Algorithms in Real Algebraic Geometry

Algorithms in Real Algebraic Geometry by Saugata Basu, Richard Pollack, Marie-Françoise Coste-Roy.

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 Authors: Basu, Saugata (Author), Pollack, Richard (Author), Coste-Roy, Marie-Françoise (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
Edition:1st ed. 2003.
Series:Algorithms and Computation in Mathematics, 10
Springer eBook Collection.
Subjects:
Algebraic geometry.
Algorithms.
Computer science—Mathematics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 0 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.

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