Let's say I have a Lie algebra $L$ and an element $x$ in $L$. I need to compute $(\mathrm{ad} \ x)^n(y)$ for several values of $y$ and a particular value of $n$. I thought the best way to do this would be to compute the matrix that represents $M = (\mathrm{ad} \ x)^n$ so that I could just multiply this with whatever.
I can get the matrix of the adjoint action using AdjointMatrix(L, x). This gives me an element of type AlgMatLieElt which makes sense. I can't raise that to the $n$th power, I need to coerce it into a MatrixAlgebra, then enxponentiate it, then coerce it back into a Matrix Lie algebra element form. Fine, call this guy $M$.
But how on earth do I multiply elements of $L$ by $M$? Whether $M$ is in matrix algebra form or Lie algebra form the command M * y gives an error. I have searched the magma handbook but I find that it doesn't do a very good job of collecting information in the location you would expect to find it in. So does anyone know how to do this?