Questions about Mathematica's rule-based replacement functionality, including functions such as Rule (->), Replace, ReplaceAll (/.) and ReplaceRepeated (//.).

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Efficient way to substitute and plot

The quatity $R$ is defined by a complicated expression in terms of $a_1,a_2,\ldots,a_n$. Now each $a_i$ is a function of $x$, $a_i(x)$. I would like to know what is the most efficient way to ...
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Efficient way to give symbolic elements symmetry

I have a symbolic expression that represents a set of operators. These operators have quite a bit of symmetry to simplify expressions: ...