Let $k$ be an [algebraically closed field](/page/Algebraically%20Closed%20Field), let $n\in \mathbb N$, and let $X\subset \mathbb A_k^n$ be an affine algebraic set. Set
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\begin{align*}
R:=k[x_1,\dots,x_n].
\end{align*}
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Suppose that the vanishing ideal $I(X)\trianglelefteq R$ is generated by polynomials $f_1,\dots,f_r\in R$. Let