  The issue of computing (co)homology generators of a cell complex is gaining a
pivotal role in various branches of science. While this issue can be rigorously
solved in polynomial time, it is still overly demanding for large scale
problems. Drawing inspiration from low-frequency electrodynamics, this paper
presents a physics inspired algorithm for first cohomology group computations
on three-dimensional complexes. The algorithm is general and exhibits orders of
magnitude speed up with respect to competing ones, allowing to handle problems
not addressable before. In particular, when generators are employed in the
physical modeling of magneto-quasistatic problems, this algorithm solves one of
the most long-lasting problems in low-frequency computational electromagnetics.
In this case, the effectiveness of the algorithm and its ease of implementation
may be even improved by introducing the novel concept of \textit{lazy
cohomology generators}.
