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, a module, 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 => ...,
Outputs:
- Ni, a hash table
- N, a hash table
- NIi, a hash table
- NI, a hash table

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

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)

DintegrationClasses -- integration classes of a D-module

Synopsis

Description

Caveat

See also

Ways to use DintegrationClasses :

Ways to use `DintegrationClasses` :