"Algorithms in Real Algebraic Geometry" is a book edited by Manuel Bronstein, Arjeh M. Cohen, Henri Cohen, David Eisenbud, and Bernd Sturmfels. It presents algorithms and computational methods in real algebraic geometry, with 40 figures. The book is written by Saugata Basu of the Georgia Institute of Technology and Richard Pollack of the Courant Institute of Mathematical Sciences, as well as Marie-Françoise Roy of the University of Rennes I. It is published by Springer-Verlag Berlin Heidelberg GmbH and is part of the "Algorithms and Computation in Mathematics" series, Volume 10. The book covers topics such as algebraically closed fields, real closed fields, semi-algebraic sets, and algorithms for real algebraic geometry. It includes detailed discussions on quantifier elimination, the transfer principle, and the topology of semi-algebraic sets. The book also discusses the decomposition of semi-algebraic sets, the complexity of basic algorithms, and the computation of roadmaps and connected components of algebraic sets. It provides an overview of the Euler-Poincaré characteristic, the Cauchy index, and the application of these concepts in real algebraic geometry. The book is structured into 16 chapters, each covering various aspects of real algebraic geometry, including the theory of real closed fields, the topology of semi-algebraic sets, and the computation of real roots. It also includes a detailed bibliography and an index for reference. The book is intended for researchers and students in mathematics and computer science who are interested in the computational aspects of algebraic geometry."Algorithms in Real Algebraic Geometry" is a book edited by Manuel Bronstein, Arjeh M. Cohen, Henri Cohen, David Eisenbud, and Bernd Sturmfels. It presents algorithms and computational methods in real algebraic geometry, with 40 figures. The book is written by Saugata Basu of the Georgia Institute of Technology and Richard Pollack of the Courant Institute of Mathematical Sciences, as well as Marie-Françoise Roy of the University of Rennes I. It is published by Springer-Verlag Berlin Heidelberg GmbH and is part of the "Algorithms and Computation in Mathematics" series, Volume 10. The book covers topics such as algebraically closed fields, real closed fields, semi-algebraic sets, and algorithms for real algebraic geometry. It includes detailed discussions on quantifier elimination, the transfer principle, and the topology of semi-algebraic sets. The book also discusses the decomposition of semi-algebraic sets, the complexity of basic algorithms, and the computation of roadmaps and connected components of algebraic sets. It provides an overview of the Euler-Poincaré characteristic, the Cauchy index, and the application of these concepts in real algebraic geometry. The book is structured into 16 chapters, each covering various aspects of real algebraic geometry, including the theory of real closed fields, the topology of semi-algebraic sets, and the computation of real roots. It also includes a detailed bibliography and an index for reference. The book is intended for researchers and students in mathematics and computer science who are interested in the computational aspects of algebraic geometry.