In 1963 [Ann. of Math. {\bf 78}, 267-288], Gerstenhaber invented a
\emph{comp(osition)} calculus in the Hochschild complex of an associative
algebra. In this paper, the first steps of the Gerstenhaber theory are exposed
in an abstract (comp system) setting. In particular, as in the Hochschild
complex, a graded Lie algebra and a pre-coboundary operator can be associated
to every comp system. A derivation deviation of the pre-coboundary operator
over the total composition is calculated in two ways, (the long) one of which
is essentially new and can be seen as an example and elaboration of the
auxiliary variables method proposed by Gerstenhaber in the early days of the
comp calculus.Comment: 18 pages, AMSLaTe
