The Method of Colored Graphs for Simplifying Expressions with Indices

Computer algebra is increasingly used in research and applied computations. An example is tensor computations or, in a wide sense, simplification of expressions containing indices. In this paper, the method of colored graphs designed for simplifying abstract expressions containing indices is develop...

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Bibliographic Details
Published in:Programming and computer software 2021, Vol.47 (1), p.25-28
Main Authors: Shpiz, G. B., Kryukov, A.P.
Format: Article
Language:English
Subjects:
Algebra
Artificial Intelligence
Canonical forms
Computer algebra
Computer Science
Graphs
Mathematical analysis
Operating Systems
Quantum field theory
Software Engineering
Software Engineering/Programming and Operating Systems
Tensors
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Summary:Computer algebra is increasingly used in research and applied computations. An example is tensor computations or, in a wide sense, simplification of expressions containing indices. In this paper, the method of colored graphs designed for simplifying abstract expressions containing indices is developed for the case when the indices are of different types. An example of such indices are upper and lower indices in tensor expressions. The proposed approach significantly reduces the number of combinations to be considered when the canonical form of the expression is sought; as a result, the computations are drastically accelerated.
ISSN:0361-7688
1608-3261
DOI:10.1134/S0361768821010102