% ==============================================================================
\newcommand*{\der}[3]{\ensuremath{\left( \dfrac{\partial #1}{\partial #2} \right)_{#3}}}
\newcommand*{\Der}[3]{\ensuremath{\left(  \frac{\partial #1}{\partial #2} \right)_{#3}}}
\newcommand*{\DER}[2]{\ensuremath{\left( \dfrac{\mathrm{d} #1}{\mathrm{d} #2} \right)}}
%
\newcommand*{\ai}[0]{\ensuremath{ \alpha^\mathrm{0} }}
\newcommand*{\aid}[0]{\ensuremath{ \alpha^\mathrm{0}_\mathrm{\delta} }}
\newcommand*{\aidd}[0]{\ensuremath{ \alpha^\mathrm{0}_\mathrm{\delta \delta} }}
\newcommand*{\aidt}[0]{\ensuremath{ \alpha^\mathrm{0}_\mathrm{\tau \delta} }}
\newcommand*{\aitd}[0]{\ensuremath{ \alpha^\mathrm{0}_\mathrm{\tau \delta} }}
\newcommand*{\ait}[0]{\ensuremath{ \alpha^\mathrm{0}_\mathrm{\tau} }}
\newcommand*{\aitt}[0]{\ensuremath{ \alpha^\mathrm{0}_\mathrm{\tau \tau} }}
\newcommand*{\aittt}[0]{\ensuremath{ \alpha^\mathrm{0}_\mathrm{\tau \tau \tau} }}
%
\newcommand*{\ar}[0]{\ensuremath{ \alpha^\mathrm{r} }}
\newcommand*{\ard}[0]{\ensuremath{ \alpha^\mathrm{r}_\mathrm{\delta} }}
\newcommand*{\ardd}[0]{\ensuremath{ \alpha^\mathrm{r}_\mathrm{\delta \delta} }}
\newcommand*{\artd}[0]{\ensuremath{ \alpha^\mathrm{r}_\mathrm{\tau \delta} }}
\newcommand*{\ardt}[0]{\ensuremath{ \alpha^\mathrm{r}_\mathrm{\tau \delta} }}
\newcommand*{\art}[0]{\ensuremath{ \alpha^\mathrm{r}_\mathrm{\tau} }}
\newcommand*{\artt}[0]{\ensuremath{ \alpha^\mathrm{r}_\mathrm{\tau \tau} }}
%
\newcommand*{\arttt}[0]{\ensuremath{ \alpha^\mathrm{r}_\mathrm{\tau \tau \tau} }}
\newcommand*{\arttd}[0]{\ensuremath{ \alpha^\mathrm{r}_\mathrm{\tau \tau \delta} }}
\newcommand*{\artdd}[0]{\ensuremath{ \alpha^\mathrm{r}_\mathrm{\tau \delta \delta} }}
\newcommand*{\arddd}[0]{\ensuremath{ \alpha^\mathrm{r}_\mathrm{\delta \delta \delta} }}
% ==============================================================================