In this report we derive all solutions of the minimal partial k-realization
problem in the form of a polynomial matrix fraction.
All solutions are parametrized by the minimal number of parameters,
i.e. a different choice for the parameter values gives a different rational
As an intermediate result we get an alternative basis for S(n,α)_k
based on the (shifted) auxiliary and solution vectors at level n.
An example is shown to clarify the theory.