  The paper displays calculations of linear systems as explained by Dr. Guido
Sterbini. We also show a simple nonlinear calculation involving a rotation
followed by an octupole kick. Some analytical calculations are compared to the
Truncated Power Series Algebra (TPSA) results. The examples use the library PTC
which is in MAD-X of CERN and BMAD of Cornell (see Ref. [1]).
