Algorithmic simplification of tensor expressions
Algorithmic simplification of tensor expressions
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DOI：
10.1088/0305-4470/32/44/313
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发表时间：
1999-11
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影响因子：
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通讯作者：
R. Portugal
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文献类型：
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作者：
R. Portugal
我们提出了简化服从一般对称性的张量表达式的有效算法。我们定义了单张量的标准形，并证明了求一般张量表达式的标准形的问题归结为求单张量的标准形。为了进一步提高效率，考虑了特殊的对称性。我们还给出了解决Riemann张量循环对称性的算法。利用这些算法，可以简化一般的黎曼张量多项式。
We present efficient algorithms for simplifying tensor expressions that obey generic symmetries. We define the canonical form of a single tensor and we show that the problem of finding the canonical form of a generic tensor expression reduces to finding the canonical form of single tensors. Special symmetries are considered in order to push the efficiency further. We also present algorithms to address the cyclic symmetry of the Riemann tensor. With these algorithms it is possible to simplify generic Riemann tensor polynomials.