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Formula Manipulation—The User’s Point of View

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Advances in Information Systems Science

Abstract

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 “Théorie 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.

The writing of this paper has been supported in part by the United States Army (Durham) Research Grant DA-ARO(D)-31-124-G721 and National Science Foundation Grant GP-5253.

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References

  1. Revised Report on the Algorithmic Language algol 60, Comm. ACM, 6, 1–17 (Jan. 1963)

    Google Scholar 

  2. R. Alpiar, The algan-I Manual (User’s Handbook for the Algebraic Fortran Programme), EIR Bericht Nr. 76, Eidgenössisches Institut für Reaktorforschung, Würenlingen, Schweiz (1965)

    Google Scholar 

  3. E. Bond et al., An Experimental Formula Manipulation Compiler, in: “Proc. 1964 ACM National Conference,” pp. K2.I-1-K2.I-11

    Google Scholar 

  4. E. Bond, Formac: An Experimental Formula Manipulation Compiler (Operating Manual and User’s Preliminary Reference Manual), Share General Library 7090 R21BM0016 (1964)

    Google Scholar 

  5. W. S. Brown, The alpak System for Nonnumerical Algebra on a Digital Computer -I. Polynomials in Several Variables and Truncated Power Series with Polynomial Coefficients, Bell System Tech. J. XLII, 2081 (1963)

    Google Scholar 

  6. W. S. Brown, J. P. Hyde, and B. A. Tague, The alpak System for Non-Numerical Algebra on a Digital Computer-II, Bell System Tech. J.XLIII (2), 785–804 (1964)

    Google Scholar 

  7. B. F. Caviness, On Canonical Forms and Simplifications, doctoral dissertation, Carnegie Institute of Technology (1967)

    Google Scholar 

  8. C. Christensen, On the Implementation of ambit, A Language for Symbol Manipulation, Comm. ACM 9, 570–573 (Aug. 1966)

    Article  Google Scholar 

  9. G. E. Collins, Pm, A System for Polynomial Manipulations, Comm. ACM 9, 578–589 (Aug. 1966)

    Article  Google Scholar 

  10. G. E. Collins, Subresultants and Reduced Polynomial Remainder Sequences, J. ACM 14, 128–142 (Jan. 1967)

    Article  Google Scholar 

  11. G. E. Collins and J. H. Griesemer, Comparison of Computing Times in alpak, formac, pm and Korsvold’s System, SICSAM Bulletin No. 4 (Sept. 1966)

    Google Scholar 

  12. G. E. Collins, The SAC-1 List Processing System, Report, Computer Sciences Department and Computer Center, University of Wisconsin (July 1967)

    Google Scholar 

  13. G. E. Collins, The SAC-1 Polynomial System, Technical Reference 2, Computer Sciences Department and Computer Center, University of Wisconsin (Jan. 1968)

    Google Scholar 

  14. G. E. Collins, Polynomial Remainder Sequences and Determinants, American Mathematical Monthly 73 (7) (Aug.-Sept. 1966)

    Google Scholar 

  15. E. W. Dijkstra, On the Design of Machine Independent Programming Languages, “Annual Review in Automatic Programming,” Vol. 3, (R. Goodman, ed.), Pergamon Press, New York (1963)

    Google Scholar 

  16. M. E. Engeli, Formal Manipulation of Algebraic Expressions with an Algorithmic Language, in “Proceedings of the IFIP Congress, New York, May 1965,” Vol. II, Spartan Books, New York (1966)

    Google Scholar 

  17. M. E. Engeli, Design and Implementation of an Algebraic Processor, Habilitationsschrift ETH, Zurich, Switzerland (April 1966)

    Google Scholar 

  18. M. E. Engeli, A Language and List Structure for an Algebraic Manipulation System, in: “Symbol Manipulation Languages” (Proc. IFIP Working Conference, Pisa, Italy, Sept. 1966)

    Google Scholar 

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

    Google Scholar 

  20. M. E. Engeli, Achievements and Problems in Formula Manipulation, paper presented at IFIP Congress Edinburgh, Aug. 1968

    Google Scholar 

  21. C. Engelman, Mathlab: A Program for On-line Assistance in Symbolic Computations, in: “Proc. 1965 FJCC,” Spartan Books, Washington, D. C

    Google Scholar 

  22. R. R. Fenichel, An On-line System for Algebraic Manipulations, doctoral dissertation, Harvard University (July 1966). [also available as Report MAC-TR-35, Project MAC, MIT, Cambridge, Mass. (Dec. 1966).]

    Google Scholar 

  23. L. Fox, “An Introduction to Numerical Linear Algebra,” Clarendon Press (1964)

    Google Scholar 

  24. J. W. Hanson, J. S. Caviness, and C. Joseph, Analytic Differentiation by Computer, Comm. ACM 5, 349–355 (July 1962)

    Article  Google Scholar 

  25. A. C. Hearns, Reduce, A User-Oriented Interactive System for Algebraic Simplification, paper presented at the ACM Symposium on Interactive Systems, Washington, D. C. (Aug. 26–28, 1967); Stanford Artificial Memo AI57

    Google Scholar 

  26. P. Henrici, Automatic Computations with Power Series, J. ACM 3, 10–15 (Jan. 1956)

    Article  Google Scholar 

  27. K. Korsvold, An On-line Program for Non-Numerical Algebra, Report E-81, Norwegian Defense Research Establishment (March 1966)

    Google Scholar 

  28. R. Iturriaga, Contributions to Mechanical Mathematics, doctoral dissertation, Carnegie Institute of Technology, Pittsburgh, Pa. (April 1967)

    Google Scholar 

  29. H. G. Kahrimanian, Analytical Differentiation on a Digital Computer, M. A. Thesis, Temple University (May 1953)

    Google Scholar 

  30. A. Lapidus, and M. Goldstein, Some Experiments in Algebraic Manipulation by Computer, New York University NYO-1480-11 (Oct. 1964)

    Google Scholar 

  31. T. C. R. Licklider, “Man-Computer Symbiosis,” IRE Trans. Human Factors Electronics HFE-1, 4–11 (March 1960)

    Article  Google Scholar 

  32. M. Manove, S. Bloom, and C. Engelman, Rational Functions in math-lab, in: “Symbol Manipulation Languages” (Proc. IFIP Working Conference, Pisa, Italy, Sept. 1966)

    Google Scholar 

  33. W. A. Martin, Symbolic Mathematical Laboratory, doctoral dissertation, MIT, Cambridge, Mass. (Jan. 1967). [Also Report TR-36, Project MAC, MIT.]

    Google Scholar 

  34. J. K. Milien, Charybdis: A lisp Program to Display Mathematical Expressions on Typewriter-like Devices, presented at ACM Symposium on Interactive Systems for Experimental Applied Mathematics, Wash., D. C. (Aug. 1967)

    Google Scholar 

  35. J. Moses, Symbolic Integration, doctoral dissertation, MIT, Cambridge, Mass., (Dec. 1967). [Also Report MAC-TR-47.]

    Google Scholar 

  36. A. J. Pedis, and R. Iturriaga, An Extension of algol for Manipulating Formulae, Comm. ACM 7, 127–130 (Feb. 1964)

    Article  Google Scholar 

  37. A. J. Perlis, R. Iturriaga, and T. A. Standish, A Definition of Formula algol, Department of Computer Science, Carnegie Institute of Technology, Pittsburgh, Pa. (March 1966)

    Google Scholar 

  38. D. Richardson, Some Unsolvable Problems Involving Functions of a Real Variable, doctoral dissertation, University of Bristol, Bristol, England (1966)

    Google Scholar 

  39. R. H. Risch, The Problem of Integration in Finite Terms, SDC document SP-2801/ 000/00 System Development Corporation, Santa Monica (23 March 1967)

    Google Scholar 

  40. H. Rutishauser, Description of algol 60, Volume I, Part a of the “Handbook for Automatic Computation,“ Springer Verlag (1967)

    Google Scholar 

  41. J. E. Sammet and E. R. Bond, Introduction to formac, IEEE Trans. on Electronic Computers EC-13 (4), 386–394 (Aug. 1964)

    Article  Google Scholar 

  42. J. E. Sammet, Survey of Formula Manipulation, Comm. ACM, 9 (8), 555–569 (Aug. 1966)

    Article  Google Scholar 

  43. J. E. Sammet, An Annotated Descriptor Based Bibliography on the Use of Computers for Non-Numerical Mathematics, Computing Review, 7 (4), B1–B31 (July 1966)

    Google Scholar 

  44. E. H. Sibley, The Engineering Assistant: Design of a Symbol Manipulation System, Technical Report CONCOMP, The University of Michigan (Aug. 1967)

    Google Scholar 

  45. J. R. Slagle, A Heuristic Program That Solves Symbolic Integration Problems in Freshman Calculus, Symbolic Automatic Integrator (SAINT), doctoral dissertation, MIT (1961). [A paper based on this thesis appears in “Computers and Thought,“ McGraw-Hill, Book Co., New York (1963).]

    Google Scholar 

  46. R. G. Tobey, R. J. Bobrow, and S. Zilles, Automatic Simplification in formac, in: “Proc. 1965 FJCC,“ Spartan Books, Washington, D. C

    Google Scholar 

  47. R. Tobey, T. Baker, R. Crews, P. Marks, and K. Victor, pl/I-formac INTERPRETER-User’s Reference Manual, IBM 360D 03.3.004 (Oct. 1967)

    Google Scholar 

  48. B. L. Van der Waerden, “Modern Algebra,“ Vol. 1, Frederick Ungar, New York (1953)

    Google Scholar 

  49. A. van Wijngarden, Generalized algol, in: “Annual Review in Automatic Programming,“ Vol. 3, (R. Goodman, ed.), Pergamon Press, New York (1963)

    Google Scholar 

  50. N. Wirth, A Generalization of algol, Comm. ACM 6, 547–554 (Sept. 1963)

    Article  Google Scholar 

  51. N. Wirth and C. A. R. Hoare, A Contribution to the Development of algol, Comm. ACM 9 (6), 413–432 (June 1966)

    Article  Google Scholar 

  52. N. Wirth and H. Weber, Euler, A Generalization of algol, and its Formal Definition, Part I, Comm. ACM 9 (1), 13–25 (Jan. 1966); Part II, Comm. ACM 9 (2), 89–99 (Feb. 1966)

    Article  Google Scholar 

  53. E. R. Berlekamp, On the Factorization of Polynomials over Finite Fields, Bell System Tech. J. 1967

    Google Scholar 

  54. D. E. Knuth, “The Art of Computer Programming,“ Vol. II, Addison Wesley Publishing Co., Reading, Mass., to be published

    Google Scholar 

  55. R. M. Risch, On the Integration of Elementary Functions which are Built up Using Algebraic Operations, SDC Document SP-2801/002/00, System Development Corporation, Santa Monica (June 26, 1968)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computing Center, FIDES Union Fiduciaire, Zurich, Switzerland

    M. E. Engeli

  2. Formerly at the Department of Computer Sciences and Computation Center, University of Texas, Austin, USA

    M. E. Engeli

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  1. M. E. Engeli
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Editors and Affiliations

  1. College of Engineering, University of Florida, Gainesville, Florida, USA

    Julius T. Tou

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© 1969 Plenum Press

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Engeli, M.E. (1969). Formula Manipulation—The User’s Point of View. In: Tou, J.T. (eds) Advances in Information Systems Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-9050-7_3

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  • DOI: https://doi.org/10.1007/978-1-4615-9050-7_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-9052-1

  • Online ISBN: 978-1-4615-9050-7

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