An algorithm to simplify tensor expressions

DOI10.1016/S0010-4655(98)00117-9zbMath1009.53013arXivgr-qc/9803023MaRDI QIDQ1807987

Yanyan Li

Publication date: 30 November 1999

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/gr-qc/9803023

zbMATH Keywords

tensorsymmetryalgorithmGröbner basiscanonical formsimplificationcanonicaldummy indicestensor symmetry

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Methods of local Riemannian geometry (53B21) Software, source code, etc. for problems pertaining to differential geometry (53-04)

Related Items (11)

Normalization in Riemann tensor polynomial ring ⋮ \textit{xTras}: a field-theory inspired \textit{xAct} package for Mathematica ⋮ FeynGrav: FeynCalc extension for gravity amplitudes ⋮ FeynGrav 2.0 ⋮ Distance invariant method for normalization of indexed differentials ⋮ New Finsler package ⋮ Cadabra: a field-theory motivated symbolic computer algebra system ⋮ Spinorial geometry, off-shell Killing spinor identities and higher derivative 5D supergravities ⋮ The method of colored graphs for simplifying expressions with indices ⋮ The vectorization expressions of Taylor series multipole-BEM for 3D elasticity problems ⋮ Simplification and normalization of indexed differentials involving coordinate transformation

Uses Software

• ATENSOR
• Maple
• Riegeom
• SHEEP
• MapleTensor
• MACSYMA
• MathTensor
• Ricci

Cites Work

• A general backtrack algorithm for the isomorphism problem of combinatorial objects
• ATENSOR -- REDUCE program for tensor simplification
• Applications of Maple to general relativity
• Enumeration of the order-14 invariants formed from the Riemann tensor
• Normal forms for tensor polynomials. I. The Riemann tensor
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