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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Computing Roadmaps and Connected Components of Semi-algebraic Sets,s 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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1431-1550 real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, or deciding whether two points belong in the same connected component of a semi-algebraic set occur in many contexts. In this first-ever graduate textbook on t

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Der entschlüsselte Wachstumscode In the next section, we algebraically characterize systems of polynomials with a finite number of solutions and prove that the corresponding quotient rings are finite dimensional vector spaces. We end the chapter defining projective space and proving a weak version of Bézout’s theorem.

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Fritz Kr?ger,Michael Tr?m,James McGrathr homology that applies only to simplicial complexes. In the second section, we show how to extend this theory to closed semi-algebraic sets using the triangulation theorem proved in Chapter 5. Finally, in the third section we define the Euler-Poincare characteristic for locally closed semi-algebraic sets.

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,Einleitung – Herangehen und Aufbau,atic forms. In Section 3, we study remainder sequences and the related notion of subresultant polynomials. The algorithms in this chapter are very basic and will be used throughout the other chapters of the book.

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