  The polarization of masers contains information on the magnetic field
strength and direction of the regions they occur in. Many maser polarization
observations have been performed over the last 30 years. However, versatile
maser polarization models that can aide in the interpretation of these
observations are not available. We aim to develop a program suite that can
compute the polarization by a magnetic field of any non-paramagnetic maser
specie at arbitrarily high maser saturation. Furthermore, we aim to investigate
the polarization of masers by non-Zeeman polarizing effects. We aim to present
a general interpretive structure for maser polarization observations. We expand
existing maser polarization theories of non-paramagnetic molecules and
incorporate these in a numerical modeling program suite. We present a modeling
program that CHAracterizes Maser Polarization (CHAMP) that can examine the
polarization of masers of arbitrarily high maser saturation and high angular
momentum. Also, hyperfine multiplicity of the maser-transition can be
incorporated. The user is able to investigate non-Zeeman polarizing mechanisms
such as anisotropic pumping and polarized incident seed radiation. We present
an analysis of the polarization of v = 1 SiO masers and the 22 GHz water maser.
We comment on the underlying polarization mechanisms, and also investigate
non-Zeeman effects. We identify the regimes where different polarizing
mechanisms will be dominant and present the polarization characteristics of the
SiO and water masers. From the results of our calculations, we identify markers
to recognize alternative polarization mechanisms.
