Skip to main content

Symbolic Computation: Past, Present and Future

  • Conference paper
GI — 8. Jahrestagung

Part of the book series: Informatik-Fachberichte ((INFORMATIK,volume 16))

Abstract

During the past decade, symbolic computation has become an important problem solving tool for many algebraic calculations in physics and engineering. In this paper, we describe the nature of the field along with some of the characteristics of presently available symbolic computation systems. Some typical applications to physical problems are then considered. Analytic integration by computer is also discussed. We conclude with some considerations about the future of the field.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Kahrimanian, H.G., Analytical differentiation by a Digital Computer, M.A. Diss, Temple University, Philadelphia, PA, 1953.

    Google Scholar 

  2. Nolan, J., Analytical Differentiation on a Digital Computer, M.A. Diss, MIT, Cambridge, MA, 1953.

    Google Scholar 

  3. Brown, W.S., ALTRAN User’s Manual, Third Edition, Bell Laboratories, 1973.

    Google Scholar 

  4. Hearn, A.C., REDUCE User’s Manual, Second Edition, University of Utah, 1973.

    Google Scholar 

  5. Jenks, R.D., The SCRATCHPAD Language, SIGPLAN Notices, ACM, New York, 9 (1974) 101–111.

    Google Scholar 

  6. Bogen, R., et al., MACSYMA Reference Manual, Project MAC, M.I.T., Cambridge, MA, 1974.

    Google Scholar 

  7. Kernighan, B.W., and Cherry, L.L., Comm. ACM 18 (1975), 151–157.

    Article  Google Scholar 

  8. Feldman, S.I., An Application of Symbolic Computation to Crystal Physics, SIGSAM Bulletin, ACM, New York, No. 34 (1975) 19–24.

    Google Scholar 

  9. Barton, D., and Fitch, J.P., Rep. Prog. Phys. 35 (1972) 235–314.

    Article  Google Scholar 

  10. Delaunay, C., Théorie du Mouvement de la Lune (Extraits des Mém. Acad. Sci.), Mallet-Bachelier, Paris, 1860.

    Google Scholar 

  11. Deprit, A., Henrard, J., and Rom, A., Science 168 (1970) 1569–1570.

    Article  Google Scholar 

  12. Jefferys, W.H., and Ries, L.M., Astronomical Journal 80 (1975) 876–884.

    Article  Google Scholar 

  13. Rom, A., Celest. Mech. 3 (1971) 331–345.

    Article  MATH  Google Scholar 

  14. Jeffreys, W.H., Celest. Mech. 2 (1970) 474–480.

    Article  Google Scholar 

  15. Fitch, J.P., CAMAL User’s Manual, Computer Lab., Cambridge, U.K. (1975).

    Google Scholar 

  16. Jeffreys, W.H., Comm. ACM 14 (1971) 538–541.

    Article  Google Scholar 

  17. Feynman, R.P., Phys. Rev. 76 (1949) 769–789.

    Article  MathSciNet  MATH  Google Scholar 

  18. Bjorken, J.D., and Drell, S.D., Relativistic Quantum Mechanics, McGraw-Hill, New York, 1964.

    Google Scholar 

  19. Kahane, J., J. Math. Phys. 9 (1968) 1732–1738.

    Article  Google Scholar 

  20. Campbell, J.A., Comp. Phys. Comm. 1 (1970) 251–264.

    Article  Google Scholar 

  21. Hearn, A.C., Comm. ACM 14 (1971) 511–516.

    Article  MATH  Google Scholar 

  22. Hearn, A.C., Computer Solution of Symbolic Problems in Theoretical Physics, Computing as a Language of Physics, IAEA, Vienna (1972) 567–596.

    Google Scholar 

  23. Campbell, J.A., Acta Phys, Austriaca Suppl. XIII (1974) 595–647.

    Google Scholar 

  24. Strubbe, H., Comp. Phys. Comm. 8 (1974) 1–30.

    Article  Google Scholar 

  25. Perisho, R.C., ASHMEDAI User’s Guide, U.S.A.E.C. Rep. No. C00–3066–44 (1975).

    Google Scholar 

  26. Petermann, A., Helv. Phys. Acta 30 (1957) 407–408.

    Google Scholar 

  27. Maison, D., and Petermann, A., Comp. Phys. Comm. 7 (1974) 121–134.

    Article  Google Scholar 

  28. Fox, J.A., and Hearn, A.C., J. Comp. Phys. 14 (1974) 301–317.

    Article  MATH  Google Scholar 

  29. Levine, M.J., Remiddi, E., and Roskies, R., g e - 2, The Current Status, Proc. of the Fourth Intern. Colloq. on Advanced Comp. Methods in Theor. Phys, St. Maximin, France (1977) 178–192.

    Google Scholar 

  30. Campbell, J.A., and Hearn, A.C., J. Comp. Phys. 5 (1970) 280–327.

    Article  MATH  Google Scholar 

  31. Sasaki, T., Automatic Generation of Feynman Graphs in QED, Rikagaku Kenkyosho, Wako-Shi, Saitama, Japan, Preprint 1975.

    Google Scholar 

  32. Tobey, R.G., et al., PL/I-FORMAC SYMBOLIC MATHEMATICS INTERPRETER, SHARE Contributed Program Library, No. 360 D-0.3.3.004 (1969).

    Google Scholar 

  33. Engeli, M., An Enhanced SYMBAL System, SIGSAM Bulletin, ACM, New York, No. 36 (1975) 21–29.

    Google Scholar 

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

    Google Scholar 

  35. Caviness, B.F., Methods for Symbolic Computation with Transcendental Functions, Proc. of the Fourth Intern. Colloq. on Advanced Comp. Methods in Theor. Phys, St. Maximin, France (1977) 16–43.

    Google Scholar 

  36. Barton, D., and Fitch, J.P., Comm. ACM 14 (1971) 542–547.

    Article  MathSciNet  Google Scholar 

  37. D’inverno, R.A., Comp. J. 12 (1969) 124–127.

    Article  Google Scholar 

  38. Moses, J., Comm. ACM 14 (1971) 527–537.

    Article  MathSciNet  MATH  Google Scholar 

  39. Wang, P., Symbolic Evaluation of definite Integrals by Residue Theory in MACSYMA, Proc. IFIP Congress 74 (1974) 823–827.

    Google Scholar 

  40. Campbell, J.A., Applications of Symbolic Programs to Complex Analysis, Proc. ACM Annual Conf. 72 (1972) 836–839.

    Google Scholar 

  41. Moses, J., Comm. ACM (1971) 548–560.

    Google Scholar 

  42. Hardy, G.H., The Integration of Functions of a Single Variable, Second Edition, CUP, Cambridge, England (1916).

    MATH  Google Scholar 

  43. Risch, R., Trans. AMS 139 (1969) 167–189.

    Article  MathSciNet  MATH  Google Scholar 

  44. Norman, A.C., and Risch, R., to be published.

    Google Scholar 

  45. Norman, A.C., and Moore, P.M.A., Implementing the New Risch Integration Algorithm, Proc. of the Fourth Intern. Colloq. on Advanced Comp. Methods in Theor. Phys, St. Maximin, France (1977) 99–110.

    Google Scholar 

  46. Harrington, S. J., A New Symbolic Integration System in REDUCE, Comp. J., to be published.

    Google Scholar 

  47. Schoichet, S.R., The LISP Machine, Mini-Micro Systems, Boston, MA, Vol. 11, No. 5 (June 1978) 68–74.

    Google Scholar 

  48. Brown, W.S., and Hearn, A.C., Applications of Symbolic Algebraic Computation, Comp. Phys. Comm., to be published.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

Hearn, A.C. (1978). Symbolic Computation: Past, Present and Future. In: Schindler, S., Giloi, W.K. (eds) GI — 8. Jahrestagung. Informatik-Fachberichte, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67091-6_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-67091-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09038-0

  • Online ISBN: 978-3-642-67091-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics