- Usage:
`N = Drestriction(M,w), NI = Drestriction(I,w), Ni = Drestriction(i,M,w),``NIi = Drestriction(i,I,w)`

- Outputs:
`Ni`, a module, the i-th derived integration module of*M*with respect to the weight vector*w*`N`, a hash table, contains entries of the form`i=>Ni``NIi`, a module, the i-th derived integration module of*D/I*with respect to the weight vector*w*`NI`, a hash table, contains entries of the form`i=>NIi`

The derived restriction modules of a D-module M are the derived inverse images in the sense of algebraic geometry but in the category of D-modules. This routine computes restrictions to coordinate subspaces, where the subspace is determined by the strictly positive entries of the weight vector*w*, e.g., *{x_i = 0 : w_i > 0}* if *D = ***C***<x_1,...,x_n,d_1,...,d_n>*. The input weight vector should be a list of *n* numbers to induce the weight *(-w,w)* on *D*.

The algorithm used appears in the paper 'Algorithims for D-modules' by Oaku-Takayama(1999). The method is to compute an adapted resolution with respect to the weight vector w and use the b-function with respect to w to truncate the resolution.

i1 : R = QQ[x_1,x_2,D_1,D_2,WeylAlgebra=>{x_1=>D_1,x_2=>D_2}] o1 = R o1 : PolynomialRing |

i2 : I = ideal(x_1, D_2-1) o2 = ideal (x , D - 1) 1 2 o2 : Ideal of R |

i3 : Drestriction(I,{1,0}) o3 = HashTable{0 => 0 } 1 => cokernel | D_2-1 | o3 : HashTable |

The module *M* should be specializable to the subspace. This is true for holonomic modules.The weight vector *w* should be a list of *n* numbers if *M* is a module over the *n*-th Weyl algebra.

- DrestrictionAll -- restriction modules of a D-module (extended version)
- DrestrictionClasses -- restriction classes of a D-module
- DrestrictionComplex -- derived restriction complex of a D-module
- DrestrictionIdeal -- restriction ideal of a D-module
- Dresolution -- resolution of a D-module
- Dintegration -- integration modules of a D-module

- Drestriction(Ideal,List)
- Drestriction(Module,List)
- Drestriction(ZZ,Ideal,List)
- Drestriction(ZZ,Module,List)