A LieElement written in the usual way has output of normal form. If the element is defined by the "formal" operators, then the output may be of non-normal form and in this case the normal form is obtained using normalFormLie.
i1 : L = lieAlgebra({a,b,c}) o1 = L o1 : LieAlgebra |
i2 : x = a b c - 3 c b a +(1/3) b a c o2 = - (4/3)(b c a) - 2 (c b a) o2 : L |
i3 : y = a@b@c/3@c@b@a++(1/3)@b@a@c o3 = (a b c) - 3 (c b a) + (1/3)(b a c) o3 : L |
i4 : normalFormLie y o4 = - (4/3)(b c a) - 2 (c b a) o4 : L |