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Algebra of Polynomials, Rational Functions, and Power Series

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

Abstract

In this chapter we present some basic concepts from algebra which are of central importance in the development of algorithms and systems for symbolic mathematical computation. The main issues distinguishing various computer algebra systems arise out of the choice of algebraic structures to be manipulated and the choice of representations for the given algebraic structures.

Keywords

Power Series Commutative Ring Integral Domain Computer Algebra Euclidean Algorithm 
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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    G. Birkoff and S. MacLanc, A Survey of Modern Algebra (3rd ed.), Macmillian (1965).Google Scholar
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    G. Birkoff and T.C. Bartee, Modern Applied Algebra, McGraw-Hill (1970).Google Scholar
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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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    D.E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms (second edition), Addison-Wesley (1981).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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