Singular Manual: polSol

| ##### 7.5.14.0. polSol Procedure from library `dmodloc.lib` (see dmodloc_lib). Usage: polSol(I[,w,m]); I ideal, w optional intvec, m optional int Assume: 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. Return: ideal, a basis of the polynomial solutions to the given system of linear PDEs with polynomial coefficients, encoded via I Remarks: If w is given, w should consist of n strictly negative entries. Otherwise and by default, w is set to -1:n. In this case, w is used as weight vector for the computation of a b-function. If m is given, m is assumed to be the minimal integer root of the b-function of I w.r.t. w. Note that this assumption is not checked. Reference: (OTT), Algorithm 2.4 Note: If printlevel=1, progress debug messages will be printed, if printlevel>=2, all the debug messages will be printed. Example:
    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 (2,-3,-2,5)
    tx*(tx+ty+4)-x*(tx+ty+2)*(tx-3),
    ty*(tx+ty+4)-y*(tx+ty+2)*(ty-2),
    (x-y)*Dx*Dy+2*Dx-3*Dy;
    intvec w = -1,-1;
    polSol(I,w);
    ==> _[1]=10*x^3*y^2-30*x^3*y-45*x^2*y^2+24*x^3+144*x^2*y+72*x*y^2-126*x^2-252\
       *x*y-42*y^2+252*x+168*y-210
See also: polSolFiniteRank; ratSol.

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