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About: About this document ratSol
Procedure from library dmodloc.lib (see dmodloc_lib).

ratSol(I); I ideal

The basering is the n-th Weyl algebra W over a field of characteristic 0 and for all 1<=i<=n the identity
var(i+n)*var(i)=var(i)*var(i+1)+1 holds, i.e. the sequence of variables is given by x(1),...,x(n),D(1),...,D(n), where D(i) is the differential operator belonging to x(i).
Moreover, assume that I is holonomic.

module, a basis of the rational solutions to the given system of linear PDEs with polynomial coefficients, encoded via I Note that each entry has two components, the first one standing for the enumerator, the second one for the denominator.

Reference: (OTT), Algorithm 3.10

If printlevel=1, progress debug messages will be printed, if printlevel>=2, all the debug messages will be printed.

LIB "dmodloc.lib";
ring r = 0,(x,y,Dx,Dy),dp;
def W = Weyl();
setring W;
poly tx,ty = x*Dx, y*Dy;
ideal I =      // Appel F1 with parameters (3,-1,1,1) is a solution
module M = ratSol(I);
// We obtain a basis of the rational solutions to I represented by a
// module / matrix with two rows.
// Each column of the matrix represents a rational function, where
// the first row correspond to the enumerator and the second row to
// the denominator.
==> x-y,              x,
==> y^4-3*y^3+3*y^2-y,y 
See also: polSol; polSolFiniteRank.