RatExt M, RatExt I; RatExt(M,f), RatExt(I,f);
RatExt(i,M), RatExt(i,I); RatExt(i,M,f), RatExt(i,I,f)
The algorithm used appears in the paper 'Polynomial and rational solutions of holonomic systems' by Oaku-Takayama-Tsai (2000). The method is to combine isomorphisms of Bjork and Kashiwara with the restriction algorithm.
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The object RatExt is a method function with options.