Efficient algorithm for computing the Euler-Poincar\'e characteristic of a semi-algebraic set defined by few quadratic inequalities
<|reference_start|>Efficient algorithm for computing the Euler-Poincar\'e characteristic of a semi-algebraic set defined by few quadratic inequalities: We present an algorithm which takes as input a closed semi-algebraic set, $S \subset \R^k$, defined by \[ P_1 \leq 0, ..., P_\ell \leq 0, P_i \in \R[X_1,...,X_k], \deg(P_i) \leq 2, \] and computes the Euler-Poincar\'e characteristic of $S$. The complexity of the algorithm is $k^{O(\ell)}$.<|reference_end|>
@article{basu2006efficient,
    title={Efficient algorithm for computing the Euler-Poincar\'e characteristic of
  a semi-algebraic set defined by few quadratic inequalities},
    author={Saugata Basu},
    journal={arXiv preprint arXiv:cs/0605082},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0605082},
    primaryClass={cs.SC cs.CG}
}