Ebook: Constructible Sets in Real Geometry

This book presents a systematic and unified report on the minimal description of constructible sets. It starts at a very basic level (almost undergraduate) and leads up to state-of-the-art results, many of which are published in book form for the very first time. The book contains numerous examples, 63 figures and each chapter ends with a section containing historical notes. The authors tried to keep the presentation as self-contained as it can possibly be.

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This book presents a systematic and unified report on the minimal description of constructible sets. It starts at a very basic level (almost undergraduate) and leads up to state-of-the-art results, many of which are published in book form for the very first time. The book contains numerous examples, 63 figures and each chapter ends with a section containing historical notes. The authors tried to keep the presentation as self-contained as it can possibly be.
Content:
Front Matter....Pages I-IX
Introduction....Pages 1-3
A First Look at Semialgebraic Geometry....Pages 5-28
Real Algebra....Pages 29-60
Spaces of Signs....Pages 61-84
Spaces of Orderings....Pages 85-123
The Main Results....Pages 125-143
Spaces of Signs of Rings....Pages 145-176
Real Algebra of Excellent Rings....Pages 177-210
Real Analytic Geometry....Pages 211-253
Back Matter....Pages 255-270

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This book presents a systematic and unified report on the minimal description of constructible sets. It starts at a very basic level (almost undergraduate) and leads up to state-of-the-art results, many of which are published in book form for the very first time. The book contains numerous examples, 63 figures and each chapter ends with a section containing historical notes. The authors tried to keep the presentation as self-contained as it can possibly be.
Content:
Front Matter....Pages I-IX
Introduction....Pages 1-3
A First Look at Semialgebraic Geometry....Pages 5-28
Real Algebra....Pages 29-60
Spaces of Signs....Pages 61-84
Spaces of Orderings....Pages 85-123
The Main Results....Pages 125-143
Spaces of Signs of Rings....Pages 145-176
Real Algebra of Excellent Rings....Pages 177-210
Real Analytic Geometry....Pages 211-253
Back Matter....Pages 255-270
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