Algorithms in Real Algebraic Geometry
By: by Saugata Basu, Richard Pollack, Marie-Franco̧ise Roy
Contributors: Pollack, Richard; Roy, Marie-Franco̧ise
Series: Algorithms and Computation in Mathematics -- 10; Algorithms and Computation in Mathematics -- 10
Publisher: Springer Berlin Heidelberg
Published: 2003
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 602
ISBN-13: 9783662053577; 9783662053553
Subjects: Mathematics; Algebra; Algorithms; Data processing; Geometry, algebraic
Description: 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 semi-algebraic set occur in many contexts. 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, and researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students.
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Table of contents: title: Introduction; title: 1 Algebraically Closed Fields; title: 2 Real Closed Fields; title: 3 Semi-Algebraic Sets; title: 4 Algebra; title: 5 Decomposition of Semi-Algebraic Sets; title: 6 Elements of Topology; title: 7 Quantitative semi-algebraic geometry; title: 8 Complexity of Basic Algorithms; title: 9 Cauchy index and applications; title: 10 Real Roots; title: 11 Polynomial System Solving; title: 12 Cylindrical decomposition algorithm; title: 13 Existential Theory of the Reals; title: 14 Quantifier Elimination; title: 15 Computing Roadmaps and Connected Components of Algebraic Sets; title: 16 Computing roadmaps and connected components of Semi-algebraic sets; title: References; title: Index.