# Singular

##### 7.7.5.0. DLoc
Procedure from library dmodapp.lib (see dmodapp_lib).

Usage:
DLoc(I, f); I an ideal, f a poly

Return:
list of ideal and list

Assume:
the basering is a Weyl algebra

Purpose:
compute the presentation of the localization of D/I w.r.t. f^s

Note:
In the output list L,
- L[1] is an ideal (given as Groebner basis), the presentation of the
localization,
- L[2] is a list containing roots with 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; // I is not holonomic, since its dimension is not 4/2=2 gkdim(I); ==> 3 list L = DLoc(I, x2-y3); L[1]; // localized module (R/I)_f is isomorphic to R/LD0 ==> _[1]=3*x*Dx+2*y*Dy+12 ==> _[2]=3*y^2*Dx+2*x*Dy ==> _[3]=y^3*Dy-x^2*Dy+6*y^2 L[2]; // description of b-function for localization ==> [1]: ==> _[1]=0 ==> _[2]=-1/6 ==> _[3]=1/6 ==> [2]: ==> 1,1,1