Algorithms in Real Algebraic GeometrySpringer Science & Business Media, 6. jul. 2006 - 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. |
Fra bogen
... Cauchy Index 2.3 Projection Theorem for Algebraic Sets 2.4 Projection Theorem for Semi - Algebraic Sets +253 44 57 63 2.5 Applications 69 2.5.1 Quantifier Elimination and the Transfer Principle 2.5.2 Semi - Algebraic Functions 69 71 2.5 ...
... Cauchy Index 113 4.3 Quadratic Forms and Root Counting 119 • 4.3.1 Quadratic Forms 119 4.3.2 Hermite's Quadratic Form 4.4 Polynomial Ideals 4.4.1 Hilbert's Basis Theorem 127 132 132 4.4.2 Hilbert's Nullstellensatz 136 4.5 Zero ...
... . . . . . 316 8.3.6 Subresultant Computation . . . . . . . . . . . . . . . . . 317 8.4 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . 322 9 Cauchy Index and Applications 9.1 Cauchy Index . . Table of Contents VII.
Saugata Basu, Richard Pollack, Marie-Françoise Roy. 9 Cauchy Index and Applications 9.1 Cauchy Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 323 9.1.1 Computing the Cauchy ...
Denne sides indhold er desværre begrænset..
Indhold
Introduction | 1 |
223 | 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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Algorithms in Real Algebraic Geometry Saugata Basu,Richard Pollack,Marie-Françoise Coste-Roy Begrænset visning - 2007 |
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