Singular

7.5.5.0. SDLoc

Usage:

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

Return:

ring (basering extended by a new variable) containing an ideal 'LD'

Purpose:

compute a generic presentation of the localization of D/I w.r.t. f^s

Assume:

the basering D is a Weyl algebra over a field of characteristic 0

Note:

Activate this ring with the setring command. In this ring,
the ideal LD (given as Groebner basis) is the presentation of the
localization.

Display:

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(); // Weyl algebra on the variables x,y,Dx,Dy
setring R;
poly F = x2-y3;
ideal I = Dx*F, Dy*F;
// note, that I is not holonomic, since it's dimension is not 2
gkdim(I);  // 3, while dim R = 4
==> 3
def W = SDLoc(I,F);
setring W; // = R[s], where s is a new variable
LD;        // Groebner basis of s-parametric presentation
==> LD[1]=3*x*Dx*s+2*y*Dy*s-6*s^2+6*s
==> LD[2]=3*y^2*Dx*s+2*x*Dy*s
==> LD[3]=y^3*Dy-x^2*Dy-3*y^2*s+3*y^2
==> LD[4]=y^3*Dx-x^2*Dx+2*x*s-2*x