makeCyclic -- finds a cyclic generator of a D-module

Synopsis

• Usage:

  makeCyclic M

• Inputs:
  • M, a matrix, that specifies a map such that coker M is a holonomic D-module
• Outputs:
  • H, a hash table, where H.Generator is a cyclic generator and H.AnnG is the annihilator ideal of this generator

Description

i1 : makeWA(QQ[x])

o1 = QQ[x, dx]

o1 : PolynomialRing, 1 differential variables

i2 : M = matrix {{dx,0,0},{0,dx,0},{0,0,dx}} -- coker M = QQ[x]^3

o2 = | dx 0  0  |
     | 0  dx 0  |
     | 0  0  dx |

                       3                 3
o2 : Matrix (QQ[x, dx])  <--- (QQ[x, dx])

i3 : h = makeCyclic M

                               3
o3 = HashTable{AnnG => ideal dx   }
               Generator => | x2 |
                            | x  |
                            | 1  |

o3 : HashTable

Caveat

See also

• isHolonomic -- determines whether a D-module (or ideal in Weyl algebra) is holonomic