Abstract
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.
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References
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).
Aman, J., Karlhede, H.: An Algorithmic Classification of Geometries in General Relativity. SYMSAC 1981, 79–84.
Anderson, J. D., Lau, E. L.: Application of MACSYMA to First Order Perturbation Theory in Celestial Mechanics. MACSYMA 77, 395–404 (1977).
Anderson, N., Wang, P. S.: MACSYMA Experiments with a Modified Khachian-Type Algorithm in Linear Programming. SIGSAM Bull. 14/1, 8–14 (1980).
Barton, D., Fitch, J. P.: A Review of Algebraic Manipulation Programs and Their Application. Comp. J. 15, 362–381 (1972).
Barton, D., Fitch, J. P.: Applications of Algebraic Manipulative Programs in Physics. Reports on Progress in Physics 35, 235–314 (1972).
Berlekamp, E. R.: Algebraic Coding Theory. New York: McGraw-Hill 1968.
Bjorken, J. D., Drell, S. D.: Relativistic Quantum Fields. New York: McGraw-Hill 1964.
Bordoni, L., Colagrossi, A.: An Application of REDUCE to Industrial Mechanics. SIGSAM Bull. 15/2, 8–12 (1981).
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).
Brenner, R. L.: The Evaluation of Feynman Diagrams in MACSYMA. MACSYMA 1979, 1–24.
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.
Brown, W. S.: ALTRAN User’s Manual, 4th ed. Murray Hill, N. J.: Bell Laboratories 1977.
Brown, W. S., Hearn, A. C.: Application of Symbolic Mathematical Computations. Comput. Phys. Commun. 17, 207–215 (1979).
Caffo, M., Remiddi, E., Turrini, S.: An Algorithm for the Analytic Evaluation of a Class of Integrals. EUROSAM 1979, 52–57.
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.
Char, B.: Using Lie Transformation Groups to Find Closed Form Solutions to First Order Ordinary Differential Equations. SYMSAC 1981, 44–50.
Chattergy, R.: Reliability Analysis of On-Line Computer Systems Using Computer Algebraic Manipulations. University of Hawali: Report A 76–1, 1976.
Computers in Non-Associative Rings and Algebra (Beck, R. E., Kolman, B., eds.). New York- London: Academic Press 1977.
Deila Dora, J., Tournier, E.: Formal Solutions of Differential Equations in the Neighbourhood of Singular Points. SYMSAC 1981, 25–29.
Deprit, A., Henrard, J., Rom, A.: Lunar Ephemeris: Delaunay’s Theory Revisited. Science 168, 1569–1570 (1970).
Feldman, H. A.: Some Symbolic Computations in Finite Fields. SYMSAM 1966, 79–96.
Felsch, V.: A KWIC Indexed Bibliography on the Use of Computers in Group Theory and Related Topics. SIGSAM Bull. 12/1, 23–86 (1978).
Fitch, J. P.: The Application of Symbolic Algebra in Physics-a Case of Creeping Flow. EUROSAM 1979, 30–41.
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.
Gastmans, R., Van Proeyen, A., Verbaeten, P.: Symbolic Evaluation of Dimensionally Regularized Feynman Diagrams. Comput. Phys. Commun. (to appear).
Geddes, K. O.: Symbolic Computation of Pade Approximants. ACM Trans. Math. Software 5, 218–233 (1979).
Good, J. J.: The Interaction of Algorithms and Practical Fourier Series. J. Royal Statist. Soc. B20, 361–372 (1958).
Gragert, P.: Symbolic Computations in Prolongation Theory. Ph.D. Thesis, Twente Univ. of Technology, 1981.
Guttag, J. V., Horowitz, E., Musser, D. R.: Abstract Data Types and Software Validation. Commun. ACM 21, 1048–1064 (1978).
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.
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).
Hayter, J. B., Penfold, J.: An Analytic Structure Factor for Macro Ion Solutions. Molecular Phys. 42, 109–118 (1981).
Holme, A.: Some Computing Aspects of Projective Geometry I. University of Bergen: Preprint 1980.
Howard, J. C.: MACSYMA as an Aid to Simulation Modelling. MACSYMA 1979, 483–521.
Howard, J. C.: Practical Applications of Symbolic Computation. Guilford, Surrey, England: LPC Sci. and Techn. Press 1980.
Howell, J. A., Smith, J. F., Waterman, M. S.: Using MACSYMA to Compute Generating Functions for RNA. MACSYMA 1979, 126–139.
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).
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.
Jenks, R. D.: Push 80. SIGSAM Bull. 13/4, 3–6 (1979).
Kahane, J.: An Algorithm for Reducing Contracted Products of y-Matrices. J. Math. Phys. 9, 1732 (1968).
Keller, H. B., Pereyra, V.: Symbolic Generation of Finite Difference Formulas. Math, of Comput. 32, 955–971 (1978).
Krupnikov, E. D.: Private Communication.
Lafferty, E. L.: Hypergeometric Function Reduction-an Adventure in Pattern Matching. MACSYMA 1979, 465–481.
Lenstra Jr., H. W.: Primality Testing Algorithms. Seminaire Bourbaki, 33-ieme annee 1980–81, expose 576. Paris: Ecole Normale Sup. 1981.
Leon, J. S., Pless, V.: CAMAC 79. EUROSAM 1979, 249–257.
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.
Mah, R. S. H., Rafal, M.: Automatic Program Generation in Chemical Engineering Computation. Trans. Inst. Chem. Eng. 49, 101–108 (1971).
Maurer, W. D.: Computer Experiments in Finite Algebra. SYMSAM 1966, 598–603.
Mejia, R., Stephenson, J. L.: Symbolics and Numerics of a Multinephron Kidney Model. MACSYMA 1979, 597–603.
Mignotte, M.: Introduction ä la cryptographie, Comptes-rendus des V-iemes Journees Informatiques, University of Nice: IMAN 1980.
Mora, F.: Computation of Finite Categories. University of Genova: Unpublished Note 1979. Neubüser
J., Bülow, R., Wondratschek, H.: On Crystallography in Higher Dimensions I, II, III. Acta Cryst. A27, 517–535 (1971).
Ng, E. W.: A Study of Alternative Methods for the Symbolic Integration of Elliptic Integrals. SYMSAC 1976, 44–50.
Ng, E. W.: Symbolic-Numeric Interface: A Review. EUROSAM 1979, 330–345.
Pavelle, R.: Applications of MACSYMA to Problems in Gravitation and Differential Geometry. MACSYMA1979, 256–276.
Pless, V., Sloane, N. J. A.: On the Classification and Enumeration of Self-Dual Codes. J. Comb. Theory18, 313–334(1975).
Ponsignon, J. P.: Decryptage des Notations Lineaires en Chimie Organique. Application ä WLN. CALSYF 1, 1981 (unpublished Bull.). (Bergman, M., Calmet, J., eds.)
Sammet, J. E.: Revised Annotated Description Based Bibliography on the Use of Computers for Non-Numerical Mathematics. IFIP 1966, 358–484.
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).
Schmidt, P.: Automatic Symbolic Solution of Differential Equations of First Order and First Degree. EUROSAM 1979, 114–125.
Shamir, A.: How to Share a Secret. Commun. ACM 22, 612–613 (1979).
Smit, J.: New Recursive Minor Expansion Algorithms, a Presentation in a Comparative Context. EUROSAM 1979, 74–87.
Smit, J.: A Cancellation Free Algorithm, with Factoring Capabilities, for the Efficient Solution of Large, Sparse Sets of Equations. SYMSAC 1981, 146–154.
Smit, J., Hulshof, B. J. A., Van Hulzen, J. A.: NETFORM and Code Optimizer Manual. Twente Univ. of Tech.: TW Memorandum 373, 1981.
Smit, J., Van Hulzen, J. A.: Symbolic-Numeric Methods in Microwave Technology. Twente Univ. of Technology: TW Memorandum 374, 1981.
Sorna, T.: Relativistic Aberration Formulas for Combined Electromagnetic Focusing-Deflection System. Optik 49, 255–262 (1977).
Squire, W.: Private Communication.
Stoutemyer, D. R.: Computer Symbolic Math. & Education: A Radical Proposal. MACSYMA 1979, 142–158, and SIGSAM Bull. 13/3, 8–24 (1979).
Stoutemyer, D. R.: Computer Symbolic Math, in Physics Education. Am. J. Phys. 49, 85–88 (1981).
Stoutemyer, D. R.: The Coming Revolution in Scientific Computation. Comput. & Educ. 5, 53–55 (1981).
Van Hulzen, J. A.: Computational Problems in Producing Taylor Coefficients for the Rotating Disk Problem. SIGSAM 14/2, 36–49 (1980).
Verbaeten, P.: The Automatic Construction of Pure Recurrence Relations. EUROSAM 1974, 96–98.
Winograd, S.: On Computing the Discrete Fourier Transform. Math. Comp. 32, 175–199 (1978).
Woll, A.: γ-Algebra Algorithms for Canonical Hypercomplex Representations. EUROSAM 1979, 546–557 (1979).
Wyman, J.: Addition No. 3, 4 and 5 to J. E. Sammet [59]. SIGSAM Bull. 10 (1968), 12 (1969), 15 (1970).
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.
Zeis, E., Cefola, P. J.: Computerized Algebraic Utilies for the Construction of Non-Singular Satellite Theories. MACSYMA 1979, 277–294.
Zimmer, H. G.: Computational Problems, Methods and Results in Algebraic Number Theory. Lecture Notes in Mathematics, Vol. 262. Berlin-Heidelberg-New York: Springer 1972.
REDUCE-Newsletters. Univ. of Utah: Symb. Comp. Group (since 1978).
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Calmet, J., van Hulzen, J.A. (1983). Computer Algebra Applications. In: Buchberger, B., Collins, G.E., Loos, R., Albrecht, R. (eds) Computer Algebra. Computing Supplementa, vol 4. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7551-4_15
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DOI: https://doi.org/10.1007/978-3-7091-7551-4_15
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