I = decompose(L)
This gives the kernel of the Lie homomorphism from [$L,L$] to the direct sum of [$L_i,L_i$], where $L_i$ is the Lie subalgebra generated by the $i$th subset in the input for the holonomy Lie algebra $L$; see holonomyLocal. The ideal is generated by the basis elements in degree 3 of the form (x y z), where not all x,y,z belong to the same $L_i$. The ideal is zero if and only if $L$ decomposes into the direct sum of the local Lie subalgebras $L_i$ in degrees $\ge \ 2$.



