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Efficient algorithm for computing the Euler-Poincaré characteristic of a semi-algebraic set defined by few quadratic inequalities

Saugata Basu
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Abstract

We present an algorithm which takes as input a closed semi-algebraic set, $S \subset \R^k$, defined by \[ P_1 \leq 0, ..., P_\ell \leq 0, P_i \in \R[X_1,...,X_k], °(P_i) \leq 2, \] and computes the Euler-Poincaré characteristic of $S$. The complexity of the algorithm is $k^{O(\ell)}$.

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Saugata Basu. 2006-05-18. Efficient algorithm for computing the Euler-Poincaré characteristic of a semi-algebraic set defined by few quadratic inequalities. https://arxiv.org/abs/cs/0605082

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