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7.5.20.0. WeylClosure1
Procedure from library dmodloc.lib (see dmodloc_lib).
- Usage:
- WeylClosure1(L); L a poly
- Assume:
- The basering is the first Weyl algebra D=K<x,d|dx=xd+1> over a field
K of characteristic 0.
- Return:
- ideal, the Weyl closure of the principal left ideal generated by L
- Remarks:
- The Weyl closure of a left ideal I in the Weyl algebra D is defined
to be the intersection of I regarded as left ideal in the rational
Weyl algebra K(x)<d> with the polynomial Weyl algebra D.
Reference: (Tsa), Algorithm 1.2.4
- Note:
- If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.
Example:
| | LIB "dmodloc.lib";
ring r = 0,(x,Dx),dp;
def W = Weyl();
setring W;
poly L = (x^3+2)*Dx-3*x^2;
WeylClosure1(L);
==> _[1]=x^3*Dx-3*x^2+2*Dx
==> _[2]=x^2*Dx^2-2*x*Dx
==> _[3]=x^2*Dx+Dx^2-3*x
==> _[4]=x*Dx^2-2*Dx
L = (x^4-4*x^3+3*x^2)*Dx^2+(-6*x^3+20*x^2-12*x)*Dx+(12*x^2-32*x+12);
WeylClosure1(L);
==> _[1]=x^4*Dx^2-4*x^3*Dx^2-6*x^3*Dx+3*x^2*Dx^2+20*x^2*Dx+12*x^2-12*x*Dx-32*\
x+12
==> _[2]=x^2*Dx^3-21/10*x^2*Dx^2+3/10*x*Dx^3-6/5*x*Dx^2+63/5*x*Dx-3/5*Dx^2-12\
/5*Dx-126/5
==> _[3]=x^3*Dx^2-43/10*x^2*Dx^2+9/10*x*Dx^3-6*x^2*Dx+12/5*x*Dx^2+109/5*x*Dx-\
9/5*Dx^2+12*x-36/5*Dx-178/5
==> _[4]=x^3*Dx^3-48/5*x^2*Dx^2+9/5*x*Dx^3+24/5*x*Dx^2+198/5*x*Dx-18/5*Dx^2-7\
2/5*Dx-336/5
==> _[5]=x^3*Dx^4-4*x^2*Dx^4+2*x^2*Dx^3+3*x*Dx^4-69/10*x^2*Dx^2+67/10*x*Dx^3-\
24/5*x*Dx^2-3*Dx^3+207/5*x*Dx-27/5*Dx^2-18/5*Dx-414/5
==> _[6]=x^3*Dx^6+8/3*x^3*Dx^5-4*x^2*Dx^6-2/3*x^2*Dx^5+3*x*Dx^6+16*x^2*Dx^4-2\
0*x*Dx^5-92/3*x*Dx^4+12*Dx^5+126/5*x^2*Dx^2-258/5*x*Dx^3-168/5*x*Dx^2+92/\
3*Dx^3-756/5*x*Dx+356/5*Dx^2+504/5*Dx+1512/5
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See also:
WeylClosure.
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