# DlocalizeMap -- localization map from a D-module to its localization

## Synopsis

• Usage:
DlocalizeMap(M,f), DlocalizeMap(I,f)
• Inputs:
• M, , over the Weyl algebra D
• I, an ideal, which represents the module M = D/I
• f, , a polynomial
• Optional inputs:
• Strategy => ..., default value OTW, strategy for computing a localization of a D-module
• Outputs:
• , which represents the natural map from M to M_f = M[f^{-1}]

## Description

A supplementary function for Dlocalize that computes the localization map.
 i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}] o1 = W o1 : PolynomialRing, 2 differential variables i2 : M = W^1/(ideal(x*Dx+1, Dy)) o2 = cokernel | xDx+1 Dy | 1 o2 : W-module, quotient of W i3 : f = x^2-y^3 3 2 o3 = - y + x o3 : W i4 : DlocalizeMap(M, f) o4 = | y6-2x2y3+x4 | o4 : Matrix