% environments shorthand
\def\bs{\begin{subequations}}
\def\es{\end{subequations}}
\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\bml{\begin{multline}}
\def\eml{\end{multline}}
\def\beq{\begin{eqnarray}}
\def\eeq{\end{eqnarray}}
\def\bd{\begin{description}}
\def\ed{\end{description}}
\def\bn{\begin{enumerate}}
\def\en{\end{enumerate}}
\def\bi{\begin{itemize}}
\def\ei{\end{itemize}}
\def\brem{\begin{remark}}
\def\erem{\end{remark}}
\def\bp{\begin{proof}}
\def\ep{\end{proof}}
\renewcommand\l{\left}
\renewcommand\r{\right}
% math shorthand                                                                                                                                                   
\newcommand{\dd}[2]{\partial_{#1}{#2}}
\newcommand{\de}{\mathrm{d}}
\newcommand{\Df}[2]{\frac{\d #1}{\d #2}}
\newcommand{\DDf}[2]{\frac{\d^2 #1}{\d #2^2}}
\newcommand{\df}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\ddf}[2]{\frac{\partial^2 #1}{\partial #2^2}}
\newcommand{\f}[2]{\frac{#1}{#2}}
\renewcommand{\div}{\mathrm{div}}
\newcommand{\grad}{\mathrm{grad}}
% text shorthand                                                                                                                                                   
% Vectors and notation
\renewcommand{\vec}[1]{\mbox{\boldmath $ #1$}}
\renewcommand{\v}{\vec}
\newcommand{\bec}{\vec}
\newcommand{\B}{\vec B}
\renewcommand{\u}{\vec u}
\newcommand{\m}{\vec v}
\newcommand{\ru}{\hat{\vec r}}
\renewcommand{\r}{\vec r}
\renewcommand{\k}{\hat{\vec k}}
\newcommand{\n}{\nabla}
\renewcommand{\.}{\cdot}
\newcommand{\x}{\times}
\newcommand{\rhobar}{\bar{\rho}}
\newcommand{\Tbar}{\bar{T}}
\newcommand{\Pbar}{\bar{P}}
\newcommand{\nubar}{\bar{\nu}}
\newcommand{\kapbar}{\bar{\kappa}}
\newcommand{\Nrho}{N_\rho}
% tor-pol
\newcommand{\pol}{v}
\newcommand{\tor}{w}
\newcommand{\polB}{h}
\newcommand{\torB}{g}
% Operators
\newcommand{\Ltwo}{L_2}
\newcommand{\A}{\mathcal{A}}
\newcommand{\K}{\mathcal{K}}
\newcommand{\D}{\mathcal{D}}
\newcommand{\E}{\mathcal{E}}
\newcommand{\M}{\mathcal{M}}
\newcommand{\Kl}{\K_l}
\newcommand{\Dl}{\D_l}
\newcommand{\El}{\E_l}
\newcommand{\Ml}{\M_l}
% truncation params
\newcommand{\Lmax}{{L_\text{max}}}
\newcommand{\Mmax}{{M_\text{max}}}
% sectioning
\newcommand{\s}[1]{\subsection{#1}}
\renewcommand{\ss}[1]{\subsubsection{#1}}
%dimles numbers
\newcommand{\R}{\mathrm{R}}
\renewcommand{\Pr}{\mathrm{Pr}}
\newcommand{\Pm}{\mathrm{Pm}}
\newcommand{\Di}{\mathrm{Di}}

\makeatother

\newcommand{\hide}[1]{}
\newcommand{\red}[1]{{\color{red} #1}}

