Precision experiments, such as the search for a deuteron electric dipole moments using a 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 textit{solely} with spin rotations textit{on the closed orbit} of the machine, and is intended to provide textit{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.
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