Softwares to determine semi-simple types of Lie algebras generated over $mathbb{R}$ or $mathbb{C}$ by a set of matrices

I wish to determine the type of a Lie algebra generated over $mathbb{R}$ or $mathbb{C}$ by a set of square matrices with irrational elements. For example,

begin{align}
n^+ =
begin{pmatrix}
0 & -frac{1}{sqrt{2}} & 0 & 1 \
0 & 0 & -frac{1}{sqrt{2}} & 0 \
0 & 0 & 0 & 0 \
0 & 0 & frac{1}{sqrt{3}} & 0
end{pmatrix}, quad
n^- =
begin{pmatrix}
0 & 0 & 0 & 0 \
frac{1}{sqrt{2}} & 0 & 0 & 0 \
0 & frac{1}{sqrt{2}} & 0 & 1 \
frac{1}{sqrt{3}} & 0 & 0 & 0
end{pmatrix}, quad
n^3 =
begin{pmatrix}
frac{1}{sqrt{2}} & 0 & 0 & 0 \
0 & 0 & 0 & 1 \
0 & 0 & -frac{1}{sqrt{2}} & 0 \
0 & -frac{1}{sqrt{3}} & 0 & 0
end{pmatrix}.
end{align}

I’ve been using GAP and it is quite good at determining the type of Lie algebras over $mathbb{Q}$, which seems to work fine when all the matrix elements are rational numbers. However, when the matrices contain irrational numbers, if I still work with Lie algebras over $mathbb{Q}$, I would get a larger Lie algebra, and in the above example, I got 8 copies of $A_1$. On the other hand, If I work with Lie algebras over cyclotomic numbers, the function SemiSimpleType would break down. Therefore I wish to know:

Is there a way of doing this with GAP? If not, are there any other softwares which can do this?