Elsevier

Advances in Computers

Volume 8, 1967, Pages 47-102
Advances in Computers

Formula Manipulation by Computer

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Publisher Summary

“Formula manipulation” refers to the use of a computer to manipulate mathematical expressions in a formal fashion. The chapter presents a discussion of the main issues in a formula manipulation system, both from language and implementation points of view. It also discusses a particular large-scale system—namely, FORMAC. In considering the general subject of formula manipulation, there are a number of technical issues that are either critical to the success of a system. The chapter discusses the question of a general purpose system versus individual capabilities, the question of level of language and system, the issue of the level of capability and type of user, and a long list of capabilities that one must at least consider providing. There is a discussion of some of the factors involved in implementing such a system. The chapter discusses a number of applications that have been developed using a variety of systems.

References (59)

  • H.A. Balmer, E.A. Witmer, W.A. Loden, A theoretical analysis and experimental study of the behavior of panels of...
  • M.D. Bernick, E.D. Callender, J.R. Sanford, ALGy–An algebraic manipulation program. Proc. Western Joint Comp. Conf.,...
  • F.W. Blackwell, ALMS–analytic language manipulation system. Presented at Assoc. Computing Machinery Nat. Conf., August,...
  • L. Bleiweiss, P. Cundall, R. Hirschkop, A time-shared algebraic desk calculator version of FORMAC. IBM Systems...
  • E. Bond, M. Auslander, S. Grisoff, R. Kenney, M. Myszewski, J. Sammet, R. Tobey, S. Zilles, FORMAC–An experimental...
  • E. Bond, M. Auslander, S. Grisoff, R. Kenney, M. Myszewski, J. Sammet, R. Tobey, and S. Zilles, Implementation of...
  • E.R. Bond, P.A. Cundall, A possible PL/I extension for mathematical symbol manipulation. IBM, Systems Development...
  • S.F. Boys et al.

    Automatic fundamental calculations of molecular structure

    Nature

    (1956)
  • W.S. Brown

    The ALPAK system for non-numerical algebra on a digital computer–I: polynomials in several variables and truncated power series with polynomial coefficients

    Bell System Tech. J.

    (1963)
  • W.S. Brown et al.

    The ALPAK system for non-numerical algebra on a digital computer–II: rational functions of several variables and truncated power series with rational-function coefficients

    Bell System Tech. J.

    (1964)
  • W.S. Brown et al.

    VPRPAK–A computer programming system for variable precision rational arithmetic. Bell Telephone Laboratories

    (1964)
  • L.C. Clapp et al.
  • An introduction to COMIT programming

    Research Laboratory of Electronics and the Computation Center

    (1961)
  • E. Cuthill, A FORMAC program for the solution of linear boundary and initial value problems. Presented at SICSAM...
  • S.D. Dunten

    An algebraic manipulation program for time-shared computer consoles

    (1963)
  • C. Engelman
  • D.J. Farber et al.

    SNOBOL, a string manipulation language

    J. Assoc. Computing Machinery

    (1964)
  • R. Fletcher et al.

    A mechanization of algebraic differentiation and the automatic generation of formulae for molecular integrals of Gaussian orbitals

    Computer J.

    (1963)
  • Formac

    Operating and User's Preliminary Reference Manual

    (1965)
  • J.M. Gerard et al.

    Mechanization of tedious algebra: the Newcomb operators of planetary theory

    Commun. Assoc. Computing Machinery

    (1965)
  • J.W. Hanson et al.

    Analytic differentiation by computer

    Commun. Assoc. Computing Machinery

    (1962)
  • T. Hart, Simplify, Artificial Intelligence Project–Memo. 11, M.I.T., Cambridge, Massachvisetts, unpublished, December,...
  • K. Hartt

    Some analytical procedures for computers and their applications to a class of multidimensional integrals

    J. Assoc. Computing Machinery

    (1964)
  • P. Herget et al.

    The calculation of literal expansions

    Astron. J.

    (1959)
  • J.P. Hyde

    The ALPAK system for non–numerical algebra on a digital computer–III: systems of linear equations and class of side relations

    Bell System Tech. J.

    (1964)
  • IBM Systems Reference Library, IBM 7090/94 IBSyS Operating System, System Monitor (IBSyS), Form...
  • IBM Systems Reference Library, IBM 7090/94 IBSyS Operating System, IBJOB Processor, Form...
  • I.G. Izsak et al.

    Construction of Newcomb operators in a digital computer

    (1964)
  • H.G. Kahrimanian

    Analytical differentiation by a digital computer

    (1953)
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