  For an adjoint action of a Lie group G (or its subgroup) on Lie algebra
Lie(G) we suggest a method for construction of invariants. The method is easy
in implementation and may shed the light on algebraical independence of
invariants. The main idea is to extent automorphisms of the Cartan subalgebra
to automorphisms of the whole Lie algebra Lie(G). Corresponding matrices in a
linear space V=Lie(G) define a Reynolds operator "gathering" invariants of
torus T in G into special polynomials. A condition for a linear combination of
polynomials to be G-invariant is equivalent to the existence of a solution for
a certain system of linear equations on the coefficients in the combination.
  As an example we consider the adjoint action of the Lie group SL(3) (and its
subgroup SL(2)) on the Lie algebra sl(3).
