Formula Manipulation—The User’s Point of View

For a number of years, formula manipulation has been a prosperous member of the large family of computer applications. It has already facilitated the solution of problems too lengthy and time-consuming for the relatively unreliable human problem-solver. The reader who has not himself encountered such problems need only recall the horrendous exercises in formula manipulation performed by the astronomers of the eighteenth and nineteenth century, e.g., as described in Delaunay’s “Theorie du mouvement de la lune,” or in E. W. Brown’s “Theory of the Motion of the Moon.” Their achievements are hardly surpassable by hand, and continue to challenge the capabilities of current systems.

[1]  Jean E. Sammet,et al.  Survey of formula manipulation , 1966, CACM.

[2]  Anthony C. Hearn.  REDUCE: A User-Oriented Interactive System for Algebraic Simplification , 1968 .

[3]  James R. Slagle,et al.  A Heuristic Program that Solves Symbolic Integration Problems in Freshman Calculus , 1963, JACM.

[4]  Paul W. Abrahams.  Symbol Manipulation Languages , 1968, Adv. Comput..

[5]  Knut Korsvold.  An on line program for non-numerical algebra , 1966, SYMSAC '66.

[6]  J. C. R. Licklider,et al.  Man-Computer Symbiosis , 1960 .

[7]  J. E. Sammet,et al.  Introduction to FORMAC , 1964, IEEE Trans. Electron. Comput..

[8]  J. Hyde,et al.  The Alpak system for nonnumerical algebra on a digital computer — II: Rational functions of several variables and truncated power series with rational-function coefficients , 1964 .

[9]  R. Risch.  The problem of integration in finite terms , 1969 .

[10]  C. Engelman.  MATHLAB: a program for on-line machine assistance in symbolic computations , 1965, AFIPS '65 (Fall, part I).

[11]  R. G. Swan,et al.  Factorization of polynomials over finite fields. , 1962 .

[12]  George E. Collins.  PM, a system for polynomial manipulation , 1966, CACM.

[13]  L. Fox.  An introduction to numerical linear algebra , 1964 .

[14]  William S. Brown,et al.  The alpak system for nonnumerical algebra on a digital computer , 1963 .

[15]  C. A. R. Hoare,et al.  A contribution to the development of ALGOL , 1966, CACM.

[16]  Max E. Engeli.  Achievements and problems in formula manipulation , 1968, IFIP Congress.

[17]  Jonathan K. Millen.  CHARYBDIS: A LISP Program to Display Mathematical Expressions on Typewriter-like Devices , 1968 .

[18]  John F Nolan,et al.  Analytical differentiation on a digital computer , 1953 .

[19]  Carlos Christensen,et al.  On the implementation of AMBIT, a language for symbol manipulation , 1966, CACM.

[20]  Niklaus Wirth,et al.  EULER: A generalization of ALGOL and its formal definition: Part 1 , 1966, Commun. ACM.

[21]  Edgar H. Sibley.  The engineering assistant: design of a symbol manipulation system , 1967 .

[22]  J. Wrench.  Table errata: The art of computer programming, Vol. 2: Seminumerical algorithms (Addison-Wesley, Reading, Mass., 1969) by Donald E. Knuth , 1970 .

[23]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[24]  Alan J. Perlis,et al.  An extension to ALGOL for manipulating formulae , 1964, CACM.

[25]  George E. Collins,et al.  Subresultants and Reduced Polynomial Remainder Sequences , 1967, JACM.

[26]  E. Berlekamp.  Factoring polynomials over finite fields , 1967 .

[27]  Arnold Lapidus,et al.  Some experiments in algebraic manipulation by computer , 1965, CACM.

[28]  George E. Collins.  Polynomial Remainder Sequences and Determinants , 1966 .

[29]  Friedrich L. Bauer,et al.  Revised report on the algorithm language ALGOL 60 , 1963, CACM.

[30]  Peter Henrici,et al.  Automatic Computations with Power Series , 1956, JACM.

[31]  Niklaus Wirth.  A generalization of ALGOL , 1963, CACM.

[32]  Alan J. Perlis,et al.  A DEFINITION OF FORMULA ALGOL. , 1966 .

[33]  Alston S. Householder,et al.  Handbook for Automatic Computation , 1960, Comput. J..

[34]  E. Feigenbaum,et al.  Computers and Thought , 1963 .

[35]  James W. Hanson,et al.  Analytic differentiation by computer , 1962, CACM.