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 semi-algebraic 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 semi-algebraic 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.

Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).

Readership

Graduate students and research mathematicians interested in algebra and algebraic geometry and their applications.

Table of Contents

• C. Andradas -- Characterization and description of basic semialgebraic sets
• D. Bailey and V. Powers -- Constructive approaches to representation theorems in finitely generated real algebras
• I. Bonnard -- Combinatorial characterizations of algebraic sets
• P. Bürgisser -- Lower bounds and real algebraic geometry
• B. Chevallier -- The Viro method applied with quadratic transforms
• A. Gabrielov and T. Zell -- On the number of connected components of the relative closure of a semi-Pfaffian family
• C. McCrory -- How to show a set is not algebraic
• P. A. Parrilo and B. Sturmfels -- Minimizing polynomial functions
• B. Reznick -- Patterns of dependence among powers of polynomials
• F. Rouillier -- Efficient algorithms based on critical points method
• F. Sottile -- Enumerative real algebraic geometry
• I. Streinu -- Combinatorial roadmaps in configuration spaces of simple planar polygons
• T. Theobald -- Visibility computations: From discrete algorithms to real algebraic geometry