Titlebook: Algorithms in Real Algebraic Geometry; Saugata Basu,Richard Pollack,Marie-Franco̧ise Roy Textbook 20031st edition Springer-Verlag Berlin H

Glucose

Semi-Algebraic Sets, and bounded semi-algebraic sets in Section 4, we introduce semi-algebraic germs in Section 3. The semi-algebraic germs over a real closed field constitute a real closed field containing infinitesimals, closely related to the field of Puiseux series, and play an important role throughout the whole b

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松鸡

Decomposition of Semi-Algebraic Sets,oduce the cylindrical decomposition which is a key technique for studying the geometry of semi-algebraic sets. In Section 2 we use the cylindrical decomposition to define and study the semi-algebraically connected components of a semi-algebraic set. In Section 3 we define the dimension of a semi-alg

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beta-carotene

Quantitative Semi-algebraic Geometry,e key method for this study is the critical point method, i.e. the consideration of the critical points of a well chosen projection. The critical point method also plays a key role for improving the complexity of algorithms in the last chapters of the book.

AMOR

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Real Roots, Descartes’s law of sign and Bernstein polynomials. These roots are characterized by intervals with rational endpoints. The method presented works only for archimedean real closed fields. In the second part of the chapter we study exact methods working in general real closed fields. Section 3 is dev

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牵连

Quantifier Elimination,ined doubly exponential complexity in the number of variables. On the other hand, we have seen in Chapter 13 an algorithm for the existential theory of the reals (which is to decide the truth or the falsity of a sentence with a single block of existential quantifiers) with complexity singly exponent