Automatically separate blocks by space in mathmode

Question

I have a document with equations containing many mathematically not strictly necessary brackets. These brackets are customary in order to simplify the identification of certain blocks of the equations. However, they also bring a lot of noise into the document. I was considering to replace the brackets with a spaces around these blocks. In order to play around with this idea I want to define a macro that defines something like a new math atom that ensures that there is a space whenever two of these new atoms are next to each other or next to a mathord atom. However, when this new atom is next to a mathrel, mathbin or another of the usual math atoms it should just behave like a mathord.

\documentclass{article}
\begin{document}
The $abc$ and $def$ are distinct blocks within the equations.
They are highlighted using brackets.
\[y = x (abc)(def) z\]
\[y = (abc) x + (def) xz\]

I would like to automatically highlight them with spaces using a macro.
The outcome should look similar to this.
\[y = x \;\, abc \;\, def \;\, z\]
\[y = abc \;\, x + def \;\, xz\]
\end{document}

Answer 1

EDIT

By more testing (even after adding extra double braces), the answer was not correct when:

• The macro is followed by another similar macro
• The macro is followed by another operator (+, -, ...)

In both cases an extra thin space is added.

---

Original Answer

You can use \operatorname in the definition of your macro, instead of spaces \, \; ,... since the former has a better control for inter spacing when two successive macros of this type are used, or when encountering another operator (+, -, =, etc).

\documentclass{article}
\usepackage{amsmath}
\newcommand*{\distinctblock}[1]{{\operatorname\relax {#1} \operatorname\relax}}
%
\begin{document}
%
%
The $abc$ and $def$ are distinct blocks within the equations.
They are highlighted using \textbf{brackets}.
\[y = x (abc)(def) z\]
\[y = (abc) x + (def) xz\]

Highlighted using the custom command \textbf{distinctblock}

\[y = x \distinctblock{abc} \distinctblock{def} z\]
\[y = \distinctblock{abc} x + \distinctblock{def} xz\]
%
\end{document}