  Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are
required in almost every branch of numerical physics. Often the exponent under
consideration has to be split into more than two operators $H=\sum_k A_k$, for
instance as local gates on quantum computers. We demonstrate how highly
optimised schemes originally derived for exactly two operators $A_{1,2}$ can be
applied to such generic Suzuki-Trotter decompositions, providing a formal proof
of correctness as well as numerical evidence of efficiency. A comprehensive
review of existing symmetric decomposition schemes up to order $n\le4$ is
presented and complemented by a number of novel schemes, including both real
and complex coefficients. We derive the theoretically most efficient unitary
and non-unitary 4th order decompositions. The list is augmented by several
exceptionally efficient schemes of higher order $n\le8$. Furthermore we show
how Taylor expansions can be used on classical devices to reach machine
precision at a computational effort at which state of the art Trotterization
schemes do not surpass a relative precision of $10^{-4}$. Finally, a short and
easily understandable summary explains how to choose the optimal decomposition
in any given scenario.
