Riemann Tensor Polynomial Canonicalization by Graph Algebra Extension
Riemann Tensor Polynomial Canonicalization by Graph Algebra Extension
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DOI：
10.1145/3087604.3087625
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发表时间：
2017-01
期刊：
影响因子：
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通讯作者：
Hongbo Li;Zhang Li;Y. Li
中科院分区：
文献类型：
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作者：
Hongbo Li;Zhang Li;Y. Li
张量表达式简化是计算机代数中一个“古老”的课题，其代表是黎曼张量多项式的规范化。实际上，对于单项规范化存在快速算法，但对于多项规范化则没有。针对多项难问题，本文建立了图代数的可拓理论，并在此基础上提出了一种黎曼张量多项式的规范化算法。
Tensor expression simplification is an "ancient" topic in computer algebra, a representative of which is the canonicalization of Riemann tensor polynomials. Practically fast algorithms exist for monoterm canonicalization, but not for multiterm canonicalization. Targeting the multiterm difficulty, in this paper we establish the extension theory of graph algebra, and propose a canonicalization algorithm for Riemann tensor polynomials based on this theory.