User-based integration software

ABSTRACT

Algorithms are not the same as user software; which is like saying that pure mathematics is not the same as its application. In earlier algebra conferences Risch and Norman (1976) and Norman and Davenport (1979) have described a new method for symbolic indefinite integration. This paper is based on the work described there, but considers the process of turning this important area of algorithm research into a module for the REDUCE algebra system, in a form that can be used by the regular REDUCE user in the same way that he would differentiate or perform substitutions. The software package that is described is the Utah version (REDUCE INT) of the original Norman and Moore (1976)implementation. Rather than describe the method again, the paper concentrates on the software engineering and human engineering aspects of the package, and changes to the procedure that may not be mathematically justified but provide a powerful tool to the end user.

REFERENCES

• 1: J H Davenport, On the Integration of Algebraic Functions, Springer-Verlag Lecture Notes in Computer Science 102, 1981
• 2: J P Fitch, Integration Notes, REDUCE Newsletter, to appear
• 3: J P Fitch & A C Norman, Implementing LISP in a High Level Language, Software Practice & Experience, 7 713, 1977
• 4: S J Harrington, A New Symbolic Integration System in REDUCE, Computer Journal 22, 1979
• 5: J B Marti et al, Standard LISP Report, University of Utah, UCP-60, 1978
• 6: Joel Moses, Symbolic integration: the stormy decade, Communications of the ACM, v.14 n.8, p.548-560, Aug. 1971 [doi>10.1145/362637.362651]
• 7: A C Norman & P M A Moore, Implementing the New Risch Integration Algorithm, Proc. 4th Int. Coll on Advanced Computing Methods in Theoretical Physics, 1977
• 8: A C Norman, P M A Moore & J H Davenport, ISIS Method, Internal Report, 1978
• 9: A. C. Norman , James H. Davenport, Integration -- the dust settles? (invited), Proceedings of the International Symposiumon on Symbolic and Algebraic Computation, p.398-407, June 01, 1979
• 10: H Rang, Private Communication, 1979
• 11: R Risch & A C Norman, A New Integration Algorithm, SYMSAC 2, Verbal Presentation, 1976

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems

          Nouns: REDUCE

Additional Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: User interfaces

General Terms:
Algorithms, Theory