A3: the coefficientwise restriction kernel

One has ${\mathcal{N}}_{\mathrm{sol}}\subseteq {\mathcal{N}}_W$. The space ${\mathcal{N}}_W$ is an ideal for ordinary pointwise polynomial multiplication, and the vector-space restriction quotient exists. These facts do not establish its compatibility with ${\star }_H$. We test that compatibility using two regular fields.