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%% 
%%  Die DANTE-Edition
%%  Ein Beispiel der LaTeX Referenz
%%  3. Auflage
%% 
%% 
%%  Copyright (C) 2013 Herbert Voss
%% 
%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%% 
%%  See http://www.latex-project.org/lppl.txt for details.
%% 
%% 
%% ==== 
% Show page(s) 1
%% 
%% 
\documentclass[]{exaarticle}
\pagestyle{empty}
\setlength\textwidth{145.16928pt}
\setlength\parindent{0pt}
%StartShownPreambleCommands
\usepackage{xparse}
\NewDocumentCommand\Abstandsvektor
  { > { \SplitArgument { 2 } { ; } } m }
  { \xyz #1 }
\NewDocumentCommand\xyz { mmm }
  {\directlua{%
    tex.print(math.sqrt(#1*#1+#2*#2+#3*#3))}}
%StopShownPreambleCommands
\begin{document}
Die Länge des Abstandsvektors des Punktes (1;2;3) ist
\Abstandsvektor{1;2;3}
\end{document}