The TensorArray receives a tensorial expression having n free indices, typically involving sums and products, and returns a corresponding n dimensional Array, which can be indexed as a single object to return the values of the tensorial expression for given values of its free indices.

To check and determine the free and repeated indices of an expression use Check.

The returned Array is constructed taking into account the covariant and contravariant character of each free index in expression. To compute the values of expression you index this array giving values between 1 and the spacetime dimension to the indices.

By default, in the returned result, summation is explicitly performed over all the repeated indices found in expression, taking into account the covariant/contravariant character of each index. To avoid performing this summation and keep repeated indices not summed pass the optional argument performsumoverrepeatedindices = false.

By default, the Array is constructed without simplifying its components; to have them simplified indicate the simplifier on the right-hand-side of the optional argument simplifier = .... A frequently convenient simplification is achieved with simplifier = `simplify/size`@simplify.

The Physics[TensorArray] command was introduced in Maple 16.

For more information on Maple 16 changes, see Updates in Maple 16.

Landau, L.D., and Lifshitz, E.M. The Classical Theory of Fields, Course of Theoretical Physics Volume 2, fourth revised English edition. Elsevier, 1975.