\log z^i = \mbox{\rm constant} \, .$$

Therefore, all Casimir invariants of (\[ND.1\]) can be easily found in this way.

An example that involves solving a less trivial Pfaffian system is the Lie-Poisson bracket associated with the Lie algebra su(3) (see Section \[S-INFINITE\]). This arises in the study of finite-mode analogs of two-dimensional hydrodynamics [@zeit]. With respect to ($i$ times the) Gell-Mann basis of su(3) [@gema], the components of J are given by

$$\label{SU3-COSYM}
\left( 
\begin{array}{cccccccc}
0 & 2 z^3 & -2 z^2 & z^7 & -z^6 & z^5 & -z^4 & 0 \\ 
-2 z^3 & 0 & 2 z^1 & z^6 & z^7 & -z^4 & -z^5 & 0 \\ 
2 z^2 & -2 z^1 & 0 & z^5 & -z^4 & -z^7 & z^6 & 0 \\ 
-z^7 & -z^6 & -z^5 & 0 & z^3 + \sqrt{3} z^8 & z^2 & z^1 & -\sqrt{3} z^5 \\ 
z^6 & -z^7 & z^4 & -z^3 - \sqrt{3} z^8 & 0 & -z^1 & z^2 & \sqrt{3} z^4 \\ 
-z^5 & z^4 & z^7 & -z^2 & z^1 & 0 & -z^3 + \sqrt{3} z^8 & -\sqrt{3} z^7 \\ 
z^4 & z^5 & -z^6 & -z^1 & -z^2 & 