7.5.14.0. polSol

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.

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