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About: About this document DLoc0
Procedure from library dmodapp.lib (see dmodapp_lib).

DLoc0(I, f); I an ideal, f a poly

ring (a Weyl algebra) containing an ideal 'LD0' and a list 'BS'

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

the basering is similar to the output ring of SDLoc procedure

activate the output ring with the setring command. In this ring,
- the ideal LD0 (given as Groebner basis) is the presentation of the
- the list BS contains roots and multiplicities of Bernstein
polynomial of (D/I)_f.

If printlevel =1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.

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