Singular Manual: rightNFWeyl

| ##### 7.5.14.0. rightNFWeyl Procedure from library `dmodloc.lib` (see dmodloc_lib). Usage: rightNFWeyl(id,k); id ideal or poly, k int Assume: The basering is the n-th Weyl algebra 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). Return: same type as id, the right normal form of id with respect to the principal right ideal generated by the k-th variable Note: No Groebner basis computation is used. Example:
    LIB "dmodloc.lib";
    ring r = 0,(x,y,Dx,Dy),dp;
    def W = Weyl();
    setring W;
    ideal I = x^3*Dx^3, y^2*Dy^2, x*Dy, y*Dx;
    rightNFWeyl(I,1); // right NF wrt principal right ideal x*W
    ==> _[1]=0
    ==> _[2]=y^2*Dy^2
    ==> _[3]=0
    ==> _[4]=y*Dx
    rightNFWeyl(I,3); // right NF wrt principal right ideal Dx*W
    ==> _[1]=-6
    ==> _[2]=y^2*Dy^2
    ==> _[3]=x*Dy
    ==> _[4]=0
    rightNFWeyl(I,2); // right NF wrt principal right ideal y*W
    ==> _[1]=x^3*Dx^3
    ==> _[2]=0
    ==> _[3]=x*Dy
    ==> _[4]=0
    rightNFWeyl(I,4); // right NF wrt principal right ideal Dy*W
    ==> _[1]=x^3*Dx^3
    ==> _[2]=2
    ==> _[3]=0
    ==> _[4]=y*Dx
    poly p = x*Dx+1;
    rightNFWeyl(p,1); // right NF wrt principal right ideal x*W
    ==> 1

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