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- W3104949800 abstract "Let $S subset R^{k + m}$ be a compact semi-algebraic set defined by a system of $ell$ polynomial inequalities of degree at most 2. $ Let $pi$ denote the standard projection from $R^{k + m}$ onto $R^m$. We prove that for any $q >0$, the sum of the first $q$ Betti numbers of $pi(S)$ is bounded by $(k + m)^{O(qell)}.$ We also present an algorithm for computing the the first $q$ Betti numbers of $pi(S)$, whose complexity is $ (k+m)^{2^{O(qell)}}.$ For fixed $q$ and $ell$, both the bounds are polynomial in $k+m$." @default.
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- W3104949800 date "2007-09-15" @default.
- W3104949800 modified "2023-09-26" @default.
- W3104949800 title "On Projections of Semi-Algebraic Sets Defined by Few Quadratic Inequalities" @default.
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- W3104949800 doi "https://doi.org/10.1007/s00454-007-9014-1" @default.
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