Analytic calculations on digital computers for applications in physics and mathematics

V.P. Gerdt, O.V. Tarasov, D.V. Shirkov^a
^aJoint Institute for Nuclear Research, 6 Joliot-Curie Str., Dubna, Moscow Region, 141980, Russian Federation

The present state of analytic calculations on computers is reviewed. Several programming systems which are used for analytic calculations are discussed: SCHOONSCHIP, CLAM, REDUCE-2, SYMBAL, CAMAL, AVTO-ANALITIK, MACSYMA, etc. It is shown that these systems can be used to solve a wide range of problems in physics and mathematics. Some physical applications are discussed in celestial mechanics, the general theory of relativity, quantum field theory, plasma physics, hydrodynamics, atomic and molecular physics, and quantum chemistry. Some mathematical applications which are discussed are evaluating indefinite integrals, solving differential equations, and analyzing mathematical expressions. This review is addressed to physicists and mathematicians working in a wide range of fields.

PACS: 89.80.+h, 02.70.+d
DOI: 10.1070/PU1980v023n01ABEH004898
URL: https://ufn.ru/en/articles/1980/1/d/
Citation: Gerdt V P, Tarasov O V, Shirkov D V "Analytic calculations on digital computers for applications in physics and mathematics" Sov. Phys. Usp. 23 59–77 (1980)

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%0 Journal Article
%T Analytic calculations on digital computers for applications in physics and mathematics
%A V. P. Gerdt
%A O. V. Tarasov
%A D. V. Shirkov
%I Physics-Uspekhi
%D 1980
%J Phys. Usp.
%V 23
%N 1
%P 59-77
%U https://ufn.ru/en/articles/1980/1/d/
%U https://doi.org/10.1070/PU1980v023n01ABEH004898

Оригинал: Гердт В П, Тарасов О В, Ширков Д В «Аналитические вычисления на ЭВМ в приложении к физике и математике» УФН 130 113–147 (1980); DOI: 10.3367/UFNr.0130.198001d.0113