The author is referring to a series of commands he has defined and that are part od the file Commons.sty
(the file can be found following a link in the site you linked to in your question); they basically are shortcuts allowing you to write fractions and matrices with or without delimiters; in the following document I've extracted the definitions from Commons.sty
and provide an example of their use:
\documentclass{article}
\usepackage{amsmath}
\usepackage{xfrac}
\newcommand{\pa}[1]{\left(#1\right)} % encloses the argument using stretchable parentheses
\newcommand{\bra}[1]{\left[#1\right]} % encloses the argument using stretchable square brackets
% matrices for displayed expressions
\newcommand{\mat}[1]{\begin{matrix}#1\end{matrix}} % no delimiters
\newcommand{\pmat}[1]{\pa{\mat{#1}}} % parentheses as delimiters
\newcommand{\bmat}[1]{\bra{\mat{#1}}} % square brackets as delimiters
% variations of \frac and \sfrac
\newcommand{\pfrac}[2]{\pa{\frac{#1}{#2}}} % enclosed in parentheses
\newcommand{\bfrac}[2]{\bra{\frac{#1}{#2}}} % enclosed in square brackets
\newcommand{\psfrac}[2]{\pa{\sfrac{#1}{#2}}} % sfrac enclosed in parentheses
\newcommand{\bsfrac}[2]{\bra{\sfrac{#1}{#2}}} % sfrac enclosed in square brackets
% for small matrices to be used in in-line expressions
\newcommand{\sm}[1]{\begin{smallmatrix}#1\end{smallmatrix}} % no delimiters
\newcommand{\psm}[1]{\pa{\sm{#1}}} % parentheses as delimiters
\newcommand{\bsm}[1]{\bra{\sm{#1}}} % square brackets as delimiters
\begin{document}
\[
\pfrac{1}{2}\quad
\bfrac{1}{2}\quad
\psfrac{1}{2}\quad
\bsfrac{1}{2}\quad
\mat{1 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 0}\quad
\pmat{1 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 0}\quad
\bmat{1 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 0}\quad
\]
$\sm{1 & 0 \\ 1 & 0}\quad\psm{1 & 0 \\ 1 & 0}\quad\bsm{1 & 0 \\ 1 & 0}$
\end{document}

Of course, if you save the file Commons.sty in a convenient place (your local tree, for example) where TeX can find it, you can load the package and directly use the commands, as in:
\documentclass{article}
\usepackage{Commons}
\begin{document}
\[
\pfrac{1}{2}\quad
\bfrac{1}{2}\quad
\psfrac{1}{2}\quad
\bsfrac{1}{2}\quad
\mat{1 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 0}\quad
\pmat{1 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 0}\quad
\bmat{1 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 0}\quad
\]
$\sm{1 & 0 \\ 1 & 0}\quad\psm{1 & 0 \\ 1 & 0}\quad\bsm{1 & 0 \\ 1 & 0}$
\end{document}
As a side note, I would have defined \pmat
and \bmat
using directly bmatrix
and pmatrix
as provided by amsmath
.