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The design of the Cambridge algebra system

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J. R. HortonAuthors Info & Claims

SYMSAC '71: Proceedings of the second ACM symposium on Symbolic and algebraic manipulation

Pages 134 - 143

https://doi.org/10.1145/800204.806278

Published: 23 March 1971 Publication History

Abstract

This paper discusses the design of the CAMbridge ALgebra system and describes some of the techniques that are used in its implementation. These techniques enable that system to provide reasonably general algebraic manipulation in an efficient way. The concepts of modularity and selection are introduced and their influence on the overall structure of the system is described. Examples of selection and editing facilities are given since these are considered to be a necessary part of any algebra system. The paper also discusses data structures that are appropriate for algebraic systems and examples are given for two of the CAMAL modules.

References

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Barron, D.W., Brown, H., Hartley, D.F. and Swinnerton-Dyer, H.P.F. Titan Autocode Programming Manual. University Mathematical Laboratory, Cambridge (1967).

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Barton, D. A new technique for the Lunar theory. Ph.D. Thesis, Cambridge University (1966).

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Barton, D. A scheme for manipulative algebra on a computer. Comp. J. 9 (1967), 340.

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Barton, D., Bourne, S.R., and Burgess, C.J. A simple algebra system. Comp. J. 11 (1968), 293.

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Barton, D., Bourne, S.R., and Fitch, J.P. An algebra system. Comp. J. 13 (1970), 32.

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Barton, D., Bourne, S.R., and Horton, J.R. The structure of the Cambridge Algebra system. Comp. J. 13 (1970), 243.

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Bourne, S.R. Automatic Algebraic Manipulation and its Application to the Lunar Theory. Ph.D. Thesis, Cambridge University (1970).

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Bourne, S.R. and Horton, J.R. The CAMAL System Manual. Computer Laboratory, Cambridge (1971).

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Brown, W.S., Hyde, J.P. and Tague, B.A. ALPAK II. Bell Tech. J. 43 (1964), 785.

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d'Inverno, R. ALAM - Atlas Lisp Algebraic Manipulator Comp. J. 12 (1969), 124.

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Engeli, M.E. User's Manual for the Formula Manipulation Language SYMBAL. Computation Center, The University of Texas at Austin (1968).

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Hearn, A.C. A program for symbolic algebraic computation. SHARE XXXIV, Denver 1970.

[13]

Irons, E.T. A syntax Directed Compiler for ALGOL 60. Comm. A.C.M. 4 (1961), 51.

Digital Library

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Martin, W.A. Symbolic Mathematical Laboratory. Ph.D. Thesis, M.I.T. (1967).

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Matthewman, J.H. Ph.D. Thesis, Cambridge University (1966).

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Richardson, D. Ph.D. Thesis, University of Bristol (1966).

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Tobey, R.G., et al. PL/1 FORMAC Interpreter. Users reference manual. IBM Contributed Program Library 360 D 03.3004, Hawthorne, N.Y. (1967).

Cited By

Fitch J(2009)CAMAL 40 Years on --- Is Small Still Beautiful?Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics10.1007/978-3-642-02614-0_8(32-44)Online publication date: 3-Jul-2009
https://dl.acm.org/doi/10.1007/978-3-642-02614-0_8
Henrard J(1988)A survey of Poisson series processorsCelestial Mechanics10.1007/BF0122900745:1-3(245-253)Online publication date: Mar-1988
https://doi.org/10.1007/BF01229007
Barton DFitch J(1974)Algebraic manipulation in CambridgeACM SIGSAM Bulletin10.1145/1086823.10868278:1(8-9)Online publication date: 1-Feb-1974
https://dl.acm.org/doi/10.1145/1086823.1086827
Show More Cited By

Index Terms

The design of the Cambridge algebra system
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Computer algebra systems
    2. Representation of mathematical objects

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cover image ACM Conferences

SYMSAC '71: Proceedings of the second ACM symposium on Symbolic and algebraic manipulation

March 1971

464 pages

ISBN:9781450377867

DOI:10.1145/800204

Copyright © 1971 ACM.

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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SIGAI: ACM Special Interest Group on Artificial Intelligence
SIGPLAN: ACM Special Interest Group on Programming Languages
SIGNUM: ACM Special Interest Group on Numerical Mathematics
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIAM: Society for Industrial and Applied Mathematics

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 23 March 1971

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Cited By

Fitch J(2009)CAMAL 40 Years on --- Is Small Still Beautiful?Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics10.1007/978-3-642-02614-0_8(32-44)Online publication date: 3-Jul-2009
https://dl.acm.org/doi/10.1007/978-3-642-02614-0_8
Henrard J(1988)A survey of Poisson series processorsCelestial Mechanics10.1007/BF0122900745:1-3(245-253)Online publication date: Mar-1988
https://doi.org/10.1007/BF01229007
Barton DFitch J(1974)Algebraic manipulation in CambridgeACM SIGSAM Bulletin10.1145/1086823.10868278:1(8-9)Online publication date: 1-Feb-1974
https://dl.acm.org/doi/10.1145/1086823.1086827
Bourne S(1972)Literal expressions for the co-ordinates of the moonCelestial Mechanics10.1007/BF012277796:2(167-186)Online publication date: Sep-1972
https://doi.org/10.1007/BF01227779
Tobey RSammet JTobey RMoses J(1971)Symbolic mathematical computation—introduction and overviewProceedings of the second ACM symposium on Symbolic and algebraic manipulation10.1145/800204.806261(1-16)Online publication date: 23-Mar-1971
https://dl.acm.org/doi/10.1145/800204.806261

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