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Solving Polynomial Equation Systems I

Solving Polynomial Equation Systems I
The Kronecker-Duval Philosophy


Part of Encyclopedia of Mathematics and its Applications

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

£ 167.00

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About the Authors
  • Polynomial equations have been long studied, both theoretically and with a view to solving them. Until recently, manual computation was the only solution method and the theory was developed to accommodate it. With the advent of computers, the situation 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, emphasising 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

    'This is an excellent book for readers interested in algebraic methods.' European Mathematical Society Newsletter

    'The book [is] a thorough success …'. Zentralblatt MATH

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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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