= Separating finite Laurent support by an integer weight
{title2=$w\cdot m$}
Given a finite set $F\subset\mathbb Z^r$ of exponent vectors, there is $w\in\mathbb Z^r$ for which the integers $w\cdot m$, $m\in F$, are pairwise distinct. For $r=2$, take $w=(1,N)$ with $N$ larger than every first-coordinate difference in $F$. In higher dimensions take $w=(1,N,\ldots,N^{r-1})$ with $N$ sufficiently large. This proves that a nonzero <Laurent polynomial> can be detected by a substitution $X_i=T^{w_i}$ without cancellation of its distinct terms.
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