Algorithms in Real Algebraic GeometrySpringer Science & Business Media, 9. mar. 2013 - 602 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, or deciding whether two points belong in the same connected component of a semi-algebraic set occur in many contexts. 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. |
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Resultater 1-5 af 52
... Elimination and the Transfer Principle . 1.5 Bibliographical Notes 2 Real Closed Fields . 2.1 Definitions and First Properties 2.2 Real Root Counting 2.2.1 Descartes's Law of Signs and the Budan - Fourier Theorem 2.2.2 The Cauchy Index ...
... Elimination . 493 14.1 Algorithm for the General Decision Problem 494 14.2 Quantifier Elimination 507 14.3 Local Quantifier Elimination 512 14.4 Dimension and Closure Semi - algebraic Sets 517 • 14.5 Bibliographical Notes 521 15 ...
... 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 equations ...
... elimination obtained in Chapter 12 using cylindrical decompo- sition are improved . The main idea is that the complexity of quantifier elimi- nation should not be doubly exponential in the number of variables but rather in the number of ...
... Elimination and the Transfer Principle Returning to logical terminology , Theorem 1.21 implies that the theory of algebraically closed fields admits quantifier elimination in the language of fields , which is the following theorem ...
Indhold
1 | |
Algebra | 91 |
པ Decomposition of SemiAlgebraic Sets | 137 |
Elements of Topology | 173 |
Quantitative Semialgebraic Geometry | 201 |
Complexity of Basic Algorithms | 241 |
Cauchy Index and Applications | 283 |
Real Roots 321 | 320 |
Cylindrical Decomposition Algorithm 421 | 420 |
Existential Theory of the Reals | 465 |
Quantifier Elimination | 493 |
Computing Roadmaps and Connected Components | 522 |
Computing Roadmaps and Connected Components | 549 |
References 587 | 586 |
Index | 595 |
Polynomial System Solving | 365 |
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