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Dmodules :: RatSols

RatSols -- rational solutions of a holonomic system



The rational solutions of a holonomic system form a finite-dimensional vector space. The only possibilities for the poles of a rational solution are the codimension one components of the singular locus. An algorithm to compute rational solutions 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).
i1 : W = QQ[x, D, WeylAlgebra=>{x=>D}]

o1 = W

o1 : PolynomialRing
i2 : I = ideal((x+1)*D+5)

o2 = ideal(x*D + D + 5)

o2 : Ideal of W
i3 : RatSols I

o3 = {-------------------------------}
       5     4      3      2
      x  + 5x  + 10x  + 10x  + 5x + 1

o3 : List


The most efficient method to find rational solutions is to find the singular locus, then try to find its irreducible factors. With these, call RatSols(I, ff, w), where w should be generic enough so that the PolySols routine will not complain of a non-generic weight vector.

See also

Ways to use RatSols :