Efficient algorithm for computing the Euler-Poincar\'e characteristic of a semi-algebraic set defined by few quadratic inequalities
Abstract
We present an algorithm which takes as input a closed semi-algebraic set, S ⊂ k, defined by \[ P1 ≤ 0, ..., P ≤ 0, Pi ∈ [X1,...,Xk], (Pi) ≤ 2, \] and computes the Euler-Poincar\'e characteristic of S. The complexity of the algorithm is kO().
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