Algorithms in Real Algebraic Geometry

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Last edited by MARC Bot
September 28, 2024 | History

Algorithms in Real Algebraic Geometry

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.

Publish Date
Language
English
Pages
602

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Edition Availability
Cover of: Algorithms in Real Algebraic Geometry
Cover of: Algorithms in Real Algebraic Geometry
Algorithms in Real Algebraic Geometry
2003, Springer Berlin Heidelberg
electronic resource / in English

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Book Details


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.

Edition Notes

Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.

Published in
Berlin, Heidelberg
Series
Algorithms and Computation in Mathematics -- 10, Algorithms and Computation in Mathematics -- 10

Classifications

Dewey Decimal Class
516.35
Library of Congress
QA564-609

The Physical Object

Format
[electronic resource] /
Pagination
1 online resource (viii, 602 p.)
Number of pages
602

Edition Identifiers

Open Library
OL27016037M
ISBN 10
3662053578, 3662053551
ISBN 13
9783662053577, 9783662053553
OCLC/WorldCat
851368312

Work Identifiers

Work ID
OL19825605W

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September 28, 2024 Edited by MARC Bot import existing book
June 28, 2019 Created by MARC Bot import new book