ATENSOR - REDUCE program for tensor simplification

ATENSOR - REDUCE program for tensor simplification
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DOI：
10.1016/0010-4655(96)00060-4
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发表时间：
1996-07
期刊：
ArXiv
影响因子：
--
通讯作者：
V. Ilyin;A. Kryukov
V. Ilyin;A. Kryukov
中科院分区：
其他
文献类型：
--
作者：
V. Ilyin;A. Kryukov

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本文提出了一个REDUCE程序，用于简化被认为是形式索引对象的张量表达式。该算法是基于考虑张量表达式作为向量在一定的线性空间。这个线性空间是由相应张量表达式的群代数的所有元素构成的。这种方法使我们能够统一地简化具有对称性、求和（虚）指标和多项恒等式的张量表达式。张量表达式的规范元素是用这个线性空间的基本向量来定义的。该算法的主要限制是线性空间的维数等于N！，其中N是张量表达式的一些指标。该程序使用REDUCE作为用户界面。
The paper presents a REDUCE program for the simplification of tensor expressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vectors in some linear space. This linear space is formed by all the elements of the group algebra of the corresponding tensor expression. Such approach permits us to simplify the tensor expressions possessing symmetry properties, summation (dummy) indices and multiterm identities by unify manner. The canonical element for the tensor expression is defined in terms of the basic vectors of this linear space. The main restriction of the algorithm is the dimension of the linear space that is equal to N!, where N is a number of indices of the tensor expression. The program uses REDUCE as user interface.