Preamble defining new maths commands for LaTeX

preamble.tex

% New definition of square root:
% it renames \sqrt as \oldsqrt
\let\oldsqrt\sqrt
% it defines the new \sqrt in terms of the old one
\def\sqrt{\mathpalette\DHLhksqrt}
\def\DHLhksqrt#1#2{%
\setbox0=\hbox{$#1\oldsqrt{#2\,}$}\dimen0=\ht0
\advance\dimen0-0.2\ht0
\setbox2=\hbox{\vrule height\ht0 depth -\dimen0}%
{\box0\lower0.4pt\box2}}

\DeclarePairedDelimiter\abs{\lvert}{\rvert}%
\DeclarePairedDelimiter\norm{\lVert}{\rVert}%

% Swap the definition of \abs* and \norm*, so that \abs
% and \norm resizes the size of the brackets, and the 
% starred version does not.
\makeatletter
\let\oldabs\abs
\def\abs{\@ifstar{\oldabs}{\oldabs*}}
%
\let\oldnorm\norm
\def\norm{\@ifstar{\oldnorm}{\oldnorm*}}
\makeatother

\newcommand{\defeq}{\stackrel{\mathclap{\normalfont\mbox{\tiny def}}}{=}}
\newcommand{\dbydt}[1]{\frac{\partial #1}{\partial t}}
\newcommand{\logg}[1]{\log \left\{ #1 \right\}}
\newcommand{\Ree}[1]{\Re \left\{ #1 \right\}}
\newcommand{\Imm}[1]{\Im \left\{ #1 \right\}}
\newcommand{\basis}[1]{\mathbf{\hat #1 }}
\newcommand{\basisgreek}[1]{\bm{\hat{ #1 }}}
\newcommand{\mymu}[0]{\frac{m \Omega}{\hbar}}
\newcommand{\colvec}[3]{\begin{pmatrix} #1 \\ #2 \\ #3 \end{pmatrix}}
\newcommand{\comm}[2]{\left[ #1 , #2 \right]}
\newcommand{\moyal}[2]{\left\{ \left\{ #1, #2 \right\} \right\}}
\newcommand{\poiss}[2]{\left\{ #1, #2 \right\}}

% Properly formatted integral 'd's
\newcommand*\dee{\mathop{}\!\mathrm{d}}
\newcommand*\Dee[1]{\mathop{}\!\mathrm{d^#1}}
\newcommand*\fdee{\mathscr{D}}
\newcommand*\fDee[1]{\mathscr{D^#1}}