DrestrictionAll -- restriction modules of a D-module (extended version)

Usage:

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

An extension of Drestriction that computes the restriction complex, restriction 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, 2 differential variable(s)

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

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

o2 : Ideal of R

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

o3 = HashTable{BFunction => (s + 1)                                           }
               Boundaries => HashTable{0 => 0        }
                                       1 => | D_2-1 |
                                            | 0     |
               Cycles => HashTable{0 => 0    }
                                   1 => | 1 |
                                        | 0 |
               HomologyModules => HashTable{0 => 0                 }
                                            1 => cokernel | D_2-1 |
                                                           1                 1
               RestrictComplex => 0  <-- 0 <-- (QQ[x , D ])  <-- (QQ[x , D ])
                                                    2   2             2   2
                                  -1     0                        
                                               1                 2
                               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 DrestrictionAll:

DrestrictionAll(Ideal,List)
DrestrictionAll(Module,List)

For the programmer

The object DrestrictionAll is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/BernsteinSato/DOC/Drestriction.m2:185:0.

DrestrictionAll -- restriction modules of a D-module (extended version)

Description

Caveat

See also

Ways to use DrestrictionAll:

For the programmer