= Lenard-Magri recursion
{c}
{title2=$\Pi_1dH_n=-\Pi_2dH_{n-1}$}
Start from a <Casimir function> $H_0$ of the first <Poisson structure>. Whenever possible, choose $H_n$ whose first <Hamiltonian vector field> is minus the second <Hamiltonian vector field> of $H_{n-1}$. A sequence extending indefinitely is the <coefficient> sequence of a formal <Casimir function> for the <Poisson pencil>. Its <functions> pairwise commute for both <Poisson brackets>. Existence at each stage is an additional solvability requirement; compatibility alone does not guarantee it.
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