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polynomialSolutions -- polynomial solutions of a holonomic system



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 Gröbner 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 homomorphisms between holonomic D-modules by Tsai and Walther (2000).

i1 : makeWA(QQ[x])

o1 = QQ[x, dx]

o1 : PolynomialRing, 1 differential variable(s)
i2 : I = ideal(dx^2, (x-1)*dx-1)

o2 = ideal (dx , x*dx - dx - 1)

o2 : Ideal of QQ[x, dx]
i3 : polynomialSolutions I

o3 = {x - 1}

o3 : List

See also

Ways to use polynomialSolutions :

For the programmer

The object polynomialSolutions is a method function with options.