computing perturbative solutions [@pert], determining stability of steady states [@stss], and studying integrable systems [@pla1; @intg; @kosc].

The ubiquity of the Poisson bracket has led to study of it in its own right. In particular, a good deal of work has gone into exploring its geometric theory [@wei1; @vais] (also see references on the related subject of symplectic geometry [@syge]). In this letter, we consider only one facet of this rich geometry, that related to Casimir invariants. These are functions whose Poisson bracket with any other function vanishes. Their existence for any finite-dimensional degenerate Poisson bracket follows from the Frobenius theorem of differential geometry [@frob].

The Casimir invariants of a given Poisson bracket are important because they are conserved quantities in any Hamiltonian system that uses that bracket. As such, they play a vital part in reducing the order [@red], or even integrating some systems [@mmof]. In addition, they are central to both the Energy-Casimir method of determining stability [@stss], and the Semenov-Tian-Shansky scheme of constructing integrable systems [@kosc]. In all these applications, the actual computation of Casimir invariants is essential.

We present a method for computing Casimir invariants. This method amounts to integrating the null covectors of the second 