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. |
Fra bogen
Resultater 1-5 af 94
... Semi - Algebraic Sets 73 3.1 Topology 73 3.2 Semi - algebraically Connected Sets 76 3.3 Semi - algebraic Germs . 77 3.4 Closed and Bounded Semi - algebraic Sets 3.5 Implicit Function Theorem 3.6 Bibliographical Notes 82 83 89 4 Algebra ...
... Algebraic Sets 137 5.1 Cylindrical Decomposition .. 137 5.2 Semi - algebraically Connected Components 147 5.3 Dimension ... 148 5.4 Semi - algebraic Description of Cells 150 5.5 Stratification .. 152 5.6 Simplicial Complexes 158 5.7 ...
... Semi - algebraic Sets 517 • 14.5 Bibliographical Notes 521 15 Computing Roadmaps and Connected Components of Algebraic Sets . 523 15.1 Pseudo - critical Values and Connectedness 524 15.2 Roadmap of an Algebraic Set 526 15.3 Computing ...
... semi - algebraic sets which constitute our main ob- jects of interest in this book . These are the subsets of R ... algebraic set is semi - algebraic . The proof , though more complicated than that for the algebraically closed case , is ...
... set in affine space is constructible . Considering projective space allows an even more satisfactory result : the pro- jection of an algebraic set ... algebraic sets , the first 0 Introduction 3 Topology 73 Semi-algebraically Connected Sets.
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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