Overview
The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this textbook the main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This second edition contains several recent results, on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number.
Full Product Details
Author: Saugata Basu ,
Richard Pollack ,
Marie-Françoise Coste-Roy
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: Softcover reprint of hardcover 2nd ed. 2006
Volume: 10
Dimensions:
Width: 15.50cm
, Height: 3.40cm
, Length: 23.50cm
Weight: 1.015kg
ISBN: 9783642069642
ISBN 10: 3642069649
Pages: 662
Publication Date: 20 November 2010
Audience:
Professional and scholarly
,
Professional and scholarly
,
College/higher education
,
Professional & Vocational
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Out of print, replaced by POD
We will order this item for you from a manufatured on demand supplier.
Reviews
From the reviews of the first edition: Gegenstand des Buches sind zentrale algorithmische Probleme der reellen algebraischen Geometrie. Hierzu zahlen beispielsweise die Frage nach der Existenz reeller Losungen einer (durch polynomiale Gleichungen und Ungleichungen) bestimmten semialgebraischen Menge oder die Frage, ob zwei Punkte zur gleichen Zusammenhangskomponente einer gegebenen semialgebraischen Menge gehoren. [...] Eine der Herausforderungen kommt daher, dass hierbei eine Reihe von Teilgebieten der Mathematik und Informatik wie Topologie, algebraische Geometrie, Computeralgebra, Komplexitatstheorie sowie der Entwurf effizienter Algorithmen eng miteinander verzahnt sind und deshalb die Literatur sehr verstreut war. In genau diese Lucke mochte das vorliegende Buch stossen - und dieses Unterfangen ist den Autoren in beeindruckender Weise gelungen! [...] Das Buch bietet eine sehr zeitgemasse, gelungene Darstellung klassischen sowie aktuellen Materials zu algorithmischen Fragen der reellen algebraischen Geometrie, die in dieser Breite bisher nicht verfugbar war. Besonders auffallig ist die erfolgreiche Absicht der Autoren, eine koharente und vor allem in sich geschlossene Darstellung zu liefern, die die verschiedenen beteiligten mathematischen Teilgebiete umfassend berucksichtigt. Aufgrund dieser Darstellungsweise bietet das Bcuh zahlreiche Einstiegs- und Verwendungsmoglichkeiten, sowohl in Lehre und Forschung als auch als Nachschlagewerk. Es wird sich schnell als Standardwerk zu dem behandelten Themenkreis etablieren. T.Theobald, Jahresberichte 107, Band (2005) Heft 1
From the reviews: The monograph gives a self-contained detailed exposition of the algorithmic real algebraic geometry. ... In general, the monograph is well written and will be useful both for beginners and for advanced readers, who work in real algebraic geometry or apply its methods in other fields. Eugenii I. Shustin, Zbl. MATH 1031.14028 ... The book under review gives a self-contained account of some of the more recent and important algorithms arising in RAG [real algebraic geometry]. ... This material has mostly appeared in other sources; however, it is very nice to have it all in one book. ...the book is wonderful reference for algorithms in RAG, for the expert and non-expert alike. V.Powers, Mathematical Reviews Clippings from Issue 2004g From the reviews of the second edition: 'Real root counting problem' is one of the main problems under consideration in Algorithms in Real Algebraic Geometry ! . the authors have posted an interactive version of the book on each of their websites. The book attempts to be self-contained and ! the authors succeed ! . Basu, Pollack, and Roy have written a detailed book with quite a few examples and ! bibliographic references. ! The websites also contain implementations of several of the algorithms ! which this reviewer found particularly illuminating. (Darren Glass, MathDL, January, 2007) Algorithms in Real Algebraic Geometry ! provides a self-contained treatment of some of the important classical and modern results in semi-algebraic geometry, many authored by some subset of the trio Basu, Pollack, and Roy. ! The authors have clearly done a tremendous service by providing a self-contained and surprisingly complete source for the foundations of algorithmic real algebraic geometry. They have also organized their material in a way that can be reasonably taught to graduate students. (J. Maurice Rojas, Foundations of computational Mathematics, Issue 8, 2008)
From the reviews: The monograph gives a self-contained detailed exposition of the algorithmic real algebraic geometry. ... In general, the monograph is well written and will be useful both for beginners and for advanced readers, who work in real algebraic geometry or apply its methods in other fields. Eugenii I. Shustin, Zbl. MATH 1031.14028 ... The book under review gives a self-contained account of some of the more recent and important algorithms arising in RAG [real algebraic geometry]. ... This material has mostly appeared in other sources; however, it is very nice to have it all in one book. ...the book is wonderful reference for algorithms in RAG, for the expert and non-expert alike. V.Powers, Mathematical Reviews Clippings from Issue 2004g From the reviews of the second edition: 'Real root counting problem' is one of the main problems under consideration in Algorithms in Real Algebraic Geometry ... . the authors have posted an interactive version of the book on each of their websites. The book attempts to be self-contained and ... the authors succeed ... . Basu, Pollack, and Roy have written a detailed book with quite a few examples and ... bibliographic references. ... The websites also contain implementations of several of the algorithms ... which this reviewer found particularly illuminating. (Darren Glass, MathDL, January, 2007) Algorithms in Real Algebraic Geometry ... provides a self-contained treatment of some of the important classical and modern results in semi-algebraic geometry, many authored by some subset of the trio Basu, Pollack, and Roy. ... The authors have clearly done a tremendous service by providing a self-contained and surprisingly complete source for the foundations of algorithmic real algebraic geometry. They have also organized their material in a way that can be reasonably taught to graduate students. (J. Maurice Rojas, Foundations of computational Mathematics, Issue 8, 2008)
