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7.5.5.0. 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