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7.7.4.0. DLoc0
Procedure from library dmodapp.lib (see dmodapp_lib).
- Usage:
- DLoc0(I, F); I an ideal, F a poly
- Return:
- ring
- Purpose:
- compute the presentation of the localization of D/I w.r.t. f^s,
where D is a Weyl Algebra, based on the output of procedure SDLoc
- Assume:
- the basering is similar to the output ring of SDLoc procedure
- Note:
- activate this ring with the
setring command. In this ring,
the ideal LD0 (in Groebner basis) is the presentation of the localization
the list BS contains roots and multiplicities of Bernstein polynomial of (D/I)_f.
- Display:
- If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.
Example:
| LIB "dmodapp.lib";
ring r = 0,(x,y,Dx,Dy),dp;
def R = Weyl(); setring R; // Weyl algebra in variables x,y,Dx,Dy
poly F = x2-y3;
ideal I = (y^3 - x^2)*Dx - 2*x, (y^3 - x^2)*Dy + 3*y^2; // I = Dx*F, Dy*F;
// moreover I is not holonomic, since its dimension is not 2 = 4/2
gkdim(I); // 3
==> 3
def W = SDLoc(I,F); setring W; // creates ideal LD in W = R[s]
def U = DLoc0(LD, x2-y3); setring U; // compute in R
LD0; // Groebner basis of the presentation of localization
==> LD0[1]=3*x*Dx+2*y*Dy+12
==> LD0[2]=3*y^2*Dx+2*x*Dy
==> LD0[3]=y^3*Dy-x^2*Dy+6*y^2
BS; // description of b-function for localization
==> [1]:
==> _[1]=0
==> _[2]=-1/6
==> _[3]=1/6
==> [2]:
==> 1,1,1
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