next | previous | forward | backward | up | top | index | toc | Macaulay2 website
HyperplaneArrangements :: isDecomposable

isDecomposable -- test if an arrangement is decomposable

Synopsis

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 :

For the programmer

The object isDecomposable is a method function.