A flexible-variable truncated power series algebra in Zlib

Zlib is a numerical library for truncated power series algebra (TPSA) and Lie algebra for application to nonlinear analysis of single particle dynamics. The first version was developed in 1990 with the use of the one-step index pointers (OSIP's). The OSIP's form the Zlib nerve that offers optimal computation and allow order grading as well as flexible initialization of the global number of variables for the TPSA. While the OSIP's are still kept for minimum index passing to achieve efficient computation, Zlib has been upgraded to allow flexible and gradable local number of variables in each C++ object of the truncated power series class. Possible applications using Zlib are discussed.