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

Synopsis

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
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
                                                                            
               IntegrateComplex => 0  <-- (QQ [x , D , WeylAlgebra => {x  =>
                                                2   2                   2   
                                   -1                                       
                                          0                                 
                               1      2      1
               VResolution => R  <-- R  <-- R
                                             
                              0      1      2
     ------------------------------------------------------------------------
                                                               }






          1                                             1
     D }])  <-- (QQ [x , D , WeylAlgebra => {x  => D }])  <-- 0
      2               2   2                   2     2          
                                                              2
                1

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.

See also

Ways to use DintegrationAll :