The Lie Algebra package LieMath, written in the Mathematica language, constructs the one-turn nonlinear map for a given lattice of optical elements. The method used is a BCH-based map concatenation. Truncated power series algebra (TPSA) techniques have been implemented to compute the Poisson bracket and extract the map faster than when one relies on the symbolic capabilities of Mathematica to operate on truncated multivariate Taylor series. In addition, this makes possible obtaining parameter-dependent numerical maps and optimization of nonlinear parameters

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