Hardcover ISBN:  9780821828632 
Product Code:  DIMACS/60 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Electronic ISBN:  9781470440183 
Product Code:  DIMACS/60.E 
List Price:  $80.00 
MAA Member Price:  $72.00 
AMS Member Price:  $64.00 

Book DetailsDIMACS  Series in Discrete Mathematics and Theoretical Computer ScienceVolume: 60; 2003; 219 ppMSC: Primary 14; 68;
Algorithmic and quantitative aspects in real algebraic geometry are becoming increasingly important areas of research because of their roles in other areas of mathematics and computer science. The papers in this volume collectively span several different areas of current research.
The articles are based on talks given at the DIMACS Workshop on “Algorithmic and Quantitative Aspects of Real Algebraic Geometry”. Topics include deciding basic algebraic properties of real semialgebraic sets, application of quantitative results in real algebraic geometry towards investigating the computational complexity of various problems, algorithmic and quantitative questions in real enumerative geometry, new approaches towards solving decision problems in semialgebraic geometry, as well as computing algebraic certificates, and applications of real algebraic geometry to concrete problems arising in robotics and computer graphics. The book is intended for researchers interested in computational methods in algebra.ReadershipGraduate students and research mathematicians interested in algebra and algebraic geometry and their applications.

Table of Contents

Chapters

Characterization and description of basic semialgebraic sets

Constructive approaches to representation theorems in finitely generated real algebras

Combinatorial characterizations of algebraic sets

Lower bounds and real algebraic geometry

The Viro method applied with quadratic transforms

On the number of connected components of the relative closure of a semiPfaffian family

How to show a set is not algebraic

Minimizing polynomial functions

Patterns of dependence among powers of polynomials

Efficient algorithms based on critical points method

Enumerative real algebraic geometry

Combinatorial roadmaps in configuration spaces of simple planar polygons

Visibility computations: From discrete algorithms to real algebraic geometry


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Algorithmic and quantitative aspects in real algebraic geometry are becoming increasingly important areas of research because of their roles in other areas of mathematics and computer science. The papers in this volume collectively span several different areas of current research.
The articles are based on talks given at the DIMACS Workshop on “Algorithmic and Quantitative Aspects of Real Algebraic Geometry”. Topics include deciding basic algebraic properties of real semialgebraic sets, application of quantitative results in real algebraic geometry towards investigating the computational complexity of various problems, algorithmic and quantitative questions in real enumerative geometry, new approaches towards solving decision problems in semialgebraic geometry, as well as computing algebraic certificates, and applications of real algebraic geometry to concrete problems arising in robotics and computer graphics. The book is intended for researchers interested in computational methods in algebra.
Graduate students and research mathematicians interested in algebra and algebraic geometry and their applications.

Chapters

Characterization and description of basic semialgebraic sets

Constructive approaches to representation theorems in finitely generated real algebras

Combinatorial characterizations of algebraic sets

Lower bounds and real algebraic geometry

The Viro method applied with quadratic transforms

On the number of connected components of the relative closure of a semiPfaffian family

How to show a set is not algebraic

Minimizing polynomial functions

Patterns of dependence among powers of polynomials

Efficient algorithms based on critical points method

Enumerative real algebraic geometry

Combinatorial roadmaps in configuration spaces of simple planar polygons

Visibility computations: From discrete algorithms to real algebraic geometry