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# DintegrationComplex -- derived integration complex of a D-module

- Usage:
    `N = DintegrationComplex(M,w), NI = DintegrationComplex(I,w)`
- Inputs:
  - M, a module, over the Weyl algebra D
  - I, an ideal, which represents the module M = D/I
  - w, a list, a weight vector
- Optional inputs:
  - Strategy => ..., default value Schreyer,
- Outputs:
  - N, a hash table
  - NI, a hash table

## Description

An extension of Dintegration that computes the derived integration complex.

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

    o1 = R

    o1 : PolynomialRing, 2 differential variable(s)

    i2 : I = ideal(x_1, D_2-1)

    o2 = ideal (x , D  - 1)
                 1   2

    o2 : Ideal of R

    i3 : DintegrationComplex(I,{1,0})

                            1                 1
    o3 = 0  <-- (QQ[x , D ])  <-- (QQ[x , D ])  <-- 0
                     2   2             2   2
         -1                                         2
                0                 1

    o3 : ChainComplex

## Caveat

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 nth Weyl algebra.

## See also

- Dintegration -- integration modules of a D-module
- DintegrationAll -- integration modules of a D-module (extended version)
- Drestriction -- restriction modules of a D-module

## Ways to use DintegrationComplex:

- `DintegrationComplex(Ideal,List)`
- `DintegrationComplex(Module,List)`

## For the programmer

The object DintegrationComplex is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/BernsteinSato/DOC/Drestriction.m2:425:0.