xTensorDoc.nb

9.8. Mapping at specified positions

We use the package ExpressionManipulation` (written by David Park & Ted Ersek) to have full control on the positions of an expression

Suppose we have an expression like this, which is clearly 0 because U is antisymmetric and S is symmetric:

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Each object in the expression can be identified in a tree-like form by its position. In this case there are four positions at level 1:

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${1} S_bc^ U_ ^abc v_a^ + {2} U_ ^abc v_a^ v_b^ v_c^ + {3} τ_bc^ v_ ^b v_ ^c + {4} -τ_de^ v_ ^d v_ ^e$

We can evaluate a given function at one or several positions:

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In order to map a function over several terms simultaneously we need to make use of the concept of ExtendedPosition (also from the ExpressionManipulation` package) and the new function NewMapAt. See notes for ExtendedPosition and eP.

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We can also localize a given pattern:

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$S_bc^ ({1, 2} U_ ^abc) v_a^ + ({2, 1} U_ ^abc) v_a^ v_b^ v_c^ + τ_bc^ v_ ^b v_ ^c - τ_de^ v_ ^d v_ ^e$

or map a function onto the occurrences of that pattern:

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In case the expression is held, we can use EvaluateAt (also from the package ExpressionManipulation`) instead of MapAt:

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Created by Mathematica (May 16, 2008)