$Apart: A generalized Mathematica Apart function

Abstract We have generalized the Mathematica function Apart from 1 to N dimensions: the generalized function $Apart can decompose any linear dependent elements in Vx* to irreducible ones. The elements in Vx* can be viewed as the corresponding propagators which involve loop momenta, and the decomposition will be useful when one tries to perform loop calculations using packages such as Fire and Reduze, which have implemented the integration by parts (IBP) identities and Lorentz invariance (LI) identitie... Title of program: $Apart Catalogue Id: AEMK_v1_0 Nature of problem The traditional method of computing cross sections for a physical process in perturbative quantum field theory involves generating the amplitudes via Feynman diagrams and performing the dimensionally regularized loop integrals [1]. Simplifications of the expressions are performed at the analytical level, there an essential part is the reduction of these loop integrals to a small number of standard integrals. This step can be performed at the amplitude level for tensor integrals or, after contrac ... Versions of this program held in the CPC repository in Mendeley Data AEMK_v1_0; $Apart; 10.1016/j.cpc.2012.03.025 AEMK_v2_0; APart 2.0; 10.1016/j.cpc.2015.09.012 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)