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The aim of this paper is to present an automatic and efficient algorithm to find cohomology generators suitable for 2-D eddy-current problems formulated by means of complementary formulations. The algorithm is general, straightforward to implement, exhibits a linear worst-case computational complexity and produces optimal representatives of generators. By optimal we mean the representatives that minimize in practical cases the fill-in of the system of equations matrix and guarantee that the current flowing in each conductor is in one-to-one correspondence with a generator. As a numerical example, the complementary formulations are used to compute the frequency-dependent per-unit-length impedance in integrated circuits.