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7.5.13.0. 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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