The risch algorithms of MACSYMA and SENAC

ABSTRACT

The purpose of this paper is to report on a computer implementation of the Risch algorithm for the symbolic integration of rational functions containing nested exponential and logarithms. For the class of transcendental functions, the Risch algorithm [4] represents a practical method for symbolic integration. Because the Risch algorithm describes a decision procedure for transcendental integration it is an ideal final step in an integration package. Although the decision characteristic cannot be fully realised in a computer system, because of major algebraic problems such as factorisation, zero-equivalence and simplification, the potential advantages are considerable.

REFERENCES

• 1: James H. Davenport, Integration - What do we want from the theory?, Proceedings of the European Computer Algebra Conference on Computer Algebra, p.2-11, March 28-30, 1983
• 2: The Mathlab Group, <i>MACSYMA Reference Manual</i>, Laboratory for Computer Science, MIT, (1977).
• 3: A. C. Norman and P. M. A. Moore, <i>Implementing the New Risch Integration Algorithm</i>, MAXIMIN 1977 (1977) -110.
• 4: R. H. Risch, <i>The problem of integration in finite terms</i>, Trans. Amer. Math. Soc 139 (1969), 167--189.
• 5: K. A. Broughan, <i>The SENAC Manual</i>, University of Waikato, (1989).
• 6: W. C. Schou, <i>An Integration Package for Transcendental Functions</i>, M.Sc. Thesis, University of Waikato, (1989).

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Algebraic algorithms

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems
          Subjects: Special-purpose algebraic systems

General Terms:
Algorithms, Design, Languages, Theory