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

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

2006-05-18

arxiv.org/abs/cs/0605082v1

Computer Science

Symbolic Computation

17 pages, accepted for publication in Computational Complexity

Scientific paper

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 $k^{O(\ell)}$.

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