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DintegrationComplex -- derived integration complex of a D-module

Synopsis

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
Outputs:
- N, a hash table
- NI, a hash table
Optional inputs:
- Strategy => ...,

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

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                 
o3 = 0  <-- (QQ [x , D , WeylAlgebra => {x  => D }])  <-- (QQ [x , D ,
                  2   2                   2     2               2   2 
     -1                                                               
            0                                             1
     ------------------------------------------------------------------------
                                1
     WeylAlgebra => {x  => D }])  <-- 0
                      2     2          
                                      2

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)