  We give a gauge description of the adiabatic charge pumping in closed
systems, both in Abelian and non-Abelian processes, and by means of asymptotic
Wilson loops in a suitable parameter manifold. Our geometric formulation
provides new insights into this issue, and a very simple algorithm for
numerical computations. Indeed, as we show first, discretized
Berry--Wilczeck--Zee holonomies are easy to implement. Finally, we study
non-Abelian pumping in a solvable four-state model, already used in several
contexts, to demonstrate the relevance of our approach.
