Cantitate/Preț
Produs
Total produse
Vezi coșul
Algorithms in Real Algebraic Geometry de Saugata Basu

Algorithms in Real Algebraic Geometry

Autor Saugata Basu, Richard Pollack, Marie-Françoise Coste-Roy
en Limba Engleză Paperback – 20 noi 2010
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.
Citește tot Restrânge

Toate formatele și edițiile

Toate formatele și edițiile Preț Express
Paperback (1) 58167 lei  6-8 săpt.
  Springer – 20 noi 2010 58167 lei  6-8 săpt.
Hardback (1) 72369 lei  6-8 săpt.
  Springer – 6 iul 2006 72369 lei  6-8 săpt.

Preț: 58167 lei

Preț vechi: 68432 lei
-15%

Puncte Express: 873
Preț estimativ în valută:
10286€ • 12128$ • 8923£

Carte tipărită la comandă

Livrare economică 21 martie-04 aprilie

 Adaugă în coș

Wish list
Gift list
Am citit!
Adaugă în listă

Specificații

ISBN-13: 9783642069642
ISBN-10: 3642069649
Pagini: 672
Ilustrații: X, 662 p.
Dimensiuni: 155 x 235 x 36 mm
Greutate: 1 kg
Ediția:Second Edition 2006
Editura: Springer
Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Graduate

Cuprins

Algebraically Closed Fields.- Real Closed Fields.- Semi-Algebraic Sets.- Algebra.- Decomposition of Semi-Algebraic Sets.- Elements of Topology.- Quantitative Semi-algebraic Geometry.- Complexity of Basic Algorithms.- Cauchy Index and Applications.- Real Roots.- Cylindrical Decomposition Algorithm.- Polynomial System Solving.- Existential Theory of the Reals.- Quantifier Elimination.- Computing Roadmaps and Connected Components of Algebraic Sets.- Computing Roadmaps and Connected Components of Semi-algebraic Sets.

Recenzii

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 ofcomputational Mathematics, Issue 8, 2008)

Textul de pe ultima copertă

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 first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing.
Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects, and 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 revised second edition contains several recent results, notably 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. An index of notation has also been added.

Caracteristici

First graduate textbook on the algorithmic aspects of real algebraic geometry