Systems of Polynomial Equations - I

The Kronecker-Duval Philosophy

Teo Mora

424 pages, parution le 07/03/2003 (2^eme édition)

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Résumé

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.

Contents

Preface

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

Bibliography

Index.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Teo Mora
Parution	07/03/2003
Édition	2^eme édition
Nb. de pages	424
Format	16 x 24
Couverture	Relié
Poids	745g
Intérieur	Noir et Blanc
EAN13	9780521811545
ISBN13	978-0-521-81154-5