The Invar tensor package
The Invar tensor package
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DOI：
10.1016/j.cpc.2007.05.015
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发表时间：
2007-04
期刊：
影响因子：
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通讯作者：
J. Martin-Garcia;R. Portugal;L. Manssur
中科院分区：
文献类型：
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作者：
J. Martin-Garcia;R. Portugal;L. Manssur
介绍了INVAR程序包，这是一个由四维度量相容连接的黎曼张量形成的通用标量多项式表达式的快速操纵器。该软件包可以在几秒钟内最大限度地简化任何包含多达七个黎曼张量的张量积的多项式。它已在数学和Maple代数系统中实现。计划摘要：计划标题：因瓦张量包目录识别符：ADZK_V1_0计划摘要URL:http://cpc.cs.qub.ac.uk/summaries/ADZK_v1_0.html计划可从：北爱尔兰贝尔法斯特女王大学CPC计划图书馆获得许可条款：标准CPC许可证，http://cpc.cs.qub.ac.uk/licence/licence.html编号。分布式程序中的行数，包括测试数据等：136 240 No.分布式程序中的字节数，包括测试数据等：2数学711Maple923分布格式：tar.gz编程语言： 和Maple计算机：任何运行 版本5.0到5.2或Maple版本9和10操作系统的计算机：LINUX，Unix，Windows XP RAM：30Mb字长：或32位分类：5外部例程：数学版本需要Xtensor和xPerm包。这些可以在http://metric.iem.csic.es/Martin-Garcia/xAct问题的本质：张量表达式的操作和简化上免费获得。特别注意简化由四维度量相容流形上的黎曼张量形成的标量多项式。求解方法：计算群论的算法，用服从排列对称的张量来简化表达式。黎曼张量的标量不变量的合子表。限制：目前的版本没有完全解决减少具有自由指数的Riemann张量的微分不变量或单项式的问题。运行时间：不到一秒，就独立不变量而言，完全减少7次Riemann张量的一个单项。
The Invar package is introduced, a fast manipulator of generic scalar polynomial expressions formed from the Riemann tensor of a four-dimensional metric-compatible connection. The package can maximally simplify any polynomial containing tensor products of up to seven Riemann tensors within seconds. It has been implemented both in Mathematica and Maple algebraic systems. PROGRAM SUMMARY: Program title:Invar Tensor Package Catalogue identifier:ADZK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZK_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 136 240 No. of bytes in distributed program, including test data, etc.:2 711 923 Distribution format:tar.gz Programming language:Mathematica and Maple Computer:Any computer running Mathematica versions 5.0 to 5.2 or Maple versions 9 and 10 Operating system:Linux, Unix, Windows XP RAM:30 Mb Word size:64 or 32 bits Classification:5 External routines:The Mathematica version requires the xTensor and xPerm packages. These are freely available at http://metric.iem.csic.es/Martin-Garcia/xAct Nature of problem:Manipulation and simplification of tensor expressions. Special attention on simplifying scalar polynomial expressions formed from the Riemann tensor on a four-dimensional metric-compatible manifold. Solution method:Algorithms of computational group theory to simplify expressions with tensors that obey permutation symmetries. Tables of syzygies of the scalar invariants of the Riemann tensor. Restrictions:The present versions do not fully address the problem of reducing differential invariants or monomials of the Riemann tensor with free indices. Running time:Less than a second to fully reduce a monomial of the Riemann tensor of degree 7 in terms of independent invariants.