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