Relations in $L$ are elements in ambient(L). When a quotient Lie algebra Q=L/I is constructed, where $I$ is a list, then the elements in $I$ must be of type $L$, but the program converts the relations so that they have type ambient(L) instead. This may be seen by looking at ideal(Q). If $I$ is of type LieIdeal, then the value of the expression ambient(Q) is L, and the value of the expression ideal(Q) is I.
i1 : M = lieAlgebra{a,b,c}
o1 = M
o1 : LieAlgebra
|
i2 : L = M/{a b}
o2 = L
o2 : LieAlgebra
|
i3 : a c o3 = - (c a) o3 : L |
i4 : Q = L/{a c}
o4 = Q
o4 : LieAlgebra
|
i5 : ideal(Q)
o5 = { - (b a), - (c a)}
o5 : List
|
i6 : class\oo
o6 = {M, M}
o6 : List
|
i7 : f=map(Q,L) o7 = f o7 : LieAlgebraMap |
i8 : I = kernel f o8 = I o8 : LieIdeal |
i9 : R = L/I o9 = R o9 : LieAlgebra |
i10 : ambient R o10 = L o10 : LieAlgebra |
i11 : ideal R o11 = I o11 : LieIdeal |