E-Book Overview
The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this textbook 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, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number.
E-Book Content
Algorithms and Computation in Mathematics • Volume 10 Editors Arjeh M. Cohen Henri Cohen David Eisenbud Michael F. Singer Bernd Sturmfels
Saugata Basu Richard Pollack Marie-Françoise Roy
Algorithms in Real Algebraic Geometry Second Edition
With 37 Figures
123
Saugata Basu Georgia Institute of Technology School of Mathematics Atlanta, GA 30332-0160 USA e-mail:
[email protected]
Richard Pollack Courant Institute of Mathematical Sciences 251 Mercer Street New York, NY 10012 USA e-mail:
[email protected]
Marie-Françoise Roy IRMAR Cam