= Ehrhart polynomial
{c}
{title2=$L_P(n)=\#(nP\cap\mathbb Z^d)$}
For a <lattice polytope> $P$, its <Ehrhart polynomial> counts integer points in dilates: $L_P(n)=\#(nP\cap\mathbb Z^d)$ for <nonnegative integers> $n$. <Ehrhart's theorem> makes this counting <function> a <polynomial>. For the <unit square>, $L_P(n)=(n+1)^2$: there are $n+1$ choices for each coordinate. This turns a geometric counting problem into <algebra>.<Computing the Continuous Discretely by Matthias Beck and Sinai Robins>[§3.3, Theorem 3.8]{ref}
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