- Usage:
`Dlocalize(M,f), Dlocalize(I,f)`

- Inputs:
`M`, a module, over the Weyl algebra*D*`I`, an ideal, which represents the module*M = D/I*`f`, a ring element, a polynomial

- Optional inputs:
- Strategy => ..., -- strategy for computing a localization of a D-module

- Outputs:
- a module, the localized module M
_{f}= M[f^{-1}] as a D-module

- a module, the localized module M

One of the nice things about D-modules is that if a finitely generated D-module is specializable along *f*, then it's localization with respect to *f* is also finitely generated. For instance, this is true for all holonomic D-modules.

There are two different algorithms for localization implemented. The first appears in the paper 'A localization algorithm for D-modules' by Oaku-Takayama-Walther (1999). The second is due to Oaku and appears in the paper 'Algorithmic computation of local cohomology modules and the cohomological dimension of algebraic varieties' by Walther(1999)

i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}] o1 = W o1 : PolynomialRing |

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 : Mf = Dlocalize(M, f) o4 = cokernel | 3xDx+2yDy+15 y3Dy-x2Dy+6y2 | 1 o4 : W-module, quotient of W |

- DlocalizeAll -- localization of a D-module (extended version)
- DlocalizeMap -- localization map from a D-module to its localization
- AnnFs -- the annihilating ideal of f^s
- Dintegration -- integration modules of a D-module

- Dlocalize(Ideal,RingElement)
- Dlocalize(Module,RingElement)