Solving Polynomial Equation Systems I: The Kronecker-Duval Philosophy

by Teo Mora

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:	03/27/2003
Series:	Encyclopedia of Mathematics and its Applications , #88
Pages:	438
Product dimensions:	6.38(w) x 9.53(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.

Editorial Reviews

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

"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

From the Publisher