rationalFunctionSolutions I
rationalFunctionSolutions(I,f)
rationalFunctionSolutions(I,f,w)
rationalFunctionSolutions(I,ff)
rationalFunctionSolutions(I,ff,w)
The rational solutions of a holonomic system form a finitedimensional vector space. The only possibilities for the poles of a rational solution are the codimension one components of the singular locus. An algorithm to compute rational solutions is based on Gröbner deformations and works for ideals $I$ of PDE's  see the paper Polynomial and rational solutions of a holonomic system by Oaku, Takayama and Tsai (2000).



The most efficient method to find rational solutions of a system of differential equations is to find the singular locus, then try to find its irreducible factors. With these, call rationalFunctionSolutions(I, ff, w), where w should be generic enough so that the polynomialSolutions routine will not complain of a nongeneric weight vector.
The object rationalFunctionSolutions is a method function.