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Symbolic derivatives without list processing, subroutines, or recursion

Author:

Peter J. SmithAuthors Info & Claims

Communications of the ACM, Volume 8, Issue 8

Pages 494 - 496

https://doi.org/10.1145/365474.365504

Published: 01 August 1965 Publication History

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Abstract

A routine has been developed which computes and prints out the symbolic derivative of an absolutely continuous elementary function of one or several variables. No use is made of list processing languages. The chain rule is applied and the result is edited to produce results as elegant and efficient as those obtained by hand computation. A subset may be imbedded in a formula translator to introduce a differentiation operator into an “algebraic” programming language.

References

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SLAOLE, J. R. Doctoral Thesis, MIT, 1961.

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HANSEN, J. n., CAVINESS, J. S., AND JOSEPH, C. Analytic differentiation by computer. Comm. ACM 6 (June 1962), 349- 355.

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WENGERT, R. R. A simple automatic derivative evaluation program. Comm. ACM 8 (Aug. 1964), 463--464.

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WILKINS, R.D. Investigation of a new Analytical method for derivative evaluation. Comm. ACM 8 (Aug. 1964), 465-471.

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HAMBLIN, C. L. Translation to and from Polish notation. Comput. J. 5 (Oct. 1962), 210-213.

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CAMPBELL, L. W., AND BECK, G. A. The FORAST programming language for ORDVAC and BRLESC. BRL Rep. No. 1172, Ballistic Res. Labs, Aberdeen Proving Ground, 1Md., Aug. 1962.

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Stoutemyer D(2012)Ways to implement computer algebra compactlyACM Communications in Computer Algebra10.1145/2110170.211018445:3/4(199-224)Online publication date: 23-Jan-2012
https://dl.acm.org/doi/10.1145/2110170.2110184
Kozhevnikova GStognii A(1976)Representation of analytic expressions for the performance of formula transformations by computerCybernetics10.1007/BF0107043611:4(571-585)Online publication date: 1976
https://doi.org/10.1007/BF01070436
Bender B(1966)A computer system for algebra and analytic differentiationProceedings of the first ACM symposium on Symbolic and algebraic manipulation10.1145/800005.807967(0201-0227)Online publication date: 1-Jan-1966
https://dl.acm.org/doi/10.1145/800005.807967

Index Terms

Symbolic derivatives without list processing, subroutines, or recursion
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
      2. Language types

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Published In

Communications of the ACM Volume 8, Issue 8

Aug. 1965

67 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/365474

Editor:
C. C. Gotlieb
Univ. of Toronto, Toront, Ont., Canada

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 August 1965

Published in CACM Volume 8, Issue 8

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Stoutemyer D(2012)Ways to implement computer algebra compactlyACM Communications in Computer Algebra10.1145/2110170.211018445:3/4(199-224)Online publication date: 23-Jan-2012
https://dl.acm.org/doi/10.1145/2110170.2110184
Kozhevnikova GStognii A(1976)Representation of analytic expressions for the performance of formula transformations by computerCybernetics10.1007/BF0107043611:4(571-585)Online publication date: 1976
https://doi.org/10.1007/BF01070436
Bender B(1966)A computer system for algebra and analytic differentiationProceedings of the first ACM symposium on Symbolic and algebraic manipulation10.1145/800005.807967(0201-0227)Online publication date: 1-Jan-1966
https://dl.acm.org/doi/10.1145/800005.807967

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Abstract

References

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Index Terms

Recommendations

Unified formulas for arbitrary order symbolic derivatives and anti-derivatives of the power-inverse hyperbolic class 1

Symbolic-numeric Gaussian cubature rules

Symbolic-Numeric Computation of the Bernstein Coefficients of a Polynomial from Those of One of Its Partial Derivatives and of the Product of Two Polynomials

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