\newcommand{\nl}{\newline}
\newcommand{\ifftmp}{\;\Leftrightarrow\;}
\newcommand{\impltmp}{\DOTSB\;\Rightarrow\;}

\newcommand{\se}{\quad \text{siten, ett�} \quad}
\newcommand{\vs}{\ {\widehat =}\ }

\newcommand{\N}{\mathbb N}
\newcommand{\Z}{\mathbb Z}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\newcommand{\C}{\mathbb C}

\newcommand{\re}{\text{Re\,}}
\newcommand{\im}{\text{Im\,}}
\newcommand{\V}[1]{{\mathbf #1}}
\renewcommand{\angle}{\sphericalangle}
\renewcommand{\vec}[1]{\overrightarrow{#1}}
\newcommand{\updownarrows}{\uparrow\negthinspace\downarrow}

\newcommand{\arccot}{\operatorname{arccot}}
\newcommand{\asin}{\operatorname{\overline{arc}sin}}
\newcommand{\acos}{\operatorname{\overline{arc}cos}}
\newcommand{\atan}{\operatorname{\overline{arc}tan}}
\newcommand{\acot}{\operatorname{\overline{arc}cot}}

\newcommand{\arsinh}{\operatorname{arsinh}}
\newcommand{\arcosh}{\operatorname{arcosh}}
\newcommand{\artanh}{\operatorname{artanh}}
\newcommand{\arcoth}{\operatorname{arcoth}}
\newcommand{\acosh}{\operatorname{\overline{ar}cosh}}

\newcommand{\sg}{\operatorname{sgn}}
\newcommand{\osder}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\grad}{\operatorname{grad}}
\newcommand{\tr}{^{\text T}}
\newcommand{\Df}{\operatorname{D}} 
\newcommand{\comp}{\operatorname{comp}}
\newcommand{\ys}[1]{\overline S_{#1}}
\newcommand{\as}[1]{\underline S_{#1}}
\newcommand{\sij}[2]{\biggl/_{\null\hskip-2mm #1}^{#2}}
\newenvironment{cmatrix}[1]{\left(\begin{array}{#1}}{\end{array}\right)}
\newenvironment{dmatrix}[1]{\left|\begin{array}{#1}}{\end{array}\right|}
\newenvironment{ematrix}[1]{\begin{array}{#1}}{\end{array}}

\newcommand{\Cal}{\mathcal}
