  We present an equation generator algorithm that utilizes second-quantized
operators in normal order with respect to a correlated or non-correlated
reference and the corresponding Wick theorem. The algorithm proposed here,
written with \textsc{mathematica}, enables the generation of non-redundant
strings of second-quantized operators that, after classification, are directly
assigned to intermediate quantities used to construct the coupled-cluster (CC)
effective Hamiltonian. We demonstrate the capabilities of the algorithm by
computing the CC amplitude equations and various blocks of the
equation-of-motion CC effective Hamiltonian. A comprehensive description of
this four-step algorithm is provided alongside concrete examples.
