- Usage:
`PolySols I, PolySols M, PolySols(I,w), PolySols(M,w)`

- Optional inputs:
- Alg => ..., -- algorithm for finding polynomial solutions

- Outputs:
- a list, a basis of the polynomial solutions of
*I*(or of D-homomorhpisms between*M*and the polynomial ring) using*w*for Groebner deformations

- a list, a basis of the polynomial solutions of

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 |

i2 : I = ideal(D^2, (x-1)*D-1) 2 o2 = ideal (D , x*D - D - 1) o2 : Ideal of W |

i3 : PolySols I o3 = {x - 1} o3 : List |

- RatSols -- rational solutions of a holonomic system
- Dintegration -- integration modules of a D-module

- PolySols(Ideal)
- PolySols(Ideal,List)
- PolySols(Module)
- PolySols(Module,List)