# DintegrationClasses -- integration classes of a D-module

## Synopsis

• Usage:
N = DintegrationClasses(M,w), NI = DintegrationClasses(I,w), Ni = DintegrationClasses(i,M,w),
NIi = DintegrationClasses(i,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
• i, an integer, nonnegative
• Optional inputs:
• Strategy => ..., default value Schreyer,
• Outputs:
• Ni,
• N,
• NIi,
• NI,

## Description

An extension of Dintegration that computes the explicit cohomology classes of a 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 variables i2 : I = ideal(x_1, D_2-1) o2 = ideal (x , D - 1) 1 2 o2 : Ideal of R i3 : DintegrationClasses(I,{1,0}) o3 = HashTable{Boundaries => HashTable{0 => | D_2-1 |}} 1 => 0 Cycles => HashTable{0 => | 1 |} 1 => 0 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 DintegrationClasses :

• "DintegrationClasses(Ideal,List)"
• "DintegrationClasses(Module,List)"
• "DintegrationClasses(ZZ,Ideal,List)"
• "DintegrationClasses(ZZ,Module,List)"

## For the programmer

The object DintegrationClasses is .