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

## Synopsis

• Usage:
N = DintegrationAll(M,w), NI = DintegrationAll(I,w)
• Inputs:
• M, , 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,
• NI,

## 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.