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7.5.5.0. DLoc0
Procedure from library dmodapp.lib (see dmodapp_lib).
- Usage:
- DLoc0(I, f); I an ideal, f a poly
- Return:
- ring (a Weyl algebra) containing an ideal 'LD0' and a list 'BS'
- 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 the output ring with the
setring command. In this ring,
- the ideal LD0 (given as 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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