Algorithms and Computation in Mathematics

Foundations, Algorithms, and Applications

By: Alicia Dickenstein (Editor), Ioannis Z. Emiris (Editor), Eduardo Cattani (Contribution by)

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Hardcover | 27 April 2005

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444 Pages

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23.5 x 15.88 x 1.91

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The subject of this book is the solution of polynomial equations, that is, s- tems 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 di?erent 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 e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied 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, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.

Industry 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 unabhaengigen Kapiteln zum Thema "Loesung polynomialer Gleichungssysteme", geschrieben von bekannten Experten. Der Schwerpunkt liegt auf spezialisierten Themen, bei denen in juengerer Zeit beachtliche Fortschritte erzielt wurden. Es gibt deshalb wenig UEberschneidungen mit anderen Buechern der Computeralgebra. [...] Insgesamt ist dieses Buch eine reiche Quelle von Informationen und eine sehr willkommene Ergaenzung zu den bereits vorhandenen Lehrbuechern im Bereich der Loesung polynomialer Gleichungssysteme. Es sollte in keinem Regal fehlen."

Peter Buergisser, 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 fuer Mathematik, Vol. 148 (4), 2006)

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You Can Find This Book In

Non-Fiction Mathematics Algebra Computing & I.T.Computer Science Computer Programming & Software Development Algorithms & Data Structures Databases Data Capture & Analysis Applied Mathematics Mathematical Theory of Computation Maths for Computer Scientists

Preface
Introduction 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
Introduction to Numerical Algebraic Geometry
Four Lectures on Polynomial Absolute Factorization
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Algorithms and Computation in Mathematics

Foundations, Algorithms, and Applications

At a Glance

Hardcover

Industry Reviews

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How to return your order

Defective items

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