Precision experiments, such as the search for a deuteron electric dipole moment using storage rings like COSY, demand for an understanding of the spin dynamics with unprecedented accuracy. In such an enterprise, numerical predictions play a crucial role for the development and later application of spin-tracking algorithms. Various measurement concepts involving polarization effects induced by an rf Wien filter and static solenoids in COSY are discussed. The matrix formalism, applied here, deals solely with spin rotations on the closed orbit of the machine, and is intended to provide numerical guidance for the development of beam and spin-tracking codes for rings that employ realistic descriptions of the electric and magnetic bending and focusing elements, solenoids, etc., and a realistically modeled rf Wien filter.