Memory usage of new commands requiring several intermediate commands

Question

The following command

\newcommand{\PDef}{\mathcal{P}_{\operatorname{Def}}}

can be defined, alternatively, by iterating several new commands:

\newcommand{\CP}{\mathcal{P}}
\newcommand{\PDef}{\CP_{\operatorname{Def}}}

or

\newcommand{\CP}{\mathcal{P}}
\DeclareMathOperator{\Def}{Def} % command provided by amsmath
\newcommand{\PDef}{\CP_{\Def}}

QUESTION: What is the best course of action for defining new commands requiring several intermediate commands (new or existent), in terms of memory usage?

Answer 1

At the time LaTeX2e was developed the number of command names was critical, and essentially the limit in PC implementations of the time determined how big LaTex2e could be and why packages like amsmath, graphicx, array,... were kept as packages and not part of the format, there simply was not space.

Looking at the end of a log file of a recent document I made

 24639 multiletter control sequences out of 65536+600000

so despite the format having preloaded expl3 and the document having loaded several packages there are still hundreds of thousands of slots left in the csname hash table.

For comparson the TeXBook shows the same log entry of a log of TeX while producing that book

 1172 multiletter control sequences out of 2500

So my latex document used almost exactly ten times the maximum number of command names that were available in that early tex.

So basically now structure your code for maintenance don't worry about the memory consumption unless you are defining thousands of commands (as might happen if defining some new Unicode support for example).

If using pdftex or xetex (not luatex) the actual memory consumption does not depend on the macros defined, the relevant arrays are fixed size depending on the texmf.cnf configuration and the memory for the definitions is allocated whether or not you use it.

Answer 2

The impact in terms of memory is negligible. What might change is execution time.

If I run LaTeX on

\documentclass{article}
\usepackage{amsmath}
\usepackage{l3benchmark}

\newcommand{\Def}{\mathrm{Def}}
\newcommand{\CP}{\mathcal{P}}

\newcommand{\PDefA}{\mathcal{P}_{\mathrm{Def}}}
\newcommand{\PDefB}{\CP_{\mathrm{Def}}}
\newcommand{\PDefC}{\CP_{\Def}}

\begin{document}

\ExplSyntaxOn
\benchmark:n { \sbox0{$\PDefA$} }
\benchmark:n { \sbox0{$\PDefB$} }
\benchmark:n { \sbox0{$\PDefC$} }
\ExplSyntaxOff

\end{document}

the output is

3.81e-6 seconds (25.2 ops)
3.83e-6 seconds (25.4 ops)
3.84e-6 seconds (25.5 ops)

The difference is in the range of tens of nanoseconds.

Note. I changed \operatorname into \mathrm because the former is the wrong choice for the job. See What's the difference between \mathrm and \operatorname?

Even if \PDefC is a tad slower than the other two, it should be preferred, because you may have to use \CP in other situations and having a single place where it is defined reduces the risks of inconsistency.