This is the first graduate textbook on the algorithmic aspects of real algebraic geometry. The main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. 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. This second edition contains several recent results on discriminants of symmetric matrices and other relevant topics.
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 Cylindrical Decomposition Algorithm.- 12 Polynomial System Solving.- 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 of Notation.- Index.
Our reader reviews allow you to share your comments on titles you liked,
or didn't, with others. By submitting an online review, you are representing to
Barnes & Noble.com that all information contained in your review is original
and accurate in all respects, and that the submission of such content by you
and the posting of such content by Barnes & Noble.com does not and will not
violate the rights of any third party. Please follow the rules below to help
ensure that your review can be posted.
Reviews by Our Customers Under the Age of 13
We highly value and respect everyone's opinion concerning the titles we offer.
However, we cannot allow persons under the age of 13 to have accounts at BN.com or
to post customer reviews. Please see our Terms of Use for more details.
What to exclude from your review:
Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the
information on the product page, please send us an email.
Reviews should not contain any of the following:
- HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
- Time-sensitive information such as tour dates, signings, lectures, etc.
- Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
- Comments focusing on the author or that may ruin the ending for others
- Phone numbers, addresses, URLs
- Pricing and availability information or alternative ordering information
- Advertisements or commercial solicitation
Reminder:
- By submitting a review, you grant to Barnes & Noble.com and its
sublicensees the royalty-free, perpetual, irrevocable right and license to use the
review in accordance with the Barnes & Noble.com Terms of Use.
- Barnes & Noble.com reserves the right not to post any review -- particularly
those that do not follow the terms and conditions of these Rules. Barnes & Noble.com
also reserves the right to remove any review at any time without notice.
- See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend
Create a Pen Name
Welcome, penname
You have successfully created your Pen Name. Start enjoying the benefits of the BN.com Community today.
If you find inappropriate content, please report it to Barnes & Noble
More About This Textbook
Overview
This is the first graduate textbook on the algorithmic aspects of real algebraic geometry. The main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. 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. This second edition contains several recent results on discriminants of symmetric matrices and other relevant topics.
Product Details
Related Subjects
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 Cylindrical Decomposition Algorithm.- 12 Polynomial System Solving.- 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 of Notation.- Index.