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Mizrahi","submitted_at":"2012-04-14T13:32:50Z","abstract_excerpt":"We define a new grading, that we call the \"level grading\", on the algebra of polynomials generated by the derivatives $u_{k+i}=\\partial^{k+i}u/\\partial x^{k+i}$ over the ring $K^{(k)}$ of $C^{\\infty}$ functions of $u,u_1,...,u_k$. This grading has the property that the total derivative and the integration by parts with respect to $x$ are filtered algebra maps. In addition, if $u$ satisfies an evolution equation $u_t=F[u]$ and $F$ is a level homogeneous differential polynomial, then the total derivative with respect to $t$, $D_t$, is also a filtered algebra map. 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