The algebraic constructor CAC: computing in construction-defined domains

  • Serge D. Meshveliani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 722)


We present a symbolic computation program which is able to build new algebraic domains. Many domains in commutative algebra can be built from the ring of integers by applying the constructors of Direct Sum, Polynomial Algebra, Fraction Ring, Quotient Ring. Certain standard arithmetic operations for the elements and ideals of such rings are defined by the system automatically.


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  1. 1.
    Buchberger, B.: Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory. CAMP. Publ. No. 83-29.0 November 1983Google Scholar
  2. 2.
    Chmutov, S.V., Gaydar, E.A., Ignatovich, I.M., Kozadoy, V.F., Nemytykh, A.P., Pinchuk, V.A.: Implementation of the Symbol Analytic Transformations Language FLAC. Lect. Notes in Comp. Sci., 429 (1990) 276–277Google Scholar
  3. 3.
    Davenport, J.H., Trager, B.M.: SCRATCHPAD's View of Algebra I: Commutative Algebra. Lect. Notes in Comp. Sci. 429 (1990) 40–54Google Scholar
  4. 4.
    Jenks, R.D., Sutor, R.S., et al.: Axiom, the Scientific Computation System. Springer-Verlag, New York-Heidelberg-Berlin (1992).Google Scholar
  5. 5.
    Kandri-Rody, A., Kapur, D.: Computing Gröbner basis of a polynomial ideal over a Euclidean domain. J. of Symbolic Computation 6 (1988) 37–57Google Scholar
  6. 6.
    Kistlerov, V.L.: Design Principles of the Computer Algebra Language FLAC. Preprint of the Institute for Control Science (in Russian) (1987) MoscowGoogle Scholar
  7. 7.
    Meshveliani, S.D.: CAC, the Commutative Algebra Constructor. User's Manual. PSI, Pereslavl-Zalessky (1992)Google Scholar
  8. 8.
    Meshveliani, S.D.: FLAC. Functional Language For Algebraic Computations. Short Manual. Manuscript, PSI, Pereslavl-Zalessky (1992)Google Scholar
  9. 9.
    Turchin, V.F.: Refal-5, Programming Guide and Reference Manual. New England Publishing Co., Holyoke, 1989Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Serge D. Meshveliani
    • 1
  1. 1.Program Systems InstitutePereslavl-ZalesskyRussia

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