Drestriction -- restriction modules of a D-module

Synopsis

• Usage:

  N = Drestriction(M,w), NI = Drestriction(I,w), Ni = Drestriction(i,M,w),
  NIi = Drestriction(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 module, the i-th derived integration module of M with respect to the weight vector w
  • N, a hash table, contains entries of the form i=>Ni
  • NIi, a module, the i-th derived integration module of D/I with respect to the weight vector w
  • NI, a hash table, contains entries of the form i=>NIi

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

i2 : I = ideal(x_1, D_2-1) 

o2 = ideal (x , D  - 1)
             1   2

o2 : Ideal of R

i3 : Drestriction(I,{1,0})

o3 = HashTable{0 => 0                 }
               1 => cokernel | D_2-1 |

o3 : HashTable

Caveat

See also

• DrestrictionAll -- restriction modules of a D-module (extended version)
• DrestrictionClasses -- restriction classes of a D-module
• DrestrictionComplex -- derived restriction complex of a D-module
• DrestrictionIdeal -- restriction ideal of a D-module
• Dresolution -- resolution of a D-module
• Dintegration -- integration modules of a D-module