The polynomial solutions of a holonomic system form a finite-dimensional vector space. There are two algorithms implemented to get these solutions. The first algorithm is based on Groebner deformations and works for ideals
I of PDE's -- see the paper 'Polynomial and rational solutions of a holonomic system' by Oaku-Takayama-Tsai (2000). The second algorithm is based on homological algebra -- see the paper 'Computing homomorphims between holonomic D-modules' by Tsai-Walther (2000).
i1 : W = QQ[x, D, WeylAlgebra=>{x=>D}]
o1 = W
o1 : PolynomialRing
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i2 : I = ideal(D^2, (x-1)*D-1)
2
o2 = ideal (D , x*D - D - 1)
o2 : Ideal of W
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i3 : PolySols I
o3 = {x - 1}
o3 : List
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