  This paper provides an algebraic framework for the generation of order
conditions for the construction of exponential integrators like splitting and
Magnus-type methods for the numerical solution of evolution equations. The
generation of order conditions is based on an analysis of the structure of the
leading local error term of such an integrator, and on a new algorithm for the
computation of coefficients of words in expressions involving exponentials. As
an application a new 8th order commutator-free Magnus-type integrator involving
only 8 exponentials is derived.
