Best practice to handle math Brackets and Parentheses

Question

I was wondering if there is already available a short reply to the best practices about using brackets in math mode. For instance, when should I use (, instead of any of the following: \left(,\left(.,\big(,\bigg(,\Big(,\Bigg(

In specific equations you may want to manually adjust the spacing and when dealing with split equations in more than one line. I have already read a couple of questions with different cases.

Is there a big picture to it?

What about when you want to define math commands and operators, for instance, the definition of the norm brackets. The size of the brackets depends on the context, but what if the context forces the splitting of the equation lines?

\newcommand{\norm}[1]{\left\lVert#1\right\rVert}

Answer 1

One time you definitely need to use explicit sizes, such as \biggl(, is when you need to break a parenthesized expression across lines. When I don’t need to do this, I often find the paired delimiters in mathtools very convenient and easy to read. They’d let me write \parens[\bigg]{...} instead of \biggl( ... \biggr} or \parens*{...} instead of \left( ... \right).

Beyond that, it comes down to personal preference. DEK himself gave some examples in the TeXBook of how he felt you shouldn’t let parentheses visually overshadow the expression just so they extend past some tiny superscript or divider. Personally, I think this is an example of what not to do:

\documentclass{article}
\usepackage{unicode-math}

\setmathfont{Asana Math}

\begin{document}
\[ f\left(x\right) \cdot f\left(y\right)
\]
\end{document}

And here is one where I would explicitly change the size:

\documentclass{article}

\begin{document}
\[ g\bigl( f(x) \cdot f(y) \bigr)
\]
\end{document}