Символы абсолютной величины

\documentclass{article}
\usepackage{mathtools}

\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*{\Value}{\frac{1}{2}x^2}%
\begin{document}
    \[\abs{\Value}  \quad \norm{\Value}  \qquad\text{non-starred}  \]
    \[\abs*{\Value} \quad \norm*{\Value} \qquad\text{starred}\qquad\]
\end{document}

\documentclass{amsart}

\begin{document}

$  \log|x||y|b $

$  \log\left|x\right|\left|y\right|b $

$  \log\mathopen|x\mathclose|\mathopen|y\mathclose|b $

\end{document}

\documentclass{article}

\usepackage{commath}

\begin{document}
\[ \norm{a \vec{u}} = \abs{a} \, \norm{\vec{v}} \]
\end{document}

\documentclass{article}

\usepackage{physics}

\begin{document}
    \[ c = \abs{-c} \]
    \[ \vu{a} = \frac{\vb{a}}{\norm{\vb{a}}} \]
\end{document}

\left\| \sum_{i=1}^{n} x^2 \right\|

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
  %begin equation
\lVert w \rVert
%end equation
\]
\end{document}