DintegrationComplex -- derived integration complex of a D-module

Synopsis

• Usage:

  N = DintegrationComplex(M,w), NI = DintegrationComplex(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

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 : DintegrationComplex(I,{1,0})

                        1                 1
o3 = 0  <-- (QQ[x , D ])  <-- (QQ[x , D ])  <-- 0
                 2   2             2   2         
     -1                                         2
            0                 1

o3 : ChainComplex

Caveat

See also

• Dintegration -- integration modules of a D-module
• DintegrationAll -- integration modules of a D-module (extended version)
• Drestriction -- restriction modules of a D-module