Maple procedures for the coupling of angular momenta II. Sum rule evaluation

Abstract
In a previous paper (S. Fritzsche, Comput. Phys. Commun. 103 (1997) 51), we defined data structures to deal with typical expressions from Racah algebra within the framework of Maple. Such expressions arise very frequently in various fields, for instance, by treating composite wave functions and tensor operators in many-particle physics. Often, these Racah expressions are written in terms of Clebsch-Gordan coefficients and Wigner n-j symbols. Our previous set of Maple procedures mainly concern...

Title of program: Racah
Catalogue Id: ADFV_v2_0 [ADHW]

Nature of problem
Computer algebra (CA) is used to evaluate and to simplify typical expressions from Racah algebra which may also include the summation over dummy quantum numbers. A large variety of sum rules is implemented in a set of Maple commands for interactive use.

Versions of this program held in the CPC repository in Mendeley Data
ADFV_v1_0; Racah; 10.1016/S0010-4655(97)00032-5
ADFV_v2_0; Racah; 10.1016/S0010-4655(98)00021-6
ADFV_v3_0; RACAH; 10.1016/S0010-4655(00)00234-4
ADFV_v4_0; RACAH; 10.1016/S0010-4655(01)00218-1
ADFV_v5_0; RACAH; 10.1016/S0010-4655(01)00219-3
ADFV_v6_0; RACAH; 10.1016/S0010-4655(02)00591-X
ADFV_v7_0; RACAH; 10.1016/S0010-4655(03)00227-3
ADFV_v8_0; RACAH; 10.1016/j.cpc.2004.11.003
ADFV_v9_0; RACAH; 10.1016/j.cpc.2005.12.008
ADFV_v10_0; RACAH; 10.1016/j.cpc.2009.06.018

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要
此前我们在一篇论文（S. Fritzsche, 《计算机物理通讯》103卷(1997年)第51页）中，于Maple软件框架内定义了用于处理拉卡代数（Racah algebra）典型表达式的数据结构。这类表达式在诸多领域中频繁出现，例如在多粒子物理领域处理复合波函数与张量算符时。此类拉卡代数表达式通常可通过克莱布希-高登系数（Clebsch-Gordan coefficients）与威格纳n-j符号（Wigner n-j symbols）进行表示。我们此前开发的一套Maple程序主要涉及……

程序名称：Racah
目录编号：ADFV_v2_0 [ADHW]

问题性质
本程序采用计算机代数（Computer Algebra，CA）方法，对拉卡代数的典型表达式进行求值与化简，此类表达式还可包含对哑量子数的求和操作。本套交互式Maple命令集合中集成了大量求和规则。

Mendeley数据平台CPC程序库中的本程序版本
ADFV_v1_0; Racah; 10.1016/S0010-4655(97)00032-5
ADFV_v2_0; Racah; 10.1016/S0010-4655(98)00021-6
ADFV_v3_0; RACAH; 10.1016/S0010-4655(00)00234-4
ADFV_v4_0; RACAH; 10.1016/S0010-4655(01)00218-1
ADFV_v5_0; RACAH; 10.1016/S0010-4655(01)00219-3
ADFV_v6_0; RACAH; 10.1016/S0010-4655(02)00591-X
ADFV_v7_0; RACAH; 10.1016/S0010-4655(03)00227-3
ADFV_v8_0; RACAH; 10.1016/j.cpc.2004.11.003
ADFV_v9_0; RACAH; 10.1016/j.cpc.2005.12.008
ADFV_v10_0; RACAH; 10.1016/j.cpc.2009.06.018

本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2018年）。