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 92
... dimensional Systems . 121 4.5 Multivariate Hermite's Quadratic Form 127 4.6 Projective Space and a Weak Bézout's ... Dimension ... 148 5.4 Semi - algebraic Description of Cells 150 5.5 Stratification .. 152 5.6 Simplicial Complexes ...
... Dimension and Closure 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 ...
... dimensional vector space . As seen in Chapter 1 , the projection of an algebraic set in affine space is ... dimension . We also describe how to triangulate a closed and bounded semi - algebraic set . Various other finiteness ...
... dimension of the algebraic set , and an algebraic part , given by the Oleinik - Petrovsky- Thom - Milnor bound . The combinatorial part of these bounds agrees with the number of connected components defined by a family of hyperplanes ...
... realizable sign conditions on an algebraic set taking advantage of the ( possibly low ) dimension of the algebraic set . We also compute the Euler - Poincaré characteristic of sign conditions defined 0 Introduction 5.
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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