How to create glossary entries for custom notation with arguments?

Question

I'm using the latex glossaries package, and trying to make it do something which it doesn't seem to want to do. Maybe I'm doing it all wrong???

In my thesis I'm defining lots of math notation which I'm using throughout the paper. I'd like the glossary at the end of my paper to list all the notation I've defined, with definition and page and section reference to where it is defined in the paper. If I create a glossary entry, then I have to do so before the \begin{document} and use \gls at the definition site. However the \gls, which is intended for words, doesn't work so with with notation such as the following example.

\newcommand{\powerset}[1]{\mathbb{P}(#1)}

In the document I have a

\begin{definition}
  ...
\end{definition}

or

\begin{notation}
  ...
\end{notation}

Where I define this notation in terms of how it is used.

\begin{notation}
  By $\powerset{U}$ we denote the power set of $U$, \ie the set of subsets of
  $U$.  Consequently we may take $V\subseteq \powerset{U}$ to mean that $V$ is a set
  of subsets, each begin a subset of $U$.
\end{notation}

How should I be doing this to be glossary compatible? What should the content (and name) of the newglossaryentry be? And how should I use \gls at the usage site? Or should I be using glossaries at all?

It seems what I'd really like to have is sort of a \footnote{...} capability, which rather than putting its content at the bottom of the page, instead puts its content into the glossary, and includes the page and section number. That way the text of the glossary entry would be right next to the definition in the body of the document and I could more easily keep them sync if one needs to change.

Answer 1

If you always want the symbol displayed as \powerset{U} then you can use:

\documentclass{article}

\usepackage{amsfonts}
\usepackage{glossaries-extra}

\newcommand{\powerset}[1]{\mathbb{P}(#1)}

\newglossaryentry{powset}% label
{
  name={\ensuremath{\powerset{U}}},% default display
  description={power set},% description
  category=symbol% category label
} 

\begin{document}
By $\gls{powset}$ we denote the power set of $U$, i.e.\ the set of subsets of
 $U$.  Consequently we may take $V\subseteq \gls{powset}$ to mean that $V$ is a set
of subsets, each begin a subset of $U$.

\printunsrtglossary[title={Symbols}]     
\end{document}

This produces:

If you want hyperlinks then just include hyperref before glossaries (or glossaries-extra in this case).

\documentclass{article}

\usepackage{amsfonts}
\usepackage{hyperref}
\usepackage{glossaries-extra}

\newcommand{\powerset}[1]{\mathbb{P}(#1)}

\newglossaryentry{powset}% label
{
  name={\ensuremath{\powerset{U}}},% default display
  description={power set},% description
  category=symbol% category label
}

\begin{document}
By $\gls{powset}$ we denote the power set of $U$, i.e.\ the set of subsets of
 $U$.  Consequently we may take $V\subseteq \gls{powset}$ to mean that $V$ is a set
of subsets, each begin a subset of $U$.

\printunsrtglossary[title={Symbols}]
\end{document}

This method doesn't include a location (page or section). You need an external tool for that. See How to effectively use List of Symbols for a thesis? (and remove the nonumberlist option).

If you're interested in an entry that may take an argument (to replace U with some other symbol) then see Symbols with optional parameter in glossaries with \newglossary.