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Physics[SubstituteTensorIndices] - perform substitution of covariant/contravariant tensor indices in tensorial expressions
Calling Sequence
SubstituteTensorIndices(mu = .., ~nu = .., ... expression)
Parameters
expression
-
any algebraic tensorial expression typically having some free and some repeated indices
mu = ... , ~nu = .., ...
the substitution equations, can be a sequence, or a set or list of them
evaluatetensor = ...
optional - can be true (default) or false, to indicate whether to evaluate the tensors after substituting on them
evaluateexpression = ...
optional - can be true or false (default), to indicate whether to evaluate expression after substituting the indices in its tensors
covariantandcontravariant = ...
optional - can be true (default) or false, to indicate whether to substitute both covariant and contravariant indices when only one of them is given as substitution equation
Description
The SubstituteTensorIndices substitutes indices in tensors. Nowhere else are the indices substituted, and the substitution can be performed in a covariant index, the corresponding contravariant one, or in both.
The tensors where indices are substituted are re-evaluated after substitution; this re-evaluation can optionally be suppressed giving the argument evaluatetensor = false. The expression where these re-evaluated tensors are introduce is by default not re-evaluated; you can change that passing the optional argument evaluateexpression = true.
To check and determine the free and repeated indices of an expression use Check.
Compatibility
The Physics[SubstituteTensorIndices] command was introduced in Maple 16.
For more information on Maple 16 changes, see Updates in Maple 16.
Examples
Define a couple of arbitrary spacetime tensors for exploration purposes
Enter, for example, this tensorial expression
To check the repeated and free indices in an expression use Check
So (3) has no free indices. Substitute now : the standard subs command will only substitute the covariant
Consequently, the resulting expression is not equivalent to (3): it now has free indices
To substitute both covariant and contravariant repeated indices obtaining an expression equivalent to original one use
See Also
Check, Define, g_, Physics, Physics conventions, Physics examples
References
Landau, L.D., and Lifshitz, E.M. The Classical Theory of Fields, Course of Theoretical Physics Volume 2, fourth revised English edition. Elsevier, 1975.
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