ABSTRACT
This chapter shows how the techniques which are rigorous and good for large machine can be modified to give rise to small machine expressions. As Feynman said about the whole of physics and as accelerator physicists did in the discussion of the global theory, they must try to motivate the description of the layout from a small set of quintessential properties. In an object-oriented computer implementation, the layout is created in a class in which a generic description of space-time is possible. The laboratory sits in a Lorentz frame whose origin can be anywhere. The action of the Euclidean group on a dynamical element of the layout is more complex because the variable measuring actual time is now a dependent variable. However, when a regular time description is used in Cartesian coordinates, the action of the Euclidean group on a transfer map from time t1 to t1 is trivially obtained by a similarity transformation.
