Computer Algebra Applications

  • J. Calmet
  • J. A. van Hulzen
Part of the Computing Supplementa book series (COMPUTING, volume 4)


A survey of applications based either on fundamental algorithms in Computer algebra or on the use of a Computer algebra system is presented. Since many survey articles are previously published, we did not attempt to be exhaustive. We discuss mainly recent work in biology, chemistry, physics, mathematics and Computer science, thus again confirming that applications have both engineering and scientific aspects, i.e. apart from delivering results they assist in gaining insight as well.


Computer Algebra Projective Geometry Chinese Remainder Theorem Abstract Data Type Feynman Parameter 


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  1. [1]
    Ablowitz, M. J., Romani, A., Segur, H.: A Connection Between Nonlinear Evolution Equations and Ordinary Differential Equations of P-Type. I. J. Math. Phys. 21/4, 715–721 (1980).CrossRefMATHGoogle Scholar
  2. [2]
    Aman, J., Karlhede, H.: An Algorithmic Classification of Geometries in General Relativity. SYMSAC 1981, 79–84.Google Scholar
  3. [3]
    Anderson, J. D., Lau, E. L.: Application of MACSYMA to First Order Perturbation Theory in Celestial Mechanics. MACSYMA 77, 395–404 (1977).Google Scholar
  4. [4]
    Anderson, N., Wang, P. S.: MACSYMA Experiments with a Modified Khachian-Type Algorithm in Linear Programming. SIGSAM Bull. 14/1, 8–14 (1980).CrossRefMATHGoogle Scholar
  5. [5]
    Barton, D., Fitch, J. P.: A Review of Algebraic Manipulation Programs and Their Application. Comp. J. 15, 362–381 (1972).CrossRefMATHGoogle Scholar
  6. [6]
    Barton, D., Fitch, J. P.: Applications of Algebraic Manipulative Programs in Physics. Reports on Progress in Physics 35, 235–314 (1972).CrossRefGoogle Scholar
  7. [7]
    Berlekamp, E. R.: Algebraic Coding Theory. New York: McGraw-Hill 1968.MATHGoogle Scholar
  8. [8]
    Bjorken, J. D., Drell, S. D.: Relativistic Quantum Fields. New York: McGraw-Hill 1964.Google Scholar
  9. [9]
    Bordoni, L., Colagrossi, A.: An Application of REDUCE to Industrial Mechanics. SIGSAM Bull. 15/2, 8–12 (1981).CrossRefMATHGoogle Scholar
  10. [10]
    Bossi, A., Colussi, L., Cobelli, C., Romanin Jacur, G.: Identifiability of Compartmental Models: Algorithms to Solve an Actual Problem by Means of Symbolic Calculus. SIGSAM Bull. 14/4, 35–40 (1980).CrossRefMATHGoogle Scholar
  11. [11]
    Brenner, R. L.: The Evaluation of Feynman Diagrams in MACSYMA. MACSYMA 1979, 1–24.Google Scholar
  12. [12]
    Brent, R. P., Gustavson, F. G., Yun, D.Y.Y.: Fast Solution of Toeplitz Systems of Equations and Computation of Pade-Approximants. Yorktown Heights, N. Y.: IBM Research, Report RC 8173 1980.Google Scholar
  13. [13]
    Brown, W. S.: ALTRAN User’s Manual, 4th ed. Murray Hill, N. J.: Bell Laboratories 1977.Google Scholar
  14. [14]
    Brown, W. S., Hearn, A. C.: Application of Symbolic Mathematical Computations. Comput. Phys. Commun. 17, 207–215 (1979).CrossRefGoogle Scholar
  15. [15]
    Caffo, M., Remiddi, E., Turrini, S.: An Algorithm for the Analytic Evaluation of a Class of Integrals. EUROSAM 1979, 52–57.Google Scholar
  16. [16]
    Calmet, J., Visconti, A.: Computing Methods in Quantum Electrodynamics. In: Fields Theory, Quantization and Statistical Physics (Tirapegui, E., ed.), pp. 33–57. Dordrecht: Reidel 1981.CrossRefGoogle Scholar
  17. [17]
    Char, B.: Using Lie Transformation Groups to Find Closed Form Solutions to First Order Ordinary Differential Equations. SYMSAC 1981, 44–50.Google Scholar
  18. [18]
    Chattergy, R.: Reliability Analysis of On-Line Computer Systems Using Computer Algebraic Manipulations. University of Hawali: Report A 76–1, 1976.Google Scholar
  19. [19]
    Computers in Non-Associative Rings and Algebra (Beck, R. E., Kolman, B., eds.). New York- London: Academic Press 1977.Google Scholar
  20. [20]
    Deila Dora, J., Tournier, E.: Formal Solutions of Differential Equations in the Neighbourhood of Singular Points. SYMSAC 1981, 25–29.Google Scholar
  21. [21]
    Deprit, A., Henrard, J., Rom, A.: Lunar Ephemeris: Delaunay’s Theory Revisited. Science 168, 1569–1570 (1970).CrossRefGoogle Scholar
  22. [22]
    Feldman, H. A.: Some Symbolic Computations in Finite Fields. SYMSAM 1966, 79–96.Google Scholar
  23. [23]
    Felsch, V.: A KWIC Indexed Bibliography on the Use of Computers in Group Theory and Related Topics. SIGSAM Bull. 12/1, 23–86 (1978).Google Scholar
  24. [24]
    Fitch, J. P.: The Application of Symbolic Algebra in Physics-a Case of Creeping Flow. EUROSAM 1979, 30–41.Google Scholar
  25. [25]
    Franchi-Zannettacci, M. P.: Evaluation d’Orbre Pour un Calcul Formel. (Sixth CAAP’ 81.) Lecture Notes in Computer Science, Vol. 111. Berlin-Heidelberg-New York: Springer 1981.Google Scholar
  26. Gastmans, R., Van Proeyen, A., Verbaeten, P.: Symbolic Evaluation of Dimensionally Regularized Feynman Diagrams. Comput. Phys. Commun. (to appear).Google Scholar
  27. [27]
    Geddes, K. O.: Symbolic Computation of Pade Approximants. ACM Trans. Math. Software 5, 218–233 (1979).CrossRefMATHMathSciNetGoogle Scholar
  28. [28]
    Good, J. J.: The Interaction of Algorithms and Practical Fourier Series. J. Royal Statist. Soc. B20, 361–372 (1958).MathSciNetGoogle Scholar
  29. [29]
    Gragert, P.: Symbolic Computations in Prolongation Theory. Ph.D. Thesis, Twente Univ. of Technology, 1981.Google Scholar
  30. [30]
    Guttag, J. V., Horowitz, E., Musser, D. R.: Abstract Data Types and Software Validation. Commun. ACM 21, 1048–1064 (1978).CrossRefMATHMathSciNetGoogle Scholar
  31. [31]
    Hajee, G.: The Investigation of Movable Critical Points of ODE’s and Mh Order Systems of ODE’s Using Formula Manipulation. MS Thesis, Dept. of Appl. Math., Twente Univ. of Technology, 1982.Google Scholar
  32. [32]
    Hawkes, P. W.: Computer Calculation of the Aberration Coefficients of High-Frequency Lenses. Proc. Sixth Int. Conf. on High Voltage Electron Microscopy, Antwerp 80. Electron Microscopy 4, 46–49 (1980).Google Scholar
  33. [33]
    Hayter, J. B., Penfold, J.: An Analytic Structure Factor for Macro Ion Solutions. Molecular Phys. 42, 109–118 (1981).CrossRefGoogle Scholar
  34. [34]
    Holme, A.: Some Computing Aspects of Projective Geometry I. University of Bergen: Preprint 1980.Google Scholar
  35. [35]
    Howard, J. C.: MACSYMA as an Aid to Simulation Modelling. MACSYMA 1979, 483–521.Google Scholar
  36. [36]
    Howard, J. C.: Practical Applications of Symbolic Computation. Guilford, Surrey, England: LPC Sci. and Techn. Press 1980.Google Scholar
  37. [37]
    Howell, J. A., Smith, J. F., Waterman, M. S.: Using MACSYMA to Compute Generating Functions for RNA. MACSYMA 1979, 126–139.Google Scholar
  38. [38]
    Hulshof, B. J. A., Van Hulzen, J. A., Smit, J.: Code Optimization Facilities, Applied in the NETFORM Context. Twente Univ. of Technology: TW Memorandum 368 (1981).Google Scholar
  39. [39]
    D’Inverno, R. A.: A Review of Algebraic Computing in General Relativity. Einstein Commemorative Volume (Held, A., et al., eds.). New York: Plenum Press 1980.Google Scholar
  40. [40]
    Jenks, R. D.: Push 80. SIGSAM Bull. 13/4, 3–6 (1979).Google Scholar
  41. [41]
    Kahane, J.: An Algorithm for Reducing Contracted Products of y-Matrices. J. Math. Phys. 9, 1732 (1968).CrossRefGoogle Scholar
  42. [42]
    Keller, H. B., Pereyra, V.: Symbolic Generation of Finite Difference Formulas. Math, of Comput. 32, 955–971 (1978).CrossRefMATHMathSciNetGoogle Scholar
  43. Krupnikov, E. D.: Private Communication.Google Scholar
  44. [44]
    Lafferty, E. L.: Hypergeometric Function Reduction-an Adventure in Pattern Matching. MACSYMA 1979, 465–481.Google Scholar
  45. [45]
    Lenstra Jr., H. W.: Primality Testing Algorithms. Seminaire Bourbaki, 33-ieme annee 1980–81, expose 576. Paris: Ecole Normale Sup. 1981.Google Scholar
  46. [46]
    Leon, J. S., Pless, V.: CAMAC 79. EUROSAM 1979, 249–257.Google Scholar
  47. [47]
    London, R. L., Musser, D. R.: The Application of a Symbolic Mathematical System to Program Verification. Proc. ACM 1974, 265–273. New York: ACM 1974.Google Scholar
  48. [48]
    Mah, R. S. H., Rafal, M.: Automatic Program Generation in Chemical Engineering Computation. Trans. Inst. Chem. Eng. 49, 101–108 (1971).Google Scholar
  49. [49]
    Maurer, W. D.: Computer Experiments in Finite Algebra. SYMSAM 1966, 598–603.Google Scholar
  50. Mejia, R., Stephenson, J. L.: Symbolics and Numerics of a Multinephron Kidney Model. MACSYMA 1979, 597–603.Google Scholar
  51. [51]
    Mignotte, M.: Introduction ä la cryptographie, Comptes-rendus des V-iemes Journees Informatiques, University of Nice: IMAN 1980.Google Scholar
  52. [52]
    Mora, F.: Computation of Finite Categories. University of Genova: Unpublished Note 1979. NeubüserGoogle Scholar
  53. [53]
    J., Bülow, R., Wondratschek, H.: On Crystallography in Higher Dimensions I, II, III. Acta Cryst. A27, 517–535 (1971).Google Scholar
  54. [54]
    Ng, E. W.: A Study of Alternative Methods for the Symbolic Integration of Elliptic Integrals. SYMSAC 1976, 44–50.Google Scholar
  55. [55]
    Ng, E. W.: Symbolic-Numeric Interface: A Review. EUROSAM 1979, 330–345.Google Scholar
  56. [56]
    Pavelle, R.: Applications of MACSYMA to Problems in Gravitation and Differential Geometry. MACSYMA1979, 256–276.Google Scholar
  57. [57]
    Pless, V., Sloane, N. J. A.: On the Classification and Enumeration of Self-Dual Codes. J. Comb. Theory18, 313–334(1975).CrossRefMATHMathSciNetGoogle Scholar
  58. [58]
    Ponsignon, J. P.: Decryptage des Notations Lineaires en Chimie Organique. Application ä WLN. CALSYF 1, 1981 (unpublished Bull.). (Bergman, M., Calmet, J., eds.)Google Scholar
  59. [59]
    Sammet, J. E.: Revised Annotated Description Based Bibliography on the Use of Computers for Non-Numerical Mathematics. IFIP 1966, 358–484.Google Scholar
  60. [60]
    Sammet, J. E., Ivinsky, V.: Brief Annotated Bibliography/Reference List of Items Relevant to the Use of Computers in Formal Mathematics. SIGSAM Bull. 27, 30 (1973).Google Scholar
  61. [61]
    Schmidt, P.: Automatic Symbolic Solution of Differential Equations of First Order and First Degree. EUROSAM 1979, 114–125.Google Scholar
  62. [62]
    Shamir, A.: How to Share a Secret. Commun. ACM 22, 612–613 (1979).CrossRefMATHMathSciNetGoogle Scholar
  63. [63]
    Smit, J.: New Recursive Minor Expansion Algorithms, a Presentation in a Comparative Context. EUROSAM 1979, 74–87.Google Scholar
  64. [64]
    Smit, J.: A Cancellation Free Algorithm, with Factoring Capabilities, for the Efficient Solution of Large, Sparse Sets of Equations. SYMSAC 1981, 146–154.Google Scholar
  65. [65]
    Smit, J., Hulshof, B. J. A., Van Hulzen, J. A.: NETFORM and Code Optimizer Manual. Twente Univ. of Tech.: TW Memorandum 373, 1981.Google Scholar
  66. [66]
    Smit, J., Van Hulzen, J. A.: Symbolic-Numeric Methods in Microwave Technology. Twente Univ. of Technology: TW Memorandum 374, 1981.Google Scholar
  67. [67]
    Sorna, T.: Relativistic Aberration Formulas for Combined Electromagnetic Focusing-Deflection System. Optik 49, 255–262 (1977).Google Scholar
  68. [68]
    Squire, W.: Private Communication.Google Scholar
  69. [69]
    Stoutemyer, D. R.: Computer Symbolic Math. & Education: A Radical Proposal. MACSYMA 1979, 142–158, and SIGSAM Bull. 13/3, 8–24 (1979).Google Scholar
  70. [70]
    Stoutemyer, D. R.: Computer Symbolic Math, in Physics Education. Am. J. Phys. 49, 85–88 (1981).Google Scholar
  71. [71]
    Stoutemyer, D. R.: The Coming Revolution in Scientific Computation. Comput. & Educ. 5, 53–55 (1981).CrossRefGoogle Scholar
  72. [72]
    Van Hulzen, J. A.: Computational Problems in Producing Taylor Coefficients for the Rotating Disk Problem. SIGSAM 14/2, 36–49 (1980).CrossRefGoogle Scholar
  73. [73]
    Verbaeten, P.: The Automatic Construction of Pure Recurrence Relations. EUROSAM 1974, 96–98.Google Scholar
  74. [74]
    Winograd, S.: On Computing the Discrete Fourier Transform. Math. Comp. 32, 175–199 (1978).CrossRefMATHMathSciNetGoogle Scholar
  75. [75]
    Woll, A.: γ-Algebra Algorithms for Canonical Hypercomplex Representations. EUROSAM 1979, 546–557 (1979).Google Scholar
  76. [76]
    Wyman, J.: Addition No. 3, 4 and 5 to J. E. Sammet [59]. SIGSAM Bull. 10 (1968), 12 (1969), 15 (1970).Google Scholar
  77. [77]
    Yun, D. Y. Y., Stoutemyer, R. D.: Symbolic Mathematical Computation. In: Encyclopedia of Computer Science and Technology (Beizer, J., Holzman, A. G., Kent, A., eds.), Vol. 15, pp. 235–310. New York-Basel: Marcel Dekker 1980.Google Scholar
  78. [78]
    Zeis, E., Cefola, P. J.: Computerized Algebraic Utilies for the Construction of Non-Singular Satellite Theories. MACSYMA 1979, 277–294.Google Scholar
  79. [79]
    Zimmer, H. G.: Computational Problems, Methods and Results in Algebraic Number Theory. Lecture Notes in Mathematics, Vol. 262. Berlin-Heidelberg-New York: Springer 1972.MATHGoogle Scholar
  80. [80]
    REDUCE-Newsletters. Univ. of Utah: Symb. Comp. Group (since 1978).Google Scholar

Copyright information

© Springer-Verlag/Wien 1983

Authors and Affiliations

  • J. Calmet
    • 1
  • J. A. van Hulzen
    • 2
  1. 1.Laboratoire d’Informatique et de Mathématiques Appliquées de GrenobleIMAGGrenoble CédexFrance
  2. 2.Department of Applied MathematicsTwente University of TechnologyAE EnschedeThe Netherlands

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