The zero set of R, denoted by Z_{\mathbf{k}}(R), is defined as the set of points (u, y) \in \mathbf{k}^d \times \mathbf{k}^{n-d} such that \mathcal{Q}(u) is true and t(u, y)=0, p(u, y)>0, for all t\in Tand all p\in P. Observe that Z_{\mathbf{k}}(R) has dimension d in the affine space \mathbf{k}^n.
