P. S. Wang, “A LISP-Based RATFOR Code Generator”, Proc. 1984 MACSYMA User's Conf., General Electric, Schenectady, New York, 1984, 319–329.Google Scholar
  4. [4]
    B. L. Gates, “GENTRAN: An Automatic Code Generation Facility for REDUCE”, SIGSAM Bulletin (to appear).Google Scholar
  5. [5]
    G. O. Cook, Jr., “Development of a Magnetohydrodynamic Code for Axisymmetric, High-beta Plasmas with Complex Magnetic Fields”, Lawrence Livermore National Laboratory Report No. UCRL-53324, 1982.Google Scholar
  6. [6]
    A. C. Hearn, “The Problem of Substitution”, Proc. of the IBM Summer Institute on Symbolic Mathematics by Computer, IBM Programming Laboratory Report No. FSC-69-0312 (1969).Google Scholar
  7. [7]
    A. C. Hearn, “Structure: The Key to Improved Algebraic Computation”, Proc. RSYMSAC, World Scientific Publ Co, Singapore, 1985 (in press).Google Scholar
  8. [8]
    W. S. Brown, “On Computing with Factored Rational Expressions”, SIGSAM Bulletin 31 (1974) 27–34.Google Scholar
  9. [9]
    A. C. Hearn, “The Structure of Algebraic Computations”, Proc. of the Fourth Colloquium on Advanced Methods in Theoretical Physics, 1–15, St. Maximin, France, 1977.Google Scholar
  10. [10]
    P. S. Wang, T. Y. P. Chang and J. A. Van Hulzen, “Code Generation and Optimization for Finite Element Analysis”, Proc. EUROSAM '84, 237–247, published as Lecture Notes on Comp. Science, No. 174, Springer-Verlag, Berlin, 1984.Google Scholar
  11. [11]
    R. S. Brenner, private communication.Google Scholar
  12. [12]
    B. J. A. Hulshof and J. A. van Hulzen, “An Expression Compression Package for REDUCE based on Factorization and Controlled Expansion”, informal contribution presented at EUROCAL 85, Linz, Austria, April 1–3, 1985.Google Scholar
  13. [13]
    J. Van Hulzen, “Code Optimization of Multivariate Polynomial Schemes: A Pragmatic Approach”, Proc. EUROCAL '83, 286–300, published as Lecture Notes on Comp. Science, No. 162, Springer-Verlag, Berlin, 1983.Google Scholar
  14. [14]
    M. A. Breuer, “Generation of Optimal Code for Expressions via Factorization”, CACM 12 (1969) 333–340.Google Scholar
  15. [15]
    B. Buchberger, “Groebner Bases: An Algorithmic Method in Polynomial Ideal Theory”, to appear in N. K. Bose (Ed.): “Recent Trends in Multidimensional Systems Theory”, D. Reidel Publ. Comp, 1984. Also available as Univ. of Linz Dept. of Math Report No. CAMP 83-29.0.Google Scholar
  16. [16]
    L. Hornfeldt, “A Sum-Substitutor used as Trigonometric Simplifier”, Proc. EUROCAM '82, 188–195, published as Lecture Notes on Comp. Science, No. 144, Springer-Verlag, Berlin, 1982.Google Scholar
  17. [17]
    P. van den Heuvel and J. Marti, “Automatic Translation vs Reimplementation — An Experiment”, to be published.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Anthony C. Hearn
    • 1
  1. 1.The Rand CorporationSanta MonicaU.S.A.

Personalised recommendations