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Homomorphisms and Chinese Remainder Algorithms

  • K. O. Geddes
  • S. R. Czapor
  • G. Labahn

Abstract

In the previous three chapters we have introduced the general mathematical framework for computer algebra systems. In Chapter 2 we discussed the algebraic domains which we will be working with. In Chapter 3 we concerned ourselves with the representations of these algebraic domains in a computer environment. In Chapter 4 we discussed algorithms for performing the basic arithmetic operations in these algebraic domains.

Keywords

Commutative Ring Integral Domain Computer Algebra Homomorphic Image Quotient Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    W.S. Brown, “On Euclid’s Algorithm and the Computation of Polynomial Greatest Divisors,” J. ACM, 18 pp. 476–504 (1971).Google Scholar
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    H. Garner, “The Residue Number System,” IRE Transactions, EC-8, pp. 140–147 (1959).Google Scholar
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    D.E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms (second edition), Addison-Wesley (1981).Google Scholar
  4. 4.
    M. Lauer, “Computing by Homomorphic Images,” pp. 139–168 in Computer Algebra — Symbolic and Algebraic Computation, ed. B. Buchberger, G.E. Collins and R. Loos, Springer-Verlag (1982).Google Scholar
  5. 5.
    J.D. Lipson, “Chinese Remainder and Interpolation Algorithms,” pp. 372–391 in Proc. SYMSAM’ 71, ed. S.R. Petrick, ACM Press (1971).Google Scholar
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    J.D. Lipson, Elements of Algebra and Algebraic Computing, Addision-Wesley (1981).Google Scholar
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    B.L. van der Waerden, Modern Algebra (Vols. I and II), Ungar (1970).Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • K. O. Geddes
    • 1
  • S. R. Czapor
    • 2
  • G. Labahn
    • 1
  1. 1.University of WaterlooCanada
  2. 2.Laurentian UniversityCanada

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