Singular Manual: dmodAction

| ##### 7.5.14.0. dmodAction Procedure from library `dmodloc.lib` (see dmodloc_lib). 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. Example:
    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

User manual for Singular version 4.4.1, 2025, generated by texi2html.