Computing rational points in convex semi-algebraic sets and SOS decompositions

Mohab Safey El Din, Lihong Zhi

Let $\mathcal{P}=\{h_1,...,h_s\}\subset \mathbb{Z}[Y_1,...,Y_k]$, $D\ge °(h_i)$ for $1\le i\le s$, $\sigma$ bounding the bit length of the coefficients of the $h_i$'s, and $\Phi$ be a quantif…