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.本数据集配套的学术论文如下： C. F. F. Karney，《论辅助纬度（On auxiliary latitudes）》，刊载于《测量评论（Survey Review）》56(395)，第165-180页（2024年）。 期刊论文：DOI 10.1080/00396265.2023.2217604 预印本：https://arxiv.org/abs/2212.05818 数据集文件如下： auxlat.mac：用于获取级数展开式的Maxima代码，文件内附该代码的使用说明。 auxvals40.mac：采用Maxima语法表示的40阶级数展开式。 auxvals6.m、auxvals16.m及auxvals40.m：分别为6阶、16阶和40阶的级数展开式，以Octave/MATLAB代码形式呈现。其中40阶级数展开式采用浮点数表示，其余则以精确分数形式给出。 AuxLatitude.hpp、AuxLatitude.cpp及example-AuxLatitude.cpp：实现各类辅助纬度之间转换的C++代码，既支持通过级数展开进行转换，也支持直接求解定义方程的方式。