2 problems

Let $\mathcal{F}=\{\mathcal{S}_j\}_{j=1}^{\infty}$ be a collection of tuples in $\mathbb{R}[x]$, and let $\mathcal{S}\in\mathcal{F}$ satisfy $\operatorname{deg}(\mathcal{S})>1$. Ma…

Let $\{\mathcal{S}_j\}_{j=1}^{\infty}$ be the collection of all tuples in $\mathbb{R}[x]$, and let $\mathcal{Z}[(\gamma^{-1}\circ\beta\circ\gamma\circ\nabla)^n(\mathcal{S}_j)]$ be…