An efficient method of computing power expansions of algebraic functions is the method of Kung and Traub and is based on exact arithmetic. This paper shows a numeric approach is both feasible and accurate while also introducing a performance improvement to Kung and Traub's method based on the ramification extent of the expansions. A new method is then described for computing radii of convergence using a series comparison test. Series accuracies are then fitted to a simple log-linear function in their domain of convergence and found to have low variance. Algebraic functions up to degree 50 were analyzed and timed. A consequence of this work provided a simple method of computing the Riemann surface genus and was used as a cycle check-sum. Mathematica ver. 13.2 was used to acquire and analyze the data on a 4.0 GHz quad-core desktop computer.

翻译：计算代数函数幂展开的高效方法是基于精确算术的Kung-Traub方法。本文证明数值方法不仅可行且准确，同时根据展开的分歧程度对Kung-Traub方法引入性能改进。随后描述了一种基于级数比较测试计算收敛半径的新方法。在收敛域内，将级数精度拟合为简单的对数线性函数，发现其具有低方差。对高达50次的代数函数进行了分析与计时。本工作的一项成果提供了计算黎曼曲面亏格的简便方法，并将其用作循环校验。使用Mathematica 13.2版本在4.0 GHz四核台式机上获取并分析数据。