If both $A$ and $B$ are instances of LieIdeal, then $S$ is of type LieIdeal. If both $A$ and $B$ are instances of LieSubAlgebra but not both of LieIdeal, then $S$ is of type LieSubAlgebra. Otherwise, $S$ is of type LieSubSpace.
i1 : L = lieAlgebra{a,b,c}
o1 = L
o1 : LieAlgebra
|
i2 : A=lieIdeal{a}
o2 = A
o2 : FGLieIdeal
|
i3 : B=lieIdeal{b}
o3 = B
o3 : FGLieIdeal
|
i4 : S=A@B
o4 = S
o4 : LieIdeal
|
i5 : basis(3,S)
o5 = {(a b a), (b b a), (c b a), (b c a)}
o5 : List
|
i6 : T=A+B
o6 = T
o6 : FGLieIdeal
|
i7 : dims(1,3,L/T)
o7 = {1, 0, 0}
o7 : List
|
i8 : dims(1,5,L/A@B)
o8 = {3, 2, 4, 6, 12}
o8 : List
|
i9 : dims(1,5,L/A++L/B)
o9 = {4, 2, 4, 6, 12}
o9 : List
|