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Algorithms in Real Algebraic Geometry /

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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...

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Bibliographic Details
Main Author: Basu, Saugata
Corporate Author: SpringerLink (Online service)
Other Authors: Pollack, Richard, Roy, M.-F. (Marie-Françoise)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2003.
Series:Algorithms and computation in mathematics ; 10.
Subjects:
Mathematics.
Algebra > Data processing.
Geometry, Algebraic.
Algorithms.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Introduction
  • 1 Algebraically Closed Fields
  • 2 Real Closed Fields
  • 3 Semi-Algebraic Sets
  • 4 Algebra
  • 5 Decomposition of Semi-Algebraic Sets
  • 6 Elements of Topology
  • 7 Quantitative semi-algebraic geometry
  • 8 Complexity of Basic Algorithms
  • 9 Cauchy index and applications
  • 10 Real Roots
  • 11 Polynomial System Solving
  • 12 Cylindrical decomposition algorithm
  • 13 Existential Theory of the Reals
  • 14 Quantifier Elimination
  • 15 Computing Roadmaps and Connected Components of Algebraic Sets
  • 16 Computing roadmaps and connected components of Semi-algebraic sets
  • References
  • Index.