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Dmodules :: isHolonomic

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

Synopsis

Description

Let $D$ be the Weyl algebra with generators $x_1,\dots,x_n$ and $\partial_1,\dots,\partial_n$. over a field. A $D$-module is holonomic if it has dimension $n$. For more details see [SST, Section 1.4].

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

Ways to use isHolonomic :

For the programmer

The object isHolonomic is a method function.