the algebra $\Bbb{C}\,({{\cal P}}_a) \otimes \Bbb{C}\,(G_a) \otimes
\Bbb{C}\,(\eta_a)$ as a derivation, $$\label{sigma}
\sigma = - {{\cal P}}_a \frac{\partial}{\partial G_a}.$$ One has $$\sigma \delta + \delta \sigma = N$$ where $N$ counts the degree in the $G$’s and the ${{\cal P}}$’s. Hence, if ${\renewcommand{\arraystretch}{.7}     \begin{array}[b]{@{}c@{}} {\scriptscriptstyle (p)} \\ D_m \end{array}}$ is the term of degree $m$ in $(G, {{\cal P}})$ of ${\renewcommand{\arraystretch}{.7}     \begin{array}[b]{@{}c@{}} {\scriptscriptstyle (p)} \\ D \end{array}}$, a solution of (\[delta-om=d\]) is given by $$\label{om-p}
{{\renewcommand{\arraystretch}{.7}     \begin{array}[b]{@{}c@{}} {\scriptscriptstyle (p+1)} \\ \Omega \end{array}}} = - \sum_m 1/m \left( \sigma {\renewcommand{\arraystretch}{.7}     \begin{array}[b]{@{}c@{}} {\scriptscriptstyle (p)} \\ D \end{array}}_m
\right)$$ since $\delta {\renewcommand{\arraystretch}{.7}     \begin{array}[b]{@{}c@{}} {\scriptscriptstyle (p)} \\ D \end{array}}=0$ [@HenTei:QuaGauSys] and $m >
0$ (one has $m \geq p$ and for $p=0$, $m \geq 1$ because $[{{\renewcommand{\arraystretch}{.7}     \begin{array}[b]{@{}c@{}} {\scriptscriptstyle (0)} \\ \Omega \end{array}}},
{{\renewcommand{\arraystretch}{.7}     \begin{array}[b]{@{}c@{}} {\scriptscriptstyle (0)} \\ \Omega \end{array}}}]$ contains $G_a$ by the first class property).

It should be stressed that the partial derivations $\partial/\partial
G_a$ in(\[sigma\]) are well defined because the functions on which they act depend only on on $G_a$. For an arbitrary function of $q^i,
p_i$, $\partial F / \partial G_a$ would not be well defined even if the constraints $G_a$ are independent (i.e. irreducible) as here. One must specify 