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

Synopsis

• Usage:

  isHolonomic M

  isHolonomic I

• Inputs:
  • M, a module, over the Weyl algebra D
  • I, an ideal, which represents the module M = D/I
• Outputs:
  • a Boolean value

Description

i1 : D = makeWA(QQ[x_1..x_3])

o1 = D

o1 : PolynomialRing, 3 differential variables

i2 : A = matrix{{1,1,1},{0,1,2}}

o2 = | 1 1 1 |
     | 0 1 2 |

              2        3
o2 : Matrix ZZ  <--- ZZ

i3 : b = {3,4}

o3 = {3, 4}

o3 : List

i4 : I = gkz(A,b,D)

                                                               2
o4 = ideal (x dx  + x dx  + x dx  - 3, x dx  + 2x dx  - 4, - dx  + dx dx )
             1  1    2  2    3  3       2  2     3  3          2     1  3

o4 : Ideal of D

i5 : isHolonomic I

o5 = true

See also

• Ddim -- dimension of a D-module
• holonomicRank -- rank of a D-module