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7.7.19.0. Dlocalization
Procedure from library dmodloc.lib (see dmodloc_lib).

Usage:
Dlocalization(I,f[,k,e]); I ideal, f poly, k,e optional ints

Assume:
The basering is the n-th Weyl algebra over a field of characteristic 0 and for all 1<=i<=n the identity
var(i+n)*var(i)=var(i)*var(i+1)+1 holds, i.e. the sequence of variables is given by x(1),...,x(n),D(1),...,D(n), where D(i) is the differential operator belonging to x(i).
Further, assume that f does not contain any D(i) and that I is holonomic on K^n\V(f).

Return:
ideal or list, computes an ideal J such that D/J is isomorphic to D/I localized at f as D-modules.
If k<>0, a list consisting of J and an integer m is returned, such that f^m represents the natural map from D/I to D/J. Otherwise (and by default), only the ideal J is returned.

Remarks:
It is known that a localization at f of a holonomic D-module is again a holonomic D-module.
Reference: (OTW)

Note:
If e<>0, std is used for Groebner basis computations, otherwise (and by default) slimgb is used.
If printlevel=1, progress debug messages will be printed, if printlevel>=2, all the debug messages will be printed.

Example:
 
See also: DLoc; DLoc0; SDLoc.


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