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

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.