Location 
Call number 
Availability 
Library Retrieval System 
516.35 BASU

Available

 Description
 viii, 602 p. ; 24 cm.
 Additional Authors
 Pollack, Richard.Roy, M.F.
 Notes
 Contents: 1. Algebraically Closed Fields  2. Real Closed Fields  3. SemiAlgebraic Sets  4. Algebra  5. Decomposition of SemiAlgebraic Sets  6. Elements of Topology  7. Quantitative Semialgebraic 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 Semialgebraic Sets.Includes bibliographical references and index.Summary: "The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, or deciding whether two points belong in the same connected component of a semialgebraic set occur in many contexts. In this firstever 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, and researchers in computer science and engineering will find the required mathematical background." "Being selfcontained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students."BOOK JACKET.