  This paper study the planar semi-quasi homogeneous polynomial differential
systems (short for PSQHPDS), which can be regard as a generalization of
semi-homogeneous and of quasi-homogeneous systems. By using the algebraic
skills, several important properties of PSQHPDS are derived and are employed to
establish an algorithm for obtaining all the explicit expressions of PSQHPDS
with a given degree. Afterward, we apply this algorithm to research the center
problem of quadratic and cubic PSQHPDS. It is proved that the quadratic one
hasn't center, and, that the cubic one has center if and only if it can be
written as $\dot{x}=x^2-y^3, \dot{y}=x$ after a linear transformation of
coordinate and a rescaling of time.
