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＜電子ブック＞
Algorithms in Real Algebraic Geometry / by Saugata Basu, Richard Pollack, Marie-Françoise Coste-Roy
(Algorithms and Computation in Mathematics ; 10)

版	1st ed. 2003.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2003
本文言語	英語
大きさ	VIII, 602 p. 9 illus : online resource
著者標目	*Basu, Saugata author Pollack, Richard author Coste-Roy, Marie-Françoise author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Algorithms LCSH:Computer science -- Mathematics  全ての件名で検索 FREE:Algebraic Geometry FREE:Algorithms FREE:Symbolic and Algebraic Manipulation
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-662-05355-3

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