Differential algebra-a new tool

An overview of the theory and implementation of the differential algebraic method is presented. The method allows a very straightforward computation of Taylor maps of beamlines. Contrary to older techniques, the method is not restricted to low order and allows the study of an arbitrary number of variables, including system parameters. The resulting Taylor maps offer a variety of useful applications, including fast short-term tracking, the computation of generating functions which can be used for symplectic tracking, and the direct computation of tuneshifts, smear, and approximate invariants.<>