Solving Polynomial Equation Systems I
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
Reviews & endorsements
"...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
Product details
December 2004Adobe eBook Reader
9780511058165
0 pages
0kg
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
