$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)

摘要
我们已将 Mathematica 函数扩展至 N 维：广义函数 $Apart 可将 Vx* 中的任意线性相关元素分解为不可约元素。Vx* 中的元素可视作涉及环动量的相应传播子，该分解对于使用 Fire 和 Reduze 等软件包进行环计算时尤为有用，这些软件包已实现分部积分（IBP）恒等式和洛伦兹不变性（LI）恒等式...

程序名称：$Apart
目录编号：AEMK_v1_0

问题性质
在微扰量子场论中计算物理过程的截面，传统方法涉及通过费曼图生成幅度，并执行维度的规整化环积分 [1]。在解析层面上对表达式进行简化，其中关键部分是将这些环积分缩减为少量标准积分。这一步骤可以在张量积分的幅度级别进行，或者在约化之后...

Mendeley 数据库中 CPC 仓库持有的本程序版本
AEMK_v1_0; $Apart; 10.1016/j.cpc.2012.03.025
AEMK_v2_0; APart 2.0; 10.1016/j.cpc.2015.09.012

本程序已从贝尔法斯特女王大学（1969-2018）的 CPC 程序库中导入。