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 Gr\"obner 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 second algorithm is based on homological algebra - see the paper Computing homomorphims between holonomic D-modules by Tsai and Walther (2000).
i1 : makeWA(QQ[x]) o1 = QQ[x, dx] o1 : PolynomialRing, 1 differential variables |
i2 : I = ideal(dx^2, (x-1)*dx-1) 2 o2 = ideal (dx , x*dx - dx - 1) o2 : Ideal of QQ[x, dx] |
i3 : PolySols I o3 = {x - 1} o3 : List |
The object PolySols is a method function with options.