Combining Cauchy and characteristic codes .1. The vacuum cylindrically symmetric problem

This paper is part of a long term program to develop combined Cauchy and characteristic codes as investigative tools in numerical relativity. We set up the necessary machinery for investigating vacuum cylindrical symmetry with two gravitational degrees of freedom. In particular, we demonstrate the need for a decomposition relative to the translational Killing direction using the technique of Geroch in order to obtain regular compactified equations.