TaylUR 3, a multivariate arbitrary-order automatic differentiation package for Fortran 95

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018) Abstract This new version of TaylUR is based on a completely new core, which now is able to compute the numerical values of all of a complex-valued function's partial derivatives up to an arbitrary order, including mixed partial derivatives. Title of program: TaylUR Catalogue Id: ADXR_v3_0 Nature of problem Problems that require potentially high orders of partial derivatives with respect to several variables or derivatives of complex-valued functions, such as e.g. momentum or mass expansions of Feynman diagrams in perturbative QFT, and which previous versions of this TaylUR [1,2] cannot handle due to their lack of support for mixed partial derivatives. Versions of this program held in the CPC repository in Mendeley Data ADXR_v1_0; TaylUR; 10.1016/j.cpc.2005.12.016 ADXR_v2_0; TaylUR; 10.1016/j.cpc.2007.03.008 ADXR_v3_0; TaylUR; 10.1016/j.cpc.2009.10.025本程序源自贝尔法斯特女王大学（Queen's University Belfast）馆藏的CPC程序库（1969-2018）。 摘要 本版TaylUR基于全新核心架构，现已可计算复值函数任意阶的全部偏导数数值，包括混合偏导数。 程序标题：TaylUR 目录编号：ADXR_v3_0 问题范畴 本程序适用于需对多变量求取高阶偏导数，或复值函数导数的场景，例如微扰量子场论（perturbative QFT）中费曼图的动量或质量展开；此前版本的TaylUR[1,2]因不支持混合偏导数，无法处理此类问题。 Mendeley数据收录的CPC程序库中本程序的版本如下： ADXR_v1_0; TaylUR; 10.1016/j.cpc.2005.12.016 ADXR_v2_0; TaylUR; 10.1016/j.cpc.2007.03.008 ADXR_v3_0; TaylUR; 10.1016/j.cpc.2009.10.025