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 => ..., default value Schreyer,
• Outputs:
  • Ni, a hash table
  • N, a hash table
  • NIi, 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 : 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

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