Literature Cited
S. A. Abramov, “The APREF System,” in: Processing Symbolic Information [in Russian], Vol. 1, Izd. Vychisl. Tsentr. Akad. Nauk SSSR, Moscow (1973).
I. R. Aksel'rod and L. F. Belous, “Input language for the SIRIUS automatic programming system,” in: Automatic Programming [in Russian], Vol. 3, Izd. Inst. Kibernetika Akad. Nauk UkrSSR, Kiev (1967).
L. F. Belous and I. R. Aksel'rod, “Realization of the SIRIUS automatic programming system on the M-20 computer,” in: Automatic Programming [in Russian], Vol. 3, Izd. Inst. Kibernetika Akad. Nauk UkrSSR, Kiev (1967).
M. M. Bezhanova, V. L. Katkov, and I. V. Pottosin, “Papers on analytic transformation in the Computer Center of the Siberian Branch of the Academy of Sciences of the USSR,” in: Computer Mathematics and Computing Technology [in Russian], Vol. 3, Izd. FTINT Akad. Nauk UkrSSR, Khar'kov (1972).
S. V. Pogrebinskii et al., “On the basic principles of the realization of the ANALITIK language in computers,” in: Automata Theory [in Russian], Vol. 2, Izd. Inst. Kibernetiki Akad. Nauk UkrSSR, Kiev (1968).
V. M. Glushkov, T. A. Grinchenko, et al., “ANALITIK (algorithmic language for the description of computational processes using analytic transformations),” Kibernetika, No. 3 (1971).
L. I. Goncharova, “The SNOBOL-A system on the BÉSM-6,” Zh. Vychisl. Mat. Fiz.,11, No. 6 (1971).
T. A. Grinchenko, “Computer representations and processing of analytic expressions,” in: Automata Theory [in Russian], Vol, 2, Izd. Inst. Kibernetiki Akad. Nauk UkrSSR, Kiev (1968).
L. V. Kantorovich, “On one mathematical symbolism convenient for performing computations on computers,” Dokl. Akad. Nauk SSSR,113, No. 4 (1957).
G. P. Kozhevnikova, “Computational complexity of procedures SRAVNIT' [COMPARE] and DIFFERENTs-IROVAT' [DIFFERENTIATE] as it applies to the languages of Lukasiewicz and Kantorovich,” in: Computer Mathematics and Computing Technology [in Russian], Vol. 3, Izd. FTINT Akad. Nauk UkrSSR, Khar'kov (1972).
G. P. Kozhevnikova, “On estimating effectiveness of algorithms for symbol transformation,” Upravl. Sistemy Mashiny, No. 1 (1974).
G. P. Kozhevnikova and Yu. A. Rybalko, “On syntactic structures of expressions with binary operations,” in: Questions of Organization of Computational Processes [in Russian], Izd. Inst. Kibernetiki Akad. Nauk UkrSSR, Kiev (1975).
N. I. Kostyukova, “The PASSIV processor,” in: Computer Mathematics and Computing Technology [in Russian], Vol. 3, Izd. FTINT Akad. Nauk UkrSSR, Khar'kov (1972).
R. B. Kukhar, On the Effectiveness of Certain Forms of Representation of Expressions for the Solution of Problems on m Homogeneous Computers Operating in Parallel [in Russian], Preprint 73-10, Izd. Inst. Kibernetiki Akad. Nauk UkrSSR, Kiev (1973).
E. N. Paskhin, “Analytic differentiation of functions on digital computers,” in: Computational Methods and Programming [in Russian], Vol. 9, Izd. MGU (1967).
L. T. Petrova, “Certain uses of scheme symbolism,” Zh. Vychisl. Mat. Fiz.,1, No. 3 (1961).
Computer Mathematics and Computing Technology [in Russian], Vol. 3, Izd. FTINT Akad. Nauk UkrSSR, Khar'kov (1972).
T. N. Smirnova, Performance on a Type M-20 Computer of Polynomial Computations with the Aid of Superintendents [in Russian], Nauka, Moscow (1967).
A. A. Stognii, “Solution on electronic computers of a problem related to the differentiation of functions,” in: Problems in Cybernetics [in Russian], Vol. 7, Moscow (1962).
V. V. Tumasonis, “System of equivalent transformations of expressions,” Zh. Vychisl. Mat. Mat. Fiz.,11, No. 5 (1971).
V. F. Turchin and V. Serdobol'skii, “The REFAL language and its use for the transformation of algebraic expressions,” Kibernetika, No. 3 (1969).
M. A. Chubarov, “Polynomial ensembles,” in: Computer Mathematics and Computing Technology [in Russian], Vol. 3, Izd. FTINT Akad. Nauk UkrSSR, Khar'kov (1972).
W. E. Ball and R. I. Berns, “Automast: automatic mathematical analysis and symbolic translation,” Commun. ACM,9, No. 8 (1966).
M. D. Bernick, E. D. Callender, and J. R. Sanford, “ALGY — an algebraic manipulation program,” in: Proceedings of the Western Joint Computer Conference, Vol. 19 (1961).
E. K. Blum, “A formal system for differentiation,” J. Assoc. Comput. Machinery,13, No. 4 (1968).
E. Bond et al., “FORMAC — an experimental formula manipulation compiler,” in: Proceedings of the 19th ACM National Conference, August (1964).
W. Brown, “The ALPAK system for nonnumerical algebra on a digital computer, Part 1. Polynomials in several variables and truncated power series with polynomial coefficients,” Bell Syst. Tech. J.,42, No. 5 (1963).
W. Brown, J. P. Hyde, and B. A. Tague, “The ALPAK system for nonnumerical algebra on a digital computer. Part 2. Rational functions of several variables and truncated power series with rational-function coefficients,” Bell Syst. Tech. J.,43, No. 3 (1964).
C. Christensen, “Examples of symbol manipulation in the AMBIT programming language,” in: Proceedings of the 20th ACM National Conference (1965).
J. Cohen and Nguyen-Huu-Dung, “Definition de procedures LISP en ALGOL, exemple d'utilisation,” Review Francaise Traitement Information,8, No. 4 (1965).
G. E. Collins, “PM, a system for polynomial manipulation,” Commun. ACM,9, No. 8 (1966).
C. Engelman, “MATHLAB: a program for on-line machine assistance in symbolic computations,” in: Proceedings of the AFIPS 1965 Fall Joint Computer Conference, Vol. 27, Part 1, November (1965).
A. Guzman and J. McIntosh, “CONVERT,” Commun. ACM,9, No. 8 (1966).
J. Hanson, J. S. Caviness, and C. Joseph, “Analytic differentiation by computer,” Commun. ACM,5, No. 6 (1962).
H. Hauer, “An IPL5 program for formal integration using tables,” Behavioral Science,7, April (1962).
A. Hearn, “Computations of algebraic properties of elementary particle reactions using a digital computer,” Commun. ACM,9, No. 8 (1966).
A. D. Holden and D. L. Johnson, “Simulation of human problem-solving methods,” in: Proceedings of the National Electronic Conference, Chicago, Illinois (1963).
J. P. Hyde, “The ALPAK system for nonnumerical algebra on a digital computer — III. Systems of linear equations and a class of side relations,” Bell Syst. Tech. J.,43, No. 4, Part 2, July (1964).
A. Lapidus and M. Goldstein, “Some experiments in algebraic manipulation by computer,” Commun. ACM,8, No. 8 (1965).
W. A. Martin, “Symbolic mathematic laboratory,” Doctoral Thesis, Massachusetts Institute of Technology, Cambridge (1967).
J. Moses, “Solution of systems of polynomial equations by elimination,” Commun. ACM,9, No. 8 (1956).
J. Moses, “Symbolic integration,” Report MAC-TR-47, Project MAC, Massachusetts Institute of Technology, Cambridge (1967).
A. Newell, J. Shaw, and H. Simon, “A general problem-solving program for a computer,” Comput. Automat.,8, No. 7 (1959).
Z. Pawlak, “New method of parentheses-free notation of formulae,” Bulletin de l'Academie Polonaise des Sciences, Serie des Sciences Techniques,8, No. 4 (1960).
“Papers from the symposium on symbolic and algebraic manipulation,” Commun. ACM,9, No. 8 (1966).
“Papers from the second symposium on symbolic and algebraic manipulation,” Commun. ACM,14, No. 8 (1971).
J. C. Reynolds, “COGENT programming manual,” in: Proceedings of the 20 th ACM National Conference (1965).
H. Schorr, “Analytic differentiation using a syntax-directed compiler,” Comput. J.,7, No. 4 (1965).
J. Slagle, “A heuristic program that solves symbolic integration problems in freshman calculus,” J. Assoc. Computing Machinery,10, No. 4, October (1963).
P. J. Smith, “Symbolic derivations without list processing, subroutines, or recursion,” Commun. ACM,8, No. 8 (1965).
Additional information
Translated from Kibernetika, No. 4, pp. 54–66, July–August, 1975.
Rights and permissions
About this article
Cite this article
Kozhevnikova, G.P., Stognii, A.A. Representation of analytic expressions for the performance of formula transformations by computer. Cybern Syst Anal 11, 571–585 (1975). https://doi.org/10.1007/BF01070436
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01070436