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

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Eine Ikonologie des Schulanfangs,ether two points belong to the same connected component. Done in a parametric way the roadmap algorithm also gives a description of the semi-algebraically connected components of an algebraic set. The complexities of the algorithms given in this chapter are much better than the one provided by cylin

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https://doi.org/10.1007/978-3-531-91698-9s provided by cylindrical decomposition in Chapter 12 for the problem of deciding connectivity properties of semi-algebraic sets (single exponential in the number of variables rather than doubly exponential).

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Algebraically Closed Fields,remainder sequences and, for the case where the coefficients have parameters, the tree of possible pseudo-remainder sequences and the set of possible greatest common divisors. Several important applications of logical nature of the projection theorem are given.

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Real Closed Fields,ets and prove that the projection of a semi-algebraic set is semi-algebraic. This is done using a parametric version of real root counting techniques described in the second section. The fourth section is devoted to several important applications of the projection theorem, of logical and geometric n