Solving Polynomial Equation Systems I: The Kronecker-Duval Philosophy (Encyclopedia of Mathematics and its Applications, Series Number 88) - Hardcover

Mora, Teo

Hardcover

ISBN 10: 0521811546 ISBN 13: 9780521811545

Publisher: Cambridge University Press, 2003

Synopsis

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.

About this title

Book Description

This is the first in a three-volume handbook presenting classical and modern work on polynomial equations, from the viewpoint of solution. Here, Mora covers 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. He shows 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.

Review

"...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

Edition details

• Publisher: Cambridge University Press
• Publication date: 2003
• Language: English
• ISBN 10: 0521811546
• ISBN 13: 9780521811545
• Binding: Hardcover
• Edition number: 1
• Number of pages: 438