Macros that keep notation honest

Every paper has notation that repeats: the real numbers, an expectation operator, an absolute value with properly sized bars. If you type \mathbb{R} in forty places and your advisor later prefers \mathbf{R}, you have forty edits to make and you will miss one. A macro turns that notation into a single named command, defined once. Change the definition and the whole document follows. That is what “keeping notation honest” means: the source can no longer drift out of sync with itself.

Defining commands with newcommand

\newcommand{\R}{\mathbb{R}}
\newcommand{\E}[1]{\mathbb{E}\left[#1\right]}
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}

The first definition is the simplest kind: \R is now pure shorthand, and typing \R anywhere produces \mathbb{R}.

The second form takes an argument. The [1] after the name declares that \E accepts one argument, and #1 marks where that argument lands in the expansion. So \E{X} becomes \mathbb{E}\left[X\right]. Notice what the definition buys beyond brevity: the \left[ and \right] pair makes the brackets grow to fit whatever is inside, so \E{\frac{X}{n}} gets tall brackets automatically. The \abs macro plays the same trick with \lvert and \rvert, the correct pair of vertical bars for absolute value. You can declare up to nine arguments and refer to them as #1 through #9.

If a command already exists, \newcommand refuses to redefine it and stops with an error, which protects you from silently breaking something. To deliberately replace an existing command, use \renewcommand instead.

The modern interface

Modern LaTeX:

\NewDocumentCommand{\citepair}{mm}{\cite{#1}, \cite{#2}}

\NewDocumentCommand is built into current LaTeX and uses an argument specification string instead of a count. Here mm means two mandatory arguments, so \citepair{knuth84}{lamport94} cites both keys. The specification language goes further than \newcommand can: o declares an optional argument in square brackets, s detects a star variant, and O{default} gives an optional argument a default value. For anything beyond simple substitution, reach for this interface.

Share the definitions

Keep a macros.sty shared across chapters. Put your definitions in that one file, load it with \usepackage{macros} from each document, and every chapter of a thesis, plus the slides and the paper version, all agree on notation. When a collaborator joins, they read one short file to learn your conventions instead of reverse-engineering them from the text. This pairs naturally with a multi-file setup.

A tip on naming: give macros meaningful names like \abs or \norm rather than appearance-based names like \bigbars. The name should say what the notation means, so the definition is free to change how it looks. And resist defining a macro for something you use twice; the payoff starts around the third use.