# A.A. Agrachev, A. Lerario, Systems of quadratic inequalities

We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of $RP^n$ defined by a system of quadratic
inequalities and the image of the homology homomorphism induced by the inclusion of this subset in $RP^n$. We do not restrict ourselves to the term $E_2$
of the spectral sequence and give a simple explicit formula for the differential $d_2$.