This article is cited in 28 papers

REVIEWS OF TOPICAL PROBLEMS

Analytic calculations on digital computers for applications in physics and mathematics

V. P. Gerdt, O. V. Tarasov, D. V. Shirkov

Joint Institute for Nuclear Research, Dubna, Moscow region

Abstract: 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.

UDC: [51 + 53]:681.142

PACS: 89.80.+h, 02.70.+d

DOI: 10.3367/UFNr.0130.198001d.0113

 English version: Physics–Uspekhi, 1980, 23:1, 59–77