Singular

7.7.22.0. dmodAction

Usage:

dmodAction(id,f[,v]); id ideal or poly, f poly, v optional intvec

Assume:

If v is not given, 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).
Otherwise, v is assumed to specify positions of variables, which form a Weyl algebra as a subalgebra of the basering:
If size(v) equals 2*n, then bracket(var(v[i]),var(v[j])) must equal 1 if and only if j equals i+n, and 0 otherwise, for all 1<=i,j<=n.
Further, assume that f does not contain any D(i).

Return:

same type as id, the result of the natural D-module action of id on f

Note:

The assumptions made are not checked.

LIB "dmodloc.lib";
ring r = 0,(x,y,z),dp;
poly f = x^2*z - y^3;
def A = annPoly(f);
setring A;
poly f = imap(r,f);
dmodAction(LD,f);
==> _[1]=0
==> _[2]=0
==> _[3]=0
==> _[4]=0
==> _[5]=0
==> _[6]=0
==> _[7]=0
==> _[8]=0
==> _[9]=0
==> _[10]=0
==> _[11]=0
==> _[12]=0
==> _[13]=0
poly P = y*Dy+3*z*Dz-3;
dmodAction(P,f);
==> 0
dmodAction(P[1],f);
==> -3*y^3