  We show how the homogeneous variational bicomplex provides a useful formalism
for describing a number of properties of single-integral variational problems,
and we introduce a subsequence of one of the rows of the bicomplex which is
locally exact with respect to the variational derivative. We are therefore able
to recover a Lagrangian from a set of equations given as a variationally-closed
differential form. As an example, we show how to recover a first-order
Lagrangian from a suitable set of second-order equations.
