Series expansions for converting between auxiliary latitudes

This data accompanies the paper C. F. F. Karney,On auxiliary latitudes,Survey Review 56(395), 165-180 (2024). Journal article: doi:10.1080/00396265.2023.2217604 Preprint: https://arxiv.org/abs/2212.05818 Files: auxlat.mac: the Maxima code used to obtain the series expansions. Instructions for using this code are included in the file. auxvals40.mac: the 40th-order series in Maxima notation. auxvals6.m, auxvals16.m, and auxvals40.m: the 6th-, 16th-, and 40th-order series as Octave/MATLAB code. The 40th-order series are given as floating-point numbers; the others are as exact fractions. AuxLatitude.hpp, AuxLatitude.cpp, and example-AuxLatitude.cpp: C++ code implementing the conversions between auxiliary latitudes both using the series expansions and with direct evaluation of the defining equations.