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Algorithms in Real Algebraic Geometry / by Saugata Basu, Richard Pollack, Marie-Françoise Coste-Roy
(Algorithms and Computation in Mathematics ; 10)
版 | 2nd ed. 2006. |
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出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 2006 |
本文言語 | 英語 |
大きさ | X, 662 p : 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 | Algebraically Closed Fields -- Real Closed Fields -- Semi-Algebraic Sets -- Algebra -- Decomposition of Semi-Algebraic Sets -- Elements of Topology -- Quantitative Semi-algebraic Geometry -- Complexity of Basic Algorithms -- Cauchy Index and Applications -- Real Roots -- Cylindrical Decomposition Algorithm -- Polynomial System Solving -- Existential Theory of the Reals -- Quantifier Elimination -- Computing Roadmaps and Connected Components of Algebraic Sets -- Computing Roadmaps and Connected Components of Semi-algebraic Sets The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. 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. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added HTTP:URL=https://doi.org/10.1007/3-540-33099-2 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783540330998 |
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EB00233960 |
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※2017年9月4日以降