isDecomposable -- test if an arrangement is decomposable

Synopsis

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

Description

An arrangement is said to be decomposable if the derived subalgebra of its holonomy Lie algebra is a direct sum of the derived subalgebras of free Lie algebras, indexed by the rank-2 flats of the arrangement. At the time of writing, it is not known if the answer depends on the characteristic of the coefficient ring.
 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

Ways to use isDecomposable :

• "isDecomposable(CentralArrangement)"
• "isDecomposable(CentralArrangement,Ring)"

For the programmer

The object isDecomposable is .