IAM, a system for interactive algebraic manipulation

ABSTRACT

The principal features of IAM, a system for interactive algebraic manipulation, are described. The primary goal of IAM is to make algebraic manipulation by computer available to a non-programming person. IAM has a JOSS-like command language, emphasizing ease of communication between the user and the system, yet still providing a stored program facility for applications which require it. In addition, the system uses a two-dimensional output format and provides convenient files for the permanent storage of expressions. The algebraic operations of IAM are oriented toward the use of a canonical form of rational functions to achieves “simplification” of expressions; and this approach dictates specialized data structures and algorithms. IAM is implemented in AMBIT/L, a high-level language for list-processing; and it is currently running under the time-sharing system of the DEC PDP-10/50.

REFERENCES

• 1: Brown, W.S. "The ALPAK system for non-numeric algebra on a digital computer." Bell System Technical Journal Volume XLII, No. 5., September 1963. pp. 2081-2119.
• 2: Sammett, J.E. and Bond, E. "Introduction to FORMAC." IEEE Transactions on Electronic Computers, Volume EC-13, August 1964. pp. 386-394.
• 3: Benevento, Francis, Christensen, Carlos and Myszewski, Mathew. "The analysis and solution of a problem in algebraic symbol manipulation." Computer Associates, Inc. (CA-6712-0411) Wakefield, Mass., December 1967.
• 4: C. Christensen, Programming Languages for Non-Numeric Processing—1: examples of symbol manipulation in the AMBIT Programming Language, Proceedings of the 1965 20th national conference, p.247-261, August 24-26, 1965, Cleveland, Ohio, United States [doi>10.1145/800197.806049]
• 5: Carlos Christensen, On the implementation of AMBIT, a language for symbol manipulation, Communications of the ACM, v.9 n.8, p.570-573, Aug. 1966 [doi>10.1145/365758.365765]
• 6: Christensen, Carlos. "An example of the manipulation of directed graphs in the AMBIT/G programming language." In Interactive Systems for Experimental Applied Mathematics, M. Klerer and J. Reinfelds, eds., Academic Press, New York, 1968.
• 7: Carlos Christensen, An introduction to AMBIT/L, a diagrammatic language for list processing, Proceedings of the second ACM symposium on Symbolic and algebraic manipulation, p.248-260, March 23-25, 1971, Los Angeles, California, United States [doi>10.1145/800204.806294]
• 8: Manove, M., Bloom, S , and Engleman, C. "Rational functions in Mathlab." In Symbolic Manipulation Languages and Techniques, D. G. Bobrow, ed., North-Holland Publishing Company, Amsterdam, 1968. pp. 86-97.
• 9: Moses, Joel. Symbolic Integration. Ph. D. Thesis, M. I. T. Department of Mathematics, Cambridge, Mass., 1967.
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• 11: Applied Data Research. An Initial Session with IAM, Revised Edition. Applied Data Research (CA-7007-0711), Wakefield, Mass.
• 12: Wheelock, Burton. IAM User Examples. Applied Data Research (CA-7003-1111), Wake-field, Mass., March 1970.
• 13: Millen, J.K. "CHARYBDIS, a LISP program to display mathematical expressions on typewriter-like devices." In Interactive Systems for Experimental and Applied. Mathematics, M. Klerer and J. Reinfelds, eds., Academic Press, New York, 1968. pp. 79-90.

INDEX TERMS

Primary Classification:
  D. Software
  D.4 OPERATING SYSTEMS
      D.4.9 Systems Programs and Utilities
          Subjects: Command and control languages

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Number-theoretic computations (e.g., factoring, primality testing)

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.0 General
      I.1.3 Languages and Systems

  K. Computing Milieux
  K.2 HISTORY OF COMPUTING

      Nouns: FORMAC

General Terms:
Algorithms, Languages, Theory