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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Kahrimanian, H.G., Analytical differentiation by a Digital Computer, M.A. Diss, Temple University, Philadelphia, PA, 1953.
Nolan, J., Analytical Differentiation on a Digital Computer, M.A. Diss, MIT, Cambridge, MA, 1953.
Brown, W.S., ALTRAN User’s Manual, Third Edition, Bell Laboratories, 1973.
Hearn, A.C., REDUCE User’s Manual, Second Edition, University of Utah, 1973.
Jenks, R.D., The SCRATCHPAD Language, SIGPLAN Notices, ACM, New York, 9 (1974) 101–111.
Bogen, R., et al., MACSYMA Reference Manual, Project MAC, M.I.T., Cambridge, MA, 1974.
Kernighan, B.W., and Cherry, L.L., Comm. ACM 18 (1975), 151–157.
Feldman, S.I., An Application of Symbolic Computation to Crystal Physics, SIGSAM Bulletin, ACM, New York, No. 34 (1975) 19–24.
Barton, D., and Fitch, J.P., Rep. Prog. Phys. 35 (1972) 235–314.
Delaunay, C., Théorie du Mouvement de la Lune (Extraits des Mém. Acad. Sci.), Mallet-Bachelier, Paris, 1860.
Deprit, A., Henrard, J., and Rom, A., Science 168 (1970) 1569–1570.
Jefferys, W.H., and Ries, L.M., Astronomical Journal 80 (1975) 876–884.
Rom, A., Celest. Mech. 3 (1971) 331–345.
Jeffreys, W.H., Celest. Mech. 2 (1970) 474–480.
Fitch, J.P., CAMAL User’s Manual, Computer Lab., Cambridge, U.K. (1975).
Jeffreys, W.H., Comm. ACM 14 (1971) 538–541.
Feynman, R.P., Phys. Rev. 76 (1949) 769–789.
Bjorken, J.D., and Drell, S.D., Relativistic Quantum Mechanics, McGraw-Hill, New York, 1964.
Kahane, J., J. Math. Phys. 9 (1968) 1732–1738.
Campbell, J.A., Comp. Phys. Comm. 1 (1970) 251–264.
Hearn, A.C., Comm. ACM 14 (1971) 511–516.
Hearn, A.C., Computer Solution of Symbolic Problems in Theoretical Physics, Computing as a Language of Physics, IAEA, Vienna (1972) 567–596.
Campbell, J.A., Acta Phys, Austriaca Suppl. XIII (1974) 595–647.
Strubbe, H., Comp. Phys. Comm. 8 (1974) 1–30.
Perisho, R.C., ASHMEDAI User’s Guide, U.S.A.E.C. Rep. No. C00–3066–44 (1975).
Petermann, A., Helv. Phys. Acta 30 (1957) 407–408.
Maison, D., and Petermann, A., Comp. Phys. Comm. 7 (1974) 121–134.
Fox, J.A., and Hearn, A.C., J. Comp. Phys. 14 (1974) 301–317.
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.
Campbell, J.A., and Hearn, A.C., J. Comp. Phys. 5 (1970) 280–327.
Sasaki, T., Automatic Generation of Feynman Graphs in QED, Rikagaku Kenkyosho, Wako-Shi, Saitama, Japan, Preprint 1975.
Tobey, R.G., et al., PL/I-FORMAC SYMBOLIC MATHEMATICS INTERPRETER, SHARE Contributed Program Library, No. 360 D-0.3.3.004 (1969).
Engeli, M., An Enhanced SYMBAL System, SIGSAM Bulletin, ACM, New York, No. 36 (1975) 21–29.
Richardson, D., Ph.D. Thesis, University of Bristol, (1966).
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.
Barton, D., and Fitch, J.P., Comm. ACM 14 (1971) 542–547.
D’inverno, R.A., Comp. J. 12 (1969) 124–127.
Moses, J., Comm. ACM 14 (1971) 527–537.
Wang, P., Symbolic Evaluation of definite Integrals by Residue Theory in MACSYMA, Proc. IFIP Congress 74 (1974) 823–827.
Campbell, J.A., Applications of Symbolic Programs to Complex Analysis, Proc. ACM Annual Conf. 72 (1972) 836–839.
Moses, J., Comm. ACM (1971) 548–560.
Hardy, G.H., The Integration of Functions of a Single Variable, Second Edition, CUP, Cambridge, England (1916).
Risch, R., Trans. AMS 139 (1969) 167–189.
Norman, A.C., and Risch, R., to be published.
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.
Harrington, S. J., A New Symbolic Integration System in REDUCE, Comp. J., to be published.
Schoichet, S.R., The LISP Machine, Mini-Micro Systems, Boston, MA, Vol. 11, No. 5 (June 1978) 68–74.
Brown, W.S., and Hearn, A.C., Applications of Symbolic Algebraic Computation, Comp. Phys. Comm., to be published.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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