= Order filtration of a Weyl algebra
{title2=$D^m=\sum_{|\beta|\le m}\mathbb C[x]\partial^\beta$}
For the relative <differential operators> over $\mathbb C$ on a polynomial ring, coordinates have order zero and partial derivatives have order one. The <associated graded ring> is $\mathbb C[x,\xi]$ with degrees zero for $x_i$ and one for $\xi_i$. This differs from the <Bernstein filtration>, in which both sets of generators have degree one and every filtration piece is finite-dimensional.
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