VEST: Abstract vector calculus simplification in Mathematica

Abstract We present a new package, VEST (Vector Einstein Summation Tools), that performs abstract vector calculus computations in Mathematica. Through the use of index notation, VEST is able to reduce three-dimensional scalar and vector expressions of a very general type to a well defined standard form. In addition, utilizing properties of the Levi-Civita symbol, the program can derive types of multi-term vector identities that are not recognized by reduction, subsequently applying these to simplify l... Title of program: VEST (Vector Einstein Summation Tools) Catalogue Id: AEQN_v1_0 Nature of problem Large scale vector calculus computations Versions of this program held in the CPC repository in Mendeley Data AEQN_v1_0; VEST (Vector Einstein Summation Tools); 10.1016/j.cpc.2013.08.021 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)### 摘要 本文介绍一款全新的程序包VEST（矢量爱因斯坦求和工具，Vector Einstein Summation Tools），可在Mathematica环境中执行抽象矢量微积分运算。借助指标记法，VEST能够将任意通用类型的三维标量与矢量表达式规约为定义明确的标准形式。此外，通过利用列维-奇维塔符号（Levi-Civita symbol）的性质，该程序可推导出规约过程无法识别的多类多项矢量恒等式，并随后运用这些恒等式对表达式进行简化。 ## 程序名称：VEST（矢量爱因斯坦求和工具，Vector Einstein Summation Tools） 目录编号：AEQN_v1_0 ## 问题本质 大规模矢量微积分运算 ## Mendeley数据中的CPC程序库收录的本程序版本 AEQN_v1_0；VEST（矢量爱因斯坦求和工具，Vector Einstein Summation Tools）；10.1016/j.cpc.2013.08.021 本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2019年）。

搜集汇总

背景与挑战

背景概述

VEST（Vector Einstein Summation Tools）是一个Mathematica包，专门用于抽象向量微积分计算，通过索引符号将三维标量和向量表达式简化到标准形式，并能推导多术语向量恒等式以简化复杂计算。该数据集针对大规模向量微积分计算问题，提供了程序版本和来源信息，适用于科学计算和数学建模领域。