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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... Notes 93 94 99 4 Algebra Discriminant and Subdiscriminant 101 101 4.2 Resultant and Subresultant Coefficients 105 4.2.1 Resultant 105 4.2.2 Subresultant Coefficients 110 4.2.3 Subresultant Coefficients and Cauchy Index 113 4.3 Quadratic ...
... Notes . . . . . . . . . . . . . . . . . . . . . . . . . Quantitative Semi-algebraic Geometry . . . . . . . . . . . . . 236 237 7.1 Morse Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 7.2 Sum of the Betti Numbers ...
... Notes . . . . . . . . . . . . . . . . . . . . . . . . . 350 10 Real Roots ... Notes . . . . . . . . . . . . . . . . . . . . . . . . . 397 401 11 Cylindrical Decomposition Algorithm . . 11.1 Computing the Cylindrical Decomposition 11.1.1 ...
... Notes 503 13 Existential Theory of the Reals 505 13.1 Finding Realizable Sign Conditions 506 13.2 A Few Applications 516 13.3 Sample Points on an Algebraic Set 519 13.4 Computing the Euler - Poincaré Characteristic of Sign Condi- tions ...
... notes at the end of the chapters . Various mistakes and typos have been corrected , and new ones introduced , for sure ... Note that the second edition has been prepared inside TEXMACS The TEXMACS files have been initially produced from ...
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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