  To follow up on the results of [1], we propose a computationally efficient
explicit cyclic decomposition of the maximal tori in the groups $SL_n(q)$ and
$SU_n(q)$ and their projective images. We also derive some corollaries to
simplify practical calculation of the maximal tori. The result is based on a
generic cyclic decomposition of a finite abelian group which might also be of
interest.
