  The algorithm for inverting covariant exterior derivative is provided. It
works for a sufficiently small star-shaped region of a fibered set - a local
subset of a vector bundle and associated vector bundle. The algorithm contains
some constraints that can fail, giving no solution, which is the expected case
for parallel transport equations. These constraints are straightforward to
obtain in the proposed approach. The relation to operational calculus and
operator theory is outlined. The upshot of this paper is to show, using the
linear homotopy operator of the Poincare lemma, that we can solve the covariant
constant and related equations in a geometric and algorithmic way. The
considerations related to the regularity of the solutions are provided.
