Algorithms in Real Algebraic Geometry

Softcover Nachdruck of hardcover 2. Auflage 2006
ISBN: 978-3-642-06964-2
Verlag: Springer

Buch, Englisch, 662 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 1001 g

Reihe: Algorithms and Computation in Mathematics

This is the first graduate textbook on the algorithmic aspects of real algebraic geometry. 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 and other relevant topics.

Zielgruppe

Graduate

Autoren/Hrsg.

Basu, Saugata

Pollack, Richard

Coste-Roy, Marie-Françoise

Fachgebiete

• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Algebraically Closed Fields.- Real Closed Fields.- Semi-Algebraic Sets.- Algebra.- Decomposition of Semi-Algebraic Sets.- Elements of Topology.- Quantitative Semi-algebraic Geometry.- Complexity of Basic Algorithms.- Cauchy Index and Applications.- Real Roots.- Cylindrical Decomposition Algorithm.- Polynomial System Solving.- Existential Theory of the Reals.- Quantifier Elimination.- Computing Roadmaps and Connected Components of Algebraic Sets.- Computing Roadmaps and Connected Components of Semi-algebraic Sets.