Normalization in Riemann tensor polynomial ring

DOI10.1007/s11424-017-6325-zzbMath1402.13024OpenAlexW2771672395MaRDI QIDQ1621171

Jiang Liu

Publication date: 8 November 2018

Published in: Journal of Systems Science and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11424-017-6325-z

zbMATH Keywords

Riemann tensorcanonical formmonoid ringEinstein summation convention\(n\mathrm D\) symbolic computation

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Related Items (2)

An extension of Gröbner basis theory to indexed polynomials without eliminations ⋮ Normalization of indexed differentials by extending Gröbner basis theory

Uses Software

• ATENSOR
• Canon
• Invar
• Riegeom
• xTensor
• MathTensor

Cites Work

• The Canon package: a fast kernel for tensor manipulators
• The Invar tensor package
• The \texttt{Invar} tensor package: differential invariants of Riemann
• Simplification and normalization of indexed differentials involving coordinate transformation
• ATENSOR -- REDUCE program for tensor simplification
• The Riegeom package: Abstract tensor calculation
• An algorithm to simplify tensor expressions
• Review of some classical gravitational superenergy tensors using computational techniques
• Normal forms for tensor polynomials. I. The Riemann tensor
• Algorithmic simplification of tensor expressions
• A complete classification of canonical forms of a class of Riemann tensor indexed expressions and its applications in differential geometry
• GROUP-THEORETIC APPROACH FOR SYMBOLIC TENSOR MANIPULATION

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