Algorithms in Real Algebraic GeometrySpringer Science & Business Media, 21. apr. 2007 - 662 sider 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 textbook the main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. 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 second edition contains several recent results, 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. |
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... Quantifier Elimination and the Transfer Principle . . . . . . . 25 1.5 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . 27 2 Real Closed Fields ............................ 29 2.1 Ordered, Real and Real Closed ...
... Quantifier Elimination . . . . . . . . . . . . . . . . . . . . . . . . 423 11.4 Lower Bound for Quantifier Elimination . . . . . . . . . . . . . 426 11.5 Computation of Stratifying Families . . . . . . . . . . . . . . . 428 11.6 ...
... Quantifier Elimination . . . . . . . . . . . . . . . . . . . . . . . . . 533 14.1 Algorithm for the General Decision Problem . . . . . . . . . . 534 14.2 Quantifier Elimination . . . . . . . . . . . . . . . . . . . . . . . . 547 14.3 ...
... quantifier elimination.” A consequence of this last result is the decidability of elementary algebra and geometry, which was Tarski's initial motivation. In particular whether there exist real solutions to a finite set of polynomial ...
... quantifier elimination obtained in Chapter 11 using cylindrical decomposition are improved. The main idea is that the complexity of quantifier elimination should not be doubly exponential in the number of variables but rather in the ...
Indhold
1 | |
11 | |
29 | |
SemiAlgebraic Sets | 83 |
4 | 100 |
Decomposition of SemiAlgebraic Sets | 159 |
6 | 195 |
Quantitative Semialgebraic Geometry | 237 |
Interval | 330 |
Existential Theory of the Reals | 505 |
Quantifier Elimination | 533 |
Computing Roadmaps and Connected Components of Alge | 563 |
Computing Roadmaps and Connected Components of Semi | 593 |
References | 635 |
132 | 641 |
Index of Notation 645 | 644 |
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Algorithms in Real Algebraic Geometry Saugata Basu,Richard Pollack,Marie-Françoise Roy Begrænset visning - 2003 |
Algorithms in Real Algebraic Geometry Saugata Basu,Richard Pollack,Marie-Françoise Roy Begrænset visning - 2006 |
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