Full Description
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. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.
Contents
0 Introduction.- 1 Algebraically Closed Fields.- 2 Real Closed Fields.- 3 Semi-Algebraic Sets.- 4 Algebra.- 5 Decomposition of Semi-Algebraic Sets.- 6 Elements of Topology.- 7 Quantitative Semi-algebraic Geometry.- 8 Complexity of Basic Algorithms.- 9 Cauchy Index and Applications.- 10 Real Roots.- 11 Polynomial System Solving.- 12 Cylindrical Decomposition Algorithm.- 13 Existential Theory of the Reals.- 14 Quantifier Elimination.- 15 Computing Roadmaps and Connected Components of Algebraic Sets.- 16 Computing Roadmaps and Connected Components of Semi-algebraic Sets.- References.
