Solving Polynomial Equation Systems I: The Kronecker-Duval Philosophy

Solving Polynomial Equation Systems I: The Kronecker-Duval Philosophy

by Teo Mora
     
 

ISBN-10: 0521811546

ISBN-13: 9780521811545

Pub. Date: 03/01/2003

Publisher: Cambridge University Press

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

Overview

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.

Product Details

ISBN-13:
9780521811545
Publisher:
Cambridge University Press
Publication date:
03/01/2003
Series:
Encyclopedia of Mathematics and its Applications Series, #88
Pages:
423
Product dimensions:
6.14(w) x 9.21(h) x 1.14(d)

Table of 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.

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