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Symbolic Computing and Its Relationship to Particle Physics

  • J. A. Campbell
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 13/1974)

Abstract

Regrettably, it is still true that “computing” means “FORTRAN” to a majority of physicists M, and that in Europe it means “ALGOL” to a majority of those physicists not included in M. The various alternative names for the type of computing which I shall describe have evolved as defences against the FORTRAN-ALGOL ideology. Firstly, as FORTRAN in particular is used for numerical computation, there is the name “non-numerical computing” for computations in systems which allow answers to be given in terms of symbols. This name is good, but not perfect, because it does not do justice to the possibility of adjoining to symbolic results integer or rational or floating-point coefficients, or even to the use of symbolic means to calculate purely numerical rational quantities (e.g. Bernoulli numbers, Clebsch-Gordan coefficients) with programs that are much more compact than programs in FORTRAN. “Algebraic computing” is a name which gives the same flavour without the limitations of the previous suggestion, but it suffers from the rather more serious defect that most “algebraic” computations in the past (e.g. (3) below) have actually dealt with problems in analysis and not algebra.

Keywords

International Atomic Energy Agency Feynman Diagram Celestial Mechanic Garbage Collection Symbolic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    W. H. Jefferys, Celest. Mech. 2, 474 (197o).Google Scholar
  2. 2.
    J. A. Campbell, Comp. Phys. Comm. 1, 251 (197o).Google Scholar
  3. 3.
    J. McCarthy et al., “LISP 1.5 Programmer’s Manual”, MIT Press, Cambridge, Massachusetts (1965).Google Scholar
  4. 4.
    A. C. Hearn, Comm. A. C. M. 14, 511 (1971).MATHGoogle Scholar
  5. 5.
    A. C. Hearn, in “Computing as a Language of Physics”, International Atomic Energy Agency, Vienna (1972), p. 567.Google Scholar
  6. 6.
    W. H. Jefferys, Comm. A. C. M. 14, 538 (1971).Google Scholar
  7. 7.
    D. Barton and J. P. Fitch, Rep. Prog. Phys. 35, 235 (1972).CrossRefADSGoogle Scholar
  8. 8.
    H. J. Kaiser, Nucl. Phys. 43, 62o (1963).MathSciNetGoogle Scholar
  9. 9.
    H. Strubbe, “Computations with SCHOONSCHIP”, Report DD/73/16, Data-Handling Division, CERN, Geneva (1973)Google Scholar
  10. 10.
    M. Veltman, Comp. Phys. Comm. (Suppi.) 3, 75 (1972).Google Scholar
  11. 11.
    G. E. Collins, in “Proceedings of the Second Symposium on Symbolic and Algebraic Manipulation”, A.C.M. Headquarters, New York (1971), p. 144.CrossRefGoogle Scholar
  12. 12.
    W. H. Jefferys, Celest. Mech. 6, 117 (1972).CrossRefADSGoogle Scholar
  13. 13.
    R. E. Griswold, J. F. Poage and I.P. Polonsky, “The SNOBOL4 Programming Language”, Prentice-Hall Inc., Englewood Cliffs, N.J. (1968).Google Scholar
  14. 14.
    J. A. Campbell, in “Computing as a Language of Physics”, International Atomic Energy Agency, Vienna (1972), p. 391.Google Scholar
  15. 15.
    C. Weissman, “LISP 1.5 Primer”, Dickenson Publishing Co., Belmont, California (1967).Google Scholar
  16. 16.
    D. Lurié, in “Computing as a Language of Physics”, International Atomic Energy Agency, Vienna (1972), p. 529.Google Scholar
  17. 17.
    A. C. Hearn, in “Proceedings of the Second Symposium on Symbolic and Algebraic Manipulation”, A.C.M. Headquarters, New York (1971), p. 128.CrossRefGoogle Scholar
  18. 18.
    D. E. Knuth, “Fundamental Algorithms”, Addison-Wesley, Reading, Massachusetts (1968).Google Scholar
  19. 19.
    D. Barton, S. R. Bourne and J. R. Horton, Comp. J. 13, 243 (197o).Google Scholar
  20. 2o.
    A. C. Hearn, Bull. Amer. Phys. Soc. 9, 436 (1964).Google Scholar
  21. 21.
    D. E. Knuth, “Seminumerical Algorithms”, Addison-Wesley, Reading, Massachusetts (1969).Google Scholar
  22. 22.
    J. A. Campbell, J. Comp. Phys. 2, 412 (1968).CrossRefMATHADSGoogle Scholar
  23. 23.
    R. H. Risch, Trans. Amer. Math. Soc. 139, 167 (1969).CrossRefMATHGoogle Scholar
  24. 24.
    J. H. Griesmer and R. D. Jenks, in “Proceedings of the Second Symposium on Symbolic and Algebraic Mani,pulation”, A.C.M. Headquarters, New York (1971),p. 42.Google Scholar
  25. 25.
    H. Strubbe, “Internal Mechanism of a SCHOONSCHIP Calculation”, Report DD/73/10, Data-Handling Division, CERN, Geneva (1973).Google Scholar
  26. 26.
    W. A. Martin and R. J. Fateman, in “Proceedings of the Second Symposium on Symbolic and Algebraic Manipulation”, A.C.M. Headquarters, New York (1971), p. 59.CrossRefGoogle Scholar
  27. 27.
    J. A. Campbell, Nucl. Phys. Bl, 283 (1967); Nucl. Phys. B10, 190 (E) (1969).Google Scholar
  28. 28.
    J. A. Fox and A. C. Hearn, J. Comp. Phys., to be published.Google Scholar
  29. 29.
    R. A. d’Inverno, Comp. J. 12, 124 (1969).CrossRefGoogle Scholar
  30. 30.
    A. D. Payne, Comp. Phys. Comm. 4, 100 (1972).Google Scholar
  31. 31.
    J. A. Campbell, W. H. Jefferys, Celest. Mech. 2, 467 (1970).CrossRefMATHADSGoogle Scholar
  32. 32.
    J. A. Campbell, A. C. Hearn, J. Comp. Phys. 5, 280 (1970).CrossRefMATHADSGoogle Scholar
  33. 33.
    Y-S. Tsai and A.C. Hearn, Phys. Rev. 140, B721 (1965).CrossRefADSGoogle Scholar
  34. 34.
    R. W. Brown, J. Smith, Phys. Rev. D3, 207 (1971).ADSGoogle Scholar
  35. 35.
    M. J. Levine, J. Comp. Phys. 1, 454 (1967).CrossRefMATHADSGoogle Scholar
  36. 36.
    M. J. Levine, J. A. Wright, Phys. Rev. Lett. 26, 1351 (1971).CrossRefADSGoogle Scholar
  37. 37.
    A. Petermann, Heiv. Phys. Acta 30, 407 (1957); C.M. Sommerfield, Ann. Phys. (N.Y.) 5, 26 (1958).Google Scholar
  38. 38.
    S. D. Drell, H. Pagels, Phys. Rev. 140, B397 (1965).CrossRefADSMathSciNetGoogle Scholar
  39. 39.
    R. G. Parsons, Phys. Rev. 168, 1562 (1968).CrossRefADSGoogle Scholar
  40. 40.
    J. Aldins, T. Kinoshita, S. J. Brodsky, A. J. Dufner, Phys. Rev. Lett. 23, 441 (1969).CrossRefADSGoogle Scholar
  41. 41.
    J. A. Mignaco, E. Remiddi, Nuov. Cim. 60A, 519 (1969).CrossRefADSGoogle Scholar
  42. 42.
    J. Aldins, S. J. Brodsky, A. J. Dufner, T. Kinoshita, Phys. Rev. Dl, 2378 (197o).Google Scholar
  43. 43.
    J. Calmet, M. Perrottet, Phys. Rev. D3, 3101 (1971).ADSGoogle Scholar
  44. 44.
    S. J. Brodsky, T. Kinoshita, Phys. Rev. D3, 356 (1971).ADSGoogle Scholar
  45. 45.
    M. A. Samuel, “Estimates of the Eighth Order Corrections to the Anomalous Magnetic Moment of the Muon’, Oklahoma State University preprint (1973).Google Scholar
  46. 46.
    B. Lautrup, A. Petermann, E. de Rafael, Phys. Rep. 3C, 193 (1972).CrossRefADSGoogle Scholar
  47. 47.
    T. Kinoshita, P. Cvitanovic, Phys. Rev. Lett. 29, 1534 (1972).CrossRefADSGoogle Scholar
  48. 48.
    J. Gilleland and A. Rich, Phys. Rev. Lett. 23, 1130 (1969).CrossRefADSGoogle Scholar
  49. 49.
    J. Kahane, J. Math. Phys. 9, 1732 (1968).CrossRefADSGoogle Scholar
  50. 50.
    J. S. R. Chisholm, J. Comp. Phys. 8, 1 (1971).CrossRefMATHADSMathSciNetGoogle Scholar
  51. 51.
    A. C. Hearn, Nuov. Cim. 21, 333 (1961).CrossRefMATHMathSciNetGoogle Scholar
  52. 52.
    R. B. Clark, B. L. Manny, R. G. Parsons, Ann. Phys. (N.Y.) 69, 522 (1972).CrossRefADSGoogle Scholar
  53. 53.
    J. Calmet, M. Perrottet, J. Comp. Phys. 7, 191 (1971).CrossRefMATHADSGoogle Scholar
  54. 54.
    P. B. James, G. R. North, J. Comp. Phys. 7, 354 (1971).CrossRefADSGoogle Scholar
  55. 55.
    M. Perrottet, in “Computing as a Language of Physics”, International Atomic Energy Agency, Vienna (1972), p. 555.Google Scholar
  56. 56.
    T. W. Pratt, D. P. Friedman, Comm. A.C.M. 14, 460 (1971).MATHMathSciNetGoogle Scholar
  57. 57.
    H. Umezawa, A. Visconti, Nuov. Cim. 1, 1079 (1955).CrossRefMATHMathSciNetGoogle Scholar
  58. 58.
    Y. Le Gaillard, A. Visconti, J. Math. Phys. 6, 1774 (1965).CrossRefADSGoogle Scholar
  59. 59.
    J. Soffer, A. Visconti, Nuov. Cim. 38, 817 (1965).CrossRefMATHGoogle Scholar
  60. 60.
    L.L. Lewin, “Dilogarithms and Associated Functions”, Macdonald, London (1958).Google Scholar
  61. 61.
    K. S. Kölbig, J. A. Mignaco, E. Remiddi, B.I.T. 10, 38 (1970).MATHGoogle Scholar
  62. 62.
    J. Moses, SIGSAM Bull. A.C.M. nr. 13, p. 14 (1969).Google Scholar
  63. 63.
    M. J. Levine, Nuov. Cim. 48, 67 (1967).CrossRefADSGoogle Scholar
  64. 64.
    A. Petermann, in “Advanced Computing Methods in Theo- retical Physics”, Centre National de laRecherche.Scientifique, Marseille (1971), vol. 2, p. IV. 62.Google Scholar
  65. 65.
    T. Appelquist, S. J. Brodsky, Phys. Rev. Lett. 24, 562 (1970). A further account of independent checks of parts of the results, again by computer, is given by S. J. Brodsky and S. D. Drell, Ann. Rev. Nucl. S.i. 20, 147 (1970). See also ref. 82.Google Scholar
  66. 66.
    J. L. Gammel, M. T. Menzel, Phys. Rev. A7, 858 (1973).CrossRefADSGoogle Scholar
  67. 67.
    C. Hewitt, in “Second International Joint Conference on Artificial Intelligence”,British Computer Society, London (1971), p. 167.Google Scholar
  68. 68.
    T. Winograd, “Understanding Natural Language”, Edinburgh University Press, Edinburgh (1972).Google Scholar
  69. 69.
    A. Deprit, Celest. Mech. 1, 12 (1969).CrossRefMATHADSMathSciNetGoogle Scholar
  70. 70.
    M. Gell-Mann, D. Horn and J. Weyers, in “Proceedings of the 1967 Heidelberg International Conference on Elementary Particles”, North-Holland, Amsterdam (1968), p. 479.Google Scholar
  71. 71.
    P. M. Morse and H. Feshbach, “Methods of Theoretical Physics”, McGraw-Hill, New York (1955), vol. 1, p. 657–666.Google Scholar
  72. 72.
    G. S. Chandler, T. Thirunamachandran, J. A. Campbell, J. Chem. Phys. 49, 3640 (1968).CrossRefADSGoogle Scholar
  73. 73.
    R. A. d’Inverno, R. A. Russell-Clark, J. Math. Phys. 12, 1258 (1971).CrossRefADSGoogle Scholar
  74. 74.
    G. W. Gibbons, R. A. Russell-Clark, Phys. Rev. Lett. 30, 398 (1973).CrossRefADSGoogle Scholar
  75. 75.
    B. Lautrup, Phys. Lett. 38B, 408 (1972).CrossRefGoogle Scholar
  76. 76.
    R. Penrose, M.A.H. MacCallum, Phys. Rep. 6C, 241 (1973).CrossRefADSMathSciNetGoogle Scholar
  77. 77.
    D. E. Knuth, “Sorting and Searching”, Addison-Wesley, Reading, Massachusetts (1973).Google Scholar
  78. 78.
    J. Schwinger, Proc. Nat. Acad. Sci. 37, 452 and 455 (1951).Google Scholar
  79. 79.
    R. P. Feynman, in The Quantum Theory of Fields“, Interscience, London (1961), p. 75–76.Google Scholar
  80. 80.
    H. G. Kahrimanian, “Analytic Differentiation by a Digital Computer”, M. A. thesis, Temple University, Philadelphia (1953)Google Scholar
  81. 81.
    J. Moses, Comm. A.C.M. 14, 548 (1971).MATHMathSciNetGoogle Scholar
  82. 82.
    E. Remiddi, Comp. Phys. Comm. 4, 193 (1972).Google Scholar
  83. 83.
    M. J. Levine, J. Wright, Phys. Rev. D8, 3171 (1973).ADSGoogle Scholar
  84. 84.
    D. Billi, M. Caffo, E. Remiddi, Lett. Nuov. Cim. 4, 657 (1972).CrossRefGoogle Scholar
  85. 85.
    M. J. Levine, R. Roskies, Phys. Rev. Lett. 30, 772 (1973).CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • J. A. Campbell
    • 1
  1. 1.King’s College Research CentreKing’s College CambridgeEngland

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