isDecomposable -- test if an arrangement is decomposable

Synopsis

• Usage:

  isDecomposable(A) or isDecomposable(A,k)

• Inputs:
  • A, a central hyperplane arrangement, a hyperplane arrangement
  • k, a ring, an optional coefficient ring, by default the coefficient ring of the arrangement
• Outputs:
  • a Boolean value, whether or not the arrangement decomposes in the sense of Papadima and Suciu [Comment. Helv. 2006]

Description

i1 : X3 = arrangement "X3"

o1 = {x , x , x , x  + x , x  + x , x  + x }
       1   2   3   1    2   1    3   2    3

o1 : Hyperplane Arrangement 

i2 : isDecomposable X3

o2 = true

i3 : isDecomposable(X3,ZZ/5)

o3 = true

i4 : isDecomposable typeA(3)

o4 = false