... Differential Algebras and Their Applications∗(Chapter of “Computational Differen tiation: Techniques, Applications, and Tools”,Martin Berz, Christian Bischof, George Corli ss, and Andreas Griewank, ... Hoffst¨atter, and W. Wan,COSY INFINITY and its applications to nonlinear dynamics, in Computational D ifferentia-tion: Techniques,Applications,andTools,M.Berz,C.Bischof,G.Corliss,andA.Griewank,eds., ... [Berz1990a] for Fortran code and w ithin its own language environment, and which is a major vehicle for studies in beam physics.Here and i n many other practi cal applications, the problem of...