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The legacy of MATHLAB 68

Author:

Carl EngelmanAuthors Info & Claims

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

Pages 29 - 41

https://doi.org/10.1145/800204.806265

Published: 23 March 1971 Publication History

Abstract

MATHLAB 68 is an on-line system providing machine aid for the mechanical symbolic processes encountered in analysis. It is capable of performing, automatically and symbolically, such common procedures as differentiation, polynomial factorization, indefinite integration, direct and inverse Laplace transforms, and the solution of linear differential equations with constant (symbolic) coefficients.

We discuss its interactive nature and its range of services which extends from ignorant bookkeeper to, on occasion, expert problem solver. We also describe the internal data representations and algorithms of the system.

The paper regards the system as a fixed object and explores its accomplishments, its contributions to future systems, the motivation and consequences of the major decisions made during its development and, perhaps most important of all, its weaknesses.

References

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Berlekamp, E. R., Factoring Polynomials over Finite Fields, Bell System Technical Journal, October 1967.

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Collins, G. E., Subresultants and Reduced Polynomial Remainder Sequences, J.A.C.M., January 1967.

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Delaunay, Ch. 1867, Mem. Acad. Sci., 28, 883 and 29, 931.

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Diffie, B. W., and Engelman, C., MATHLAB Project Report, M69-72, The MITRE Corporation, Sept. 1969.

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Engelman, C., MATHLAB 68. In A. J. H. Morrell (Ed.). Information Processing 68, North-Holland, Amsterdam, 1969, pp. 462-467.

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Manove, M., Bloom, S., and Engelman, C., Rational Functions in MATHLAB. In Bobrow, D. G., (Ed.), Symbolic Manipulation Languages and Techniques, North Holland, Amsterdam, 1968, pp. 86-102.

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Martin, W. A., Symbolic Mathematical Laboratory, Ph.D. Thesis, E. E. Dept., M.I.T., January 1967.

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Millen, J. K., CHARYBDIS: A LISP Program to Display Mathematical Expressions on Typewriter-like Devices. In Klerer, M., and Reinfelds, J., (Eds.), Interactive Systems for Experimental Applied Mathematics, Academic Press, New York and London, 1968, pp. 155-163.

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Moses, J., Symbolic Integration, Ph.D. Thesis, Math. Dept., M.I.T., December 1967.

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Moses, J., Engelman, C., and Martin, W. A., The Hierarchical Organization of an Algebraic Manipulation System. In Linguaggi nella Societa e nella Tecnica, Edizioni di Comunita, Milano, 1970, pp. 349-369.

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Moses, J., The Integration of a Class of Special Functions with the Risch Algorithm, SIGSAM Bulletin No. 13, ACM Special Interest Group on Symbolic and Algebraic Manipulation, December 1969, pp. 14-27.

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van der Waerden, B. L., Modern Algebra, Frederick Ungar, New York, 1949.

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Wang, P., User Manual for Engelman MATHLAB, Internal Document, Applied Mathematics Laboratory, M.I.T., February 1970.

Cited By

Galán-García JRodríguez-Cielos PPadilla-Domínguez YGalán-García MAtencia IRodríguez-Padilla PAguilera-Venegas G(2021)SMIS: A Stepwise Multiple Integration Solver Using a CASMathematics10.3390/math92228669:22(2866)Online publication date: 11-Nov-2021
https://doi.org/10.3390/math9222866
Camberos JLambe LLuczak R(2012)CFD with Hybrid Symbolic-Numeric Methodology42nd AIAA Aerospace Sciences Meeting and Exhibit10.2514/6.2004-242Online publication date: 21-Jun-2012
https://doi.org/10.2514/6.2004-242
Schmalhofer F(2001)Expert Systems in Cognitive ScienceInternational Encyclopedia of the Social & Behavioral Sciences10.1016/B0-08-043076-7/01615-6(5128-5135)Online publication date: 2001
https://doi.org/10.1016/B0-08-043076-7/01615-6
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Index Terms

The legacy of MATHLAB 68
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Computer algebra systems
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Number-theoretic computations

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Published In

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

Galán-García JRodríguez-Cielos PPadilla-Domínguez YGalán-García MAtencia IRodríguez-Padilla PAguilera-Venegas G(2021)SMIS: A Stepwise Multiple Integration Solver Using a CASMathematics10.3390/math92228669:22(2866)Online publication date: 11-Nov-2021
https://doi.org/10.3390/math9222866
Camberos JLambe LLuczak R(2012)CFD with Hybrid Symbolic-Numeric Methodology42nd AIAA Aerospace Sciences Meeting and Exhibit10.2514/6.2004-242Online publication date: 21-Jun-2012
https://doi.org/10.2514/6.2004-242
Schmalhofer F(2001)Expert Systems in Cognitive ScienceInternational Encyclopedia of the Social & Behavioral Sciences10.1016/B0-08-043076-7/01615-6(5128-5135)Online publication date: 2001
https://doi.org/10.1016/B0-08-043076-7/01615-6
Sammet J(1996)The beginning and development of FORMACHistory of programming languages---II10.1145/234286.1057824(429-469)Online publication date: 1-Jan-1996
https://dl.acm.org/doi/10.1145/234286.1057824
Sammet J(1993)The beginning and development of FORMAC (FORmula MAnipulation Compiler)ACM SIGPLAN Notices10.1145/155360.15537228:3(209-230)Online publication date: 1-Mar-1993
https://dl.acm.org/doi/10.1145/155360.155372
Sammet JLee JSammet J(1993)The beginning and development of FORMAC (FORmula MAnipulation Compiler)The second ACM SIGPLAN conference on History of programming languages10.1145/154766.155372(209-230)Online publication date: 1-Apr-1993
https://dl.acm.org/doi/10.1145/154766.155372
Fateman R(1989)A Review of MacsymaIEEE Transactions on Knowledge and Data Engineering10.1109/69.434091:1(133-145)Online publication date: 1-Mar-1989
https://dl.acm.org/doi/10.1109/69.43409
Liberatore AManetti S(1988)SAPEC-a personal computer program for the symbolic analysis of electric circuits1988., IEEE International Symposium on Circuits and Systems10.1109/ISCAS.1988.15068(897-900)Online publication date: 1988
https://doi.org/10.1109/ISCAS.1988.15068
Engelman CJoseph EWhite J(1975)MATHLAB tutorialProceedings of the 1975 annual conference10.1145/800181.810339(268-269)Online publication date: 1-Jan-1975
https://dl.acm.org/doi/10.1145/800181.810339
Griesmer JJenks RJoseph EWhite J(1975)The SCRATCHPAD systemProceedings of the 1975 annual conference10.1145/800181.810338(266-267)Online publication date: 1-Jan-1975
https://dl.acm.org/doi/10.1145/800181.810338
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