On the History of Computer Algebra at the Keldysh Institute of Applied Mathematics

  • G. B. Efimov
  • I. B. Tshenkov
  • E. Yu Zueva
Conference paper
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 357)

Abstract

The authors consider the history of Computer Algebra (CA) development and applications at the famous Keldysh Institute of Applied Mathematics (Russia Academy of Science). At the Institute CA was used in various areas: Applied Celestial Mechanics, Mathematics, Robotics, Hydromechanics, and Methods of Calculation. Authors compared and classified the existing systems and their possibilities. An attention is paid to REFAL (REcursive Functions Algorithmic Language), developed in the Institute. The modern state of investigations is also concerned. The list of the main references is presented.

Keywords

Computer algebra mechanics mathematics programming history KIAM REFAL 

References

  1. 1.
    Calculus mathematics and computer facilities. All-Union seminar. Inst. of Low Temperature Physics AS UkrSSR (3), 152 (1972) Google Scholar
  2. 2.
    Ershov, A.P., Shura-Bura, M.R.: Development of programming in USSR. Part 1. Initial development. Part 2. Step to second generation of languages and computers. Preprints No. 12, 13 of Computer Center of Siberian Branch AS URSS. Also: Cybernetika (6) 141–160 (1976) Google Scholar
  3. 3.
    Computer analytical calculations and their application in theoretical Physics. In: Materials of International Conference, Dubna (1979); p. 187. JINR, Dubna (1980), p. 260 (1983), p. 420 (1985) Google Scholar
  4. 4.
    Gerdt, V.P., Tarasov, O.V., Shirkov, D.V.: Analytical Calculations on ECM applied to Physics and Mathematics. Uspehi Phys. Nauk. 30(1), 113–147 (1980) Google Scholar
  5. 5.
    Miola, A.M., Pottosin, I.V.: A bibliography of soviet works in algebraic manipulations. SIGSAM Bull. 15(1), 5–7 (1981) Google Scholar
  6. 6.
    Grosheva, M. V., Efimov, G.B., Brumberg, V.A., et all.: Computer analytical calculation systems (Applied Analytical Packages). Papers Seminar in Mechanics Institute of MSU, (1981); Informator. Keldysh Institute of Applied Mathematics AS USSR (1), 65 (1983) Google Scholar
  7. 7.
    Systems for Analytical Manipulation in Mechanics. In: All-Union Conference, Gorky (1984); Abstracts. GSU, Gorky. p. 147 (1984) Google Scholar
  8. 8.
    Applied Program Packages. Analytical manipulations, p. 156. Nauka, M. (1988) Google Scholar
  9. 9.
    Grosheva, M.V., Efimov, G.B.: Computer analytical calculation systems. In: Applied programs packages. Analytical manipulations. pp. 5–30. Nauka, M. (1988) Google Scholar
  10. 10.
    Brumberg, V.A., Tarasevich, S.V., Vasiliev, N.N.: Specialized Celestial Mechanics systems for Symbolic Manipulations. Celestial Mech. 45(1-3), 145–162 (1988/1989) Google Scholar
  11. 11.
    Klimov, D.M., Rudenko, V.M.: Computer Algebra Methods in Mechanical problems, p. 215. Nauka, M. (1989) Google Scholar
  12. 12.
    Computer Algebra in Physical Research. Int. Conf. Computer Algebra Phys. Res. Dubna, USSR (1990); Memorial Volume for N.N. Govorun, p. 453. World Scientific, Singapore (1991); Abstracts, p. 90. JINR, Dubna (1990) Google Scholar
  13. 13.
    Abramov, S.A., Zima, E.B., Rostovzev, V.A.: Computer Algebra. Programirovanie (5), 4–25 (1992) Google Scholar
  14. 14.
    The History of Computer Algebra Applications. Session. In: 4-the International IMACS Conference on Applications of Computer Algebra, IMACS ACA 1998, Prague, August 9–11, 35 p (1998) Google Scholar
  15. 15.
    Grosheva, M.V., Efimov, G.B., Samsonov, V.A.: Symbolic Manipulations in Control Theory. Izvestiya Akademii Nauk. The Control Theory & Systems (3), 80–91 (1998)Google Scholar
  16. 16.
    Efimov, G.B., Yu, Z.E., Tshenkov, I.B.: Computer Algebra at Keldysh Institute of Applied Mathematics. Mathematical Simulation 13(6), 11–18 (2001)MATHGoogle Scholar
  17. 17.
    Grosheva, M.V., Efimov, G.B., Samsonov, V.A.: A History of Computer Symbolic Manipulation and its Applications in Mechanics. Keldysh Institute of Applied Mathematics of RAS, M., 87 p (2005)Google Scholar
  18. 18.
    Dorodnitcin, A.A.: Solution of mathematical and logical tasks on computer. In: All-Union Confer., Moscow, March 12–17 (1956); Plenary reports. VINITI. M (1956)Google Scholar
  19. 19.
    Okhotsimsky, D.E.: Research of motion in central field of forces under the influence of constant tangent acceleration. Cosmic Research. 2(6), 817–842 (1964); PЖMex, 11A29 (1965)Google Scholar
  20. 20.
    Kantorovich, L.V.: On a mathematical symbolic system convenient for computer’s calculations. Doklady AS USSR, 113(4), 738–739 (1957); Kantorovich, L.V., Petrova, L.T.: 3th All-Union Mathemat. Congress. Rep. (2), 151(1956); Smirnova, T.N.: Trans. Steklov Mathematical Institute. M. L. (1962); Pervozvanskaya, T.N., Ibid., Smirnova, T.N.: Polynomial PRORAB. Nauka, L. (1967)Google Scholar
  21. 21.
    Stogny, A.A.: Solution on DCM of one task concerning differentiation of functions. In: Problems of Cybernetic, vol. (7), pp. 189–200. Nauka, M. (1962)Google Scholar
  22. 22.
    Shurygin, V.A., Yanenko, N.N.: On a realization of algebraic differential algorithms on ECM. In: Problems of Cybernetic, vol. (6), pp. 33–43. Nauka, M. (1961)Google Scholar
  23. 23.
    Brumberg, V.A.: Polynomial Series in Three Bodies Problem. Bull. ITA AS USSR, 9(4), 234–256 (1963); Brumberg, V.A.: Presentation of Planet’s coordinates by trigonometric series. Reports of Institute Theoretical Astronomy (ITA AS USSR). L. (11), 3–88 (1966); Polozova, N.G., Shor, V.A.: Problems of motion of artificial Spacecrafts of Celestial bodies, M. (1963) Google Scholar
  24. 24.
    Kabulov, V.K.: On deduce of differential equations of elasticity and construction mechanics. Doklady AS UzbekSSR, Tashkent, (9) (1963); Tolok V.A.: Problems of computer Math. & Techn. Tashkent (3) (1964); Kabulov, V.K.: Algorithmization in elasticity and deformational plasticity theory. “Fan” AS UsbekSSR, Tashkent (1966) Google Scholar
  25. 25.
    Turchin, V.F.: Metaalgortmic Language. Cybernetika (4), 45–54 (1968); PЖMaT, 2B86 (1971); Turchin, V.F., Serdobolsky, V.I.: The REFAL and its application for transformations of algebraic expressions. Cybernetika (3), 58–62 (1969); Turchin, V.F.: Programming on REFAL. KIAM Preprint N. 41, 43, 44, 48, 49 (1971). PЖMaT, 1B993 -996 (1972) Google Scholar
  26. 26.
    Turchin, V.F.: Refal-5. In: Programming Guide and Reference Manual, New England Publishing Co., Holyoke (1989), http://refal.ru Google Scholar
  27. 27.
    Zadyhaylo, I.B., Kamynin, S.S., Lyubimsky, E.Z.: Some problems of Computer design from blocks of high qualification. KIAM Preprint. M (1971)Google Scholar
  28. 28.
    Myamlin, A.N., Smirnov, V.K., Golovkov, S.L.: Specialized Symbol Processor. In: Woods, J.V. (ed.) Fifth Generation Architecture. New-Holland (1980)Google Scholar
  29. 29.
    Smirnov, V.K.: Hardware REFAL realization at KIAM. KIAM Preprint N 99. M (2003)Google Scholar
  30. 30.
    Zabrodin, A.V.: Super-Computers MVS-100, MVS-1000 and its applications to problems of physics and mechanics problems. Mathematical Simulation 12(5), 61-66 (2000)Google Scholar
  31. 31.
    Bruno, A.D., Edneral, V.F. Steinberg, S.: Foreword. Mathematics and Computers in Simulation. 45, 409-411 (1998); Bruno, A.D.: Normal Forms. Mathematics and Computers in Simulation. 45, 413-427 (1998); Soleev, A., Aranson A.B.: KIAM Preprint N 36 (1994) Google Scholar
  32. 32.
    Bruno, A.D., Varin, V.P.: The limit problems for equation of oscillations of a satellite. Celestial Mechan. and Dynam. Astron. 67, 1-40 (1997); KIAM Preprint N 124, 128 (1995) Sadov, S.Yu.: KIAM Preprint N 37 (1998) Google Scholar
  33. 33.
    Kuleshov, A.S.: On the first integrals of Equation of motion of a Heavy Rotational Symmetric Body on a Perfectly Rough Plane. KIAM Preprint N 68 (2002) Google Scholar
  34. 34.
    Niukkanen, A.W., Shchenkov, I.B.: Operator factorization technique of formula derivation in the theory of simple and multiple hyper-geometric functions of one and several variables. KIAM Preprint N 81 (2003); A project of a globally universal interactive program of formula derivation based on operator factorization method. KIAM Preprint N 82 (2003) Google Scholar
  35. 35.
    Pogorelov, D.Yu.: Some developments in computational techniques in modeling advanced mechanical systems. In: Sympos. on Interaction betw. Dyn. & Control in Adv. Mechan. Systems, pp. 313–320. Kluger Acad. Publ, Dordrecht (1997); Pogorelov, D.Yu.: Differential-algebraic equations in multi-body system modeling. Numerical Algorithms 19, 183-194 (1988) Google Scholar
  36. 36.
    Belousov, I.R.: Calculation of the Robot Manipulator Dynamic Equation. KIAM Preprint N 45 (2002); Balaban, I.Y., Borovin, G.K., Sazonov, V.V.: The language for programming right-hand sides of mechanical system motion equations. KIAM Preprint N 62 (1998) Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2011

Authors and Affiliations

  • G. B. Efimov
    • 1
  • I. B. Tshenkov
    • 1
  • E. Yu Zueva
    • 1
  1. 1.Keldysh Institute of Applied Mathematics, RASRussia

Personalised recommendations