Bounding the Betti numbers and computing the Euler-Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials

Saugata Basu, Dmitrii V. Pasechnik, Marie-Francoise Roy

Let $\mathbb{R}$ be a real closed field, $\mathcal{Q}\subset \mathbb{R}[Y_1,...,Y_{\ell },X_1,...,X_k],$ with $ °_{Y}(Q) \leq 2, °_{X}(Q) \leq d, Q \in {\mathcal Q}, #({\mathcal Q})=m,$ and $ {\m…