pseudotensor, fundamental orienting pseudoscalar, permutation symbol, covariant derivative, gradient

The paper is devoted to the an algebraic algorithm for the systematic reduction of one-point pseudotensors of an arbitrary valency and weight to absolute tensors. The weight of a pseudotensor is assumed to be an integer. The algorithm is based on the transformation of a one-point pseudotensor of an arbitrary valency and weight by the permutation symbols, both covariant and contravariant types. Notions and requisite equations from Algebra and the Analysis of pseudotensors are recalled and discussed. An implementation of covariant differentiation of a one-point pseudotensor field of an arbitrary valency and weight is manifested and derived by the proposed algebraic algorithm of pseudotensor transformation. The definition of the pseudotensor field gradient is introduced and discussed.

Evgenii V. Murashkin, Cand. Sc., PhD, MD, Senior Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences,

101, korp. 1, pr. Vernadskogo, Moscow, 119526, Russian Federation.

Yuri N. Radayev, D. Sc., PhD, MSc, Professor of Continuum Mechanics, Leading Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 101, korp. 1, pr. Vernadskogo, Moscow, 119526, Russian Federation.