= Polynomial evaluation map on a finite point set
{title2=$E_P:\mathcal P_{\le d}(\mathbb R^n)\to\mathbb R^P$}
Evaluation of bounded-degree <multivariate polynomials> on a finite set defines a <linear map> $E_P:f\mapsto(f(p))_{p\in P}$. Its rank is at most $|P|$ and its kernel is the space of polynomials vanishing on $P$. The <rank-nullity theorem> gives $\dim\ker E_P\ge\binom{d+n}{n}-|P|$ for degree at most $d$ in $n$ variables. Dependent point constraints only enlarge the kernel.
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