Although the PDG can be done in a CAS (ie Mathematica), it won't translate to other CASes without having associated Godel indices.
Symbols can be composed of other symbols. Example: $E$ and $\vec{E}$, $\partial$ and $\frac{\partial}{\partial t}$
Symbols can be operators, ie $\frac{\partial}{\partial t}$
Operators, ie $+$, can act on symbols
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