# Singular

##### 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 ```