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
Optional inputs:
- Strategy => ...,
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

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.

Ways to use `DintegrationComplex` :

DintegrationComplex(Ideal,List)
DintegrationComplex(Module,List)

DintegrationComplex -- derived integration complex of a D-module

Synopsis

Description

Caveat

See also

Ways to use DintegrationComplex :

Ways to use `DintegrationComplex` :