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Dmodules :: PolySols

PolySols -- polynomial solutions of a holonomic system

Synopsis

Description

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

See also

Ways to use PolySols :