Abstract
This paper offers a short survey of two topics. In the first section we describe
a new bound on the Betti numbers of semi-algebraic sets whose proof rely on
the Thom-Milnor bound for algebraic sets and the Mayer-Vietoris long exact
sequence. The second section describes the best complexity results and practical
implementations currently available for finding real solutions of systems of
polynomial equations and inequalities. In both sections, the consideration of
critical points will play a key role.
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Roy, MF. (2003). Some Recent Quantitative and Algorithmic Results in Real Algebraic Geometry. In: Aronov, B., Basu, S., Pach, J., Sharir, M. (eds) Discrete and Computational Geometry. Algorithms and Combinatorics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55566-4_34
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DOI: https://doi.org/10.1007/978-3-642-55566-4_34
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