Solving Polynomial Equations: Foundations, Algorithms, and Applications / Edition 1

by Alicia Dickenstein, Ioannis Z. Emiris

Overview

The subject of this book is the solution of polynomial equations, that is, systems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in different branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in effective algebraic geometry and computer algebra has extended well beyond its original constituency of pure and applied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, differential equations and number theory to discrete geometry, combinatorics and complexity theory. The goal of this book is to provide a general introduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.

Product Details

ISBN-13:	9783642063619
Publisher:	Springer Berlin Heidelberg
Publication date:	12/15/2010
Series:	Algorithms and Computation in Mathematics , #14
Edition description:	Softcover reprint of hardcover 1st ed. 2005
Pages:	426
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

to residues and resultants.- Solving equations via algebras.- Symbolic-numeric methods for solving polynomial equations and applications.- An algebraist’s view on border bases.- Tools for computing primary decompositions and applications to ideals associated to Bayesian networks.- Algorithms and their complexities.- Toric resultants and applications to geometric modelling.- to numerical algebraic geometry.- Four lectures on polynomial absolute factorization.

Editorial Reviews

From the reviews of the first edition:

"[...] The editors of the book — Alicia Dickenstein and Ioannis Emiris — have done a very good job in collecting a set of expository lectures on a very interesting branch of mathematics. I imagine that this book will be of use to anyone working in the area, and would be a good introduction for a graduate student or someone wishing to start working in the field. [...]"

Darren Glass, MAA Review, January 2006

"Dieses Buch besteht aus neun weitgehend unabhängigen Kapiteln zum Thema "Lösung polynomialer Gleichungssysteme", geschrieben von bekannten Experten. Der Schwerpunkt liegt auf spezialisierten Themen, bei denen in jüngerer Zeit beachtliche Fortschritte erzielt wurden. Es gibt deshalb wenig Überschneidungen mit anderen Büchern der Computeralgebra. [...] Insgesamt ist dieses Buch eine reiche Quelle von Informationen und eine sehr willkommene Ergänzung zu den bereits vorhandenen Lehrbüchern im Bereich der Lösung polynomialer Gleichungssysteme. Es sollte in keinem Regal fehlen."

Peter Bürgisser, Computeralgebra, Ausgabe 39, Oktober 2006

"Although about 15 authors have contributed to this book it constitutes a unified whole. Its subjects are the diverse methods, techniques and algorithms in solving multivariate (non-linear) polynomial equations or systems of them, which mostly have been developed in recent years. … All in all there is presented a detailed account, which often leads to the front of research." (G. Kowol, Monatshefte für Mathematik, Vol. 148 (4), 2006)

From the Publisher