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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Resultater 1-5 af 61
... Decomposition of Semi - Algebraic Sets 159 5.1 Cylindrical Decomposition . 159 5.2 Semi - algebraically Connected Components 168 5.3 Dimension 170 5.4 Semi - algebraic Description of Cells 172 5.5 Stratification 174 5.6 Simplicial ...
... Cylindrical Decomposition Algorithm . . 11.1 Computing the Cylindrical Decomposition 11.1.1 Outline of the Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 404 404 11.1.2 Details of the ...
... decomposition is called a cylindrical decomposition: a semi-algebraic set is decomposed into a finite number of pieces, each homeomorphic to an open cube. A finer decomposition provides a stratification, i.e. a decomposition into a ...
... cylindrical decomposition which had been already studied in Chapter 5. The basic idea of this algorithm is to successively eliminate variables, using subresul- tants. Cylindrical decomposition has numerous applications among which are ...
... cylindrical decom- position are improved. The main idea is that the complexity of quantifier elimination should not ... cylindrical decomposition. Our construction of parametrized paths gives an algorithm for computing coverings of semi ...
Indhold
1 | |
43 | |
94 | 77 |
3 | 83 |
Algebra | 100 |
པ | 159 |
213 | 183 |
Elements of Topology | 195 |
Real Roots | 365 |
Cylindrical Decomposition Algorithm | 402 |
Polynomial System Solving | 445 |
Existential Theory of the Reals | 505 |
Quantifier Elimination | 533 |
Computing Roadmaps and Connected Components of Alge | 564 |
Computing Roadmaps and Connected Components of Semi | 593 |
References | 635 |
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