Algorithms in Real Algebraic Geometry

Forsideomslag
Springer 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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Indhold

Algebraically Closed Fields
9
Real Closed Fields
25
Applications
60
SemiAlgebraic Sets
73
Decomposition of SemiAlgebraic Sets
137
Elements of Topology
173
Quantitative Semialgebraic Geometry
201
Cauchy Index and Applications
283
Polynomial System Solving
365
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

Real Roots 321
320

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