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

Synopsis

Usage:

N = DintegrationAll(M,w), NI = DintegrationAll(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 integration complex, integration classes, etc.

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 : DintegrationAll(I,{1,0})

o3 = HashTable{BFunction => (s)                                                }
               Boundaries => HashTable{0 => | D_2-1 |}
                                       1 => 0
               Cycles => HashTable{0 => | 1 |}
                                   1 => 0
               HomologyModules => HashTable{0 => cokernel | D_2-1 |}
                                            1 => 0
                                                      1                 1
               IntegrateComplex => 0  <-- (QQ[x , D ])  <-- (QQ[x , D ])  <-- 0
                                               2   2             2   2         
                                   -1                                         2
                                          0                 1
                               1      2      1
               VResolution => R  <-- R  <-- R
                                             
                              0      1      2

o3 : HashTable

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 DintegrationAll:

DintegrationAll(Ideal,List)
DintegrationAll(Module,List)

For the programmer

The object DintegrationAll is a method function with options.