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Solving Polynomial Equation Systems I

Solving Polynomial Equation Systems I
The Kronecker-Duval Philosophy

$220.00 (C)

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: March 2003
  • availability: Available
  • format: Hardback
  • isbn: 9780521811545

$ 220.00 (C)

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About the Authors
  • With the advent of computers, theoretical studies and solution methods for polynomial equations have changed dramatically. Many classical results can be more usefully recast within a different framework which in turn lends itself to further theoretical development tuned to computation. This first book in a trilogy is devoted to the new approach. It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasizing computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval Model and the Thom Codification. Mora aims to show that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.

    • A survey of the state-of-the-art for solving univariate polynomials
    • Covers the classical and more recent results
    • Unique in stressing modern framework for computational work and solution methods
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    Reviews & endorsements

    "...a fabulous undergraduate introduction to modern algebra, simultaneously foundational and computational. Highly recommended."

    "I took great pleasure in reading this book and, in my opinion, it should become the livre de chevet of people working in the part of computer algebra that deals with univariate polynomials."
    Mathematical Reviews

    "Many topics pursued in detail...likely to find the SPES volumes useful"
    David Roberts, MAA Reviews, MathDL

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    Product details

    • Date Published: March 2003
    • format: Hardback
    • isbn: 9780521811545
    • length: 438 pages
    • dimensions: 242 x 162 x 29 mm
    • weight: 0.747kg
    • availability: Available
  • Table of Contents

    Part I. The Kronecker-Duval Philosophy:
    1. Euclid
    2. Intermezzo: Chinese remainder theorems
    3. Cardano
    4. Intermezzo: multiplicity of roots
    5. Kronecker I: Kronecker's philosophy
    6. Intermezzo: Sylvester
    7. Galois I: finite fields
    8. Kronecker II: Kronecker's model
    9. Steinitz
    10. Lagrange
    11. Duval
    12. Gauss
    13. Sturm
    14. Galois II
    Part II. Factorization:
    15. Ouverture
    16. Kronecker III: factorization
    17. Berlekamp
    18. Zassenhaus
    19. Fermeture

  • Author

    Teo Mora, University of Genoa

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