  An algorithm for constructing primitive adjoint-invariant functions on a
complex simple Lie algebra is presented. The construction is intrinsic in the
sense that it does not resort to any representation. A primitive invariant
function on the whole Lie algebra is obtained by lifting a coordinate function
on a Kostant slice of the Lie algebra. Such an intrinsic construction of
invariant functions is most useful for the bigger exceptional Lie algebras such
as the E's. The Maple implementation of this algorithm is outlined at the end
and will be applied to these exceptional Lie algebras in a future work.

Representation Theory;Commutative Algebra