= Hamiltonian trace functional on monic differential operators
{c}
{title2=$l_P(L)=c+\sum_{l=0}^{m-1}\int a_lu_l\,dx$}
For a fixed <formal pseudodifferential operator> $P=\sum_j p_j\partial^j$ and a monic <differential operator> $L=\partial^m+\sum_{l=0}^{m-1}u_l\partial^l$, cyclicity of the <Adler trace> gives $l_P(L)=\operatorname{Tr}(PL)$ with $c=\int p_{-m-1}\,dx$ and $a_l=\operatorname{res}(\partial^lP)=\sum_{k=0}^l\binom lk p_{k-l-1}^{(k)}$. The <function> is affine in the variable <coefficients>; its <variational derivative> with respect to $u_l$ is $a_l$.
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