\setlength{\textwidth}{175mm}
\setlength{\textheight}{260mm}
\setlength{\columnwidth}{\textwidth}
\setlength{\hoffset}{-25mm}
\setlength{\voffset}{-27mm}

\renewcommand{\baselinestretch}{0.9}
\def\contentsname{}%{Inhaltsverzeichnis}

%%%%    Packages

\NeedsTeXFormat{LaTeX2e}

\usepackage[english,ngerman]{babel}
% \usepackage[latin1]{inputenc}
\usepackage[utf8x]{inputenc}
\usepackage{eurosym,multicol,times}
\usepackage{color}
\usepackage{fancybox,texdraw}
\usepackage[hyphens]{url}
\usepackage{slidesec,lscape}
\usepackage{tabularx,colortbl}
\usepackage{multido,algorithmic}
\usepackage{amsmath,amssymb,nicefrac}
\usepackage{booktabs}
\usepackage{alltt}
\usepackage{color}
\usepackage{qrcode} % fuer Mietgliedsantrag

\def\l@section#1#2{\addpenalty{\@secpenalty}% good place for page break
   \addvspace{0.4em plus\p@}%
   \@tempdima 1.5em
   \begingroup
     \parindent \z@ \rightskip \@pnumwidth
     \parfillskip -\@pnumwidth
     \bf
     \leavevmode
      \advance\leftskip\@tempdima
      \hskip -\leftskip
     #1\nobreak\leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern \@dotsep
       mu$} \hfil \nobreak\hbox to 15pt{\hfil\reset@font\rm #2}\par
   \endgroup}
\def\l@subsection#1#2{\addpenalty{\@secpenalty}% good place for page break
   \addvspace{0.0em plus\p@}%
   \@tempdima 1.5em
   \begingroup
     \parindent \z@ \rightskip \@pnumwidth
     \parfillskip -\@pnumwidth
     \bf
     \leavevmode
      \advance\leftskip\@tempdima
      \hskip -\leftskip
     #1\nobreak\leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern \@dotsep
       mu$} \hfil \nobreak\hbox to 15pt{\hfil\reset@font\rm #2}\par
   \endgroup}

\usepackage{hyperref}
\hypersetup{
    colorlinks=false,
    pdfborder={0 0 0},
    baseurl={}
}
\usepackage{listings}

\lstset{ %
  language=bash,
  basicstyle=\scriptsize\ttfamily,
  xleftmargin=0pt,
  showspaces=false,
  showstringspaces=false,
  showtabs=false,
  frame=tb,     
  tabsize=2,      
  captionpos=b,     
  breaklines=true,    
  breakatwhitespace=false,
  escapeinside={\%*}{*)},
  keywords={}
}

\usepackage{bbm}
\usepackage{wrapfig}
\usepackage[pdftex]{graphicx}
\usepackage{subfigure}

\usepackage[margin=10pt,
font=small,
labelfont=bf,
textfont=it,
justification=raggedright,
position=bottom,
]{caption}

\abovecaptionskip=10pt
\setlength{\intextsep}{0pt}


%%%% PACKAGES, die früher in car61.tex waren:
% jetzt (ab car61/62) hierhin kopiert

\usepackage{paralist}
\usepackage{pgf}
\usepackage{tabularx}
\usepackage{pifont}
\usepackage{xspace}
\usepackage{pict2e}
\usepackage{enumerate}
\usepackage{enumitem}
\usepackage{soul}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage{tcolorbox}
\usetikzlibrary{matrix,fit,positioning,shapes.geometric,patterns,backgrounds}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{arrows,calc}
\tikzstyle{bigbox} = [draw=blue!50, thick, rounded corners, rectangle]
\tikzset{
>=stealth'
}
\usepackage{framed}
\usepackage{fancyvrb}
\usepackage{color}


%%%%    NewCommands

\newcommand{\tm}{$^{\rm tm}$}
\newcommand{\voidbox}[1]{#1}
\newcommand{\elib}{eLib}
\newcommand{\cais}{{\sc CAIS}}
\newcommand{\infocais}{Genauere Informationen finden Sie im \cais.}

\newcommand{\asharp}{{\sc A}$^\#$}
%\newcommand{\axiom}{{\sc AXIOM}}
\newcommand{\derive}{{\sc Derive}}
\newcommand{\macsyma}{{\sc Macsyma}}
\newcommand{\maple}{{\sc Maple}}
\newcommand{\mathematica}{{\sc Mathematica}}
\newcommand{\mathem}{{\sc Mathematica}}
\newcommand{\webm}{{\sc webMathematica}}
\newcommand{\reduce}{{\sc REDUCE}}
\newcommand{\aldessac}{{\sc Aldes/SAC-2}}
\newcommand{\sac}{{\sc SAC-2}}
\newcommand{\aldes}{{\sc ALDES}}
\newcommand{\cayley}{{\sc Cayley}}
\newcommand{\magma}{{\sc MAGMA}}
\newcommand{\cocoa}{{\sf CoCoA}}
\newcommand{\felix}{{\sc FELIX}}
%\newcommand{\form}{{\sc FORM}}
\newcommand{\GAP}{{\sf GAP}}
\newcommand{\kant}{{\sc KANT-V2}}
\newcommand{\lidia}{{\sf LiDIA}}
\newcommand{\mas}{{MAS}}
\newcommand{\masyca}{{MASYCA}}
\newcommand{\mathcad}{{\sc Mathcad}}
\newcommand{\matlab}{{\sc MATLAB}}
\newcommand{\macauley}{{\sc Macaulay}}
\newcommand{\mupad}{{\rm MuPAD}}
\newcommand{\chevie}{{\sf CHEVIE}}
\newcommand{\qpic}{{\sc Quotpic}}
\newcommand{\pari}{{PARI}}
\newcommand{\posso}{{P\kern-0.2em o\kern -0.1em S\kern -0.1em S\kern -0.1em o}}
\newcommand{\reve}{{\sc Reve}}
\newcommand{\orme}{{\sc ORME}}
\newcommand{\simath}{{\sc Simath}}
\newcommand{\parsac}{{\sc Parsac}}
\newcommand{\symmetrica}{{\sc Symmetrica}}
\newcommand{\reptiles}{{\sc RepTiles}}
\newcommand{\symmpad}{{\sc SymmPAD}}
\newcommand{\singular}{{SINGULAR}}
\newcommand{\theorist}{{\sc Theorist}}
\newcommand{\algep}{{\sc ALGEB}}
\newcommand{\algeb}{{\sc ALGEB}}
\newcommand{\amore}{{AMORE}}
\newcommand{\crep}{{CREP}}
\newcommand{\meataxe}{{\sc Meat-Axe}}
\newcommand{\moc}{{\sc MOC}}
\newcommand{\redux}{{\sc ReDuX}}
\newcommand{\sisyphos}{{\sc Sisyphos}}
\newcommand{\SD}{{\sc Symbolic\-Data}}
\newcommand{\Thomson}{International Thomson Publishing}
\newcommand{\AThomson}{Bonn, Albany, Belmont}
\newcommand{\Brooks}{Brooks/Cole Publishing Company}
\newcommand{\ABrooks}{Pacific Grove, California}
\newcommand{\Wiley}{John Wiley \& Sons}
\newcommand{\AWiley}{Chichester}
\newcommand{\AddisonWesley}{Addison-Wesley}
\newcommand{\AAddisonWesley}{Bonn, Paris, Reading Mass.}
\newcommand{\Birkhaeuser}{Birkh"auser Verlag}
\newcommand{\ABirkhaeuser}{Basel, Boston}
\newcommand{\Springer}{Springer Verlag}
\newcommand{\ASpringer}{Berlin, Heidelberg, New York}
\newcommand{\Vieweg}{Vie\-weg Verlag}
\newcommand{\AVieweg}{Braunschweig, Wiesbaden}
\newcommand{\AcademicPress}{Academic Press}
\newcommand{\AAcademicPress}{}
\newcommand{\dpunkt}{dpunkt Verlag}
\newcommand{\Adpunkt}{Heidelberg}
\newcommand{\Teubner}{Teubner Verlag}
\newcommand{\ATeubner}{}
\newcommand{\VDF}{vdf Hochschulverlag}
\newcommand{\AVDF}{Z"urich}
\newcommand{\Cambridge}{Cambridge University Press}
\newcommand{\ACambridge}{Cambridge}
\newcommand{\Oldenbourg}{Verlag Oldenbourg}
\newcommand{\AOldenbourg}{}
\newcommand{\FBVLeipzig}{Fachbuchverlag Leipzig}
\newcommand{\AFBVLeipzig}{Leipzig}
\newcommand{\CRC}{Chapman \& Hall/CRC}
\newcommand{\ACRC}{London, Boca Raton}
\newcommand{\AMS}{American Mathematical Society}
\newcommand{\AAMS}{}
\newcommand{\Siam}{SIAM}
\newcommand{\ASiam}{}
\newcommand{\Magma}{{\sc Magma}}
\newcommand{\axiom}{{\tt axiom}}
\newcommand{\FriCAS}{{\tt FriCAS}}
\newcommand{\SPAD}{{\tt SPAD}}
\newcommand{\Aldor}{$\mathcal Aldor$}

\def\CA{Com\-pu\-ter\-al\-ge\-bra}
\def\ca{Com\-pu\-ter\-al\-ge\-bra}
\def\cas{Com\-pu\-ter\-al\-ge\-bra-Sy\-stem}
\newcommand{\mexp}{\textit{Mathematical Explorer}}
\newcommand{\befehl}[2]{\\[\parskip]\texttt{#1}{#2}\\[\parskip]}
%%% used for latex-compilation:
\providecommand{\htmladdnormallink}{}% defines \htmladdnormallink if not already defined
\renewcommand{\htmladdnormallink}[2]{{#2}}
\newcommand{\Mail}[1]{{\tt #1}}
\newcommand{\imMail}[1]{{\tt
  \usefont{T1}{cmtt}{m}{n}\fontsize{8pt}{9pt}\selectfont
  #1}}
\newcommand{\imURL}[1]{{\tt
  \usefont{T1}{cmtt}{m}{n}\fontsize{6pt}{7pt}\selectfont
  \url{#1}}}

\newcommand{\nint}{{\rm nint }}
\newcommand{\li}{{\rm Li }}
\newcommand{\real}{{\rm Real }}

\newcommand{\GL}{\mathrm{GL}}
\newcommand{\SL}{\mathrm{SL}}
\newcommand{\CC}{\mathbb{C}}
\newcommand{\FF}{\mathbb{F}}
\newcommand{\HH}{\mathbb{H}}
\newcommand{\QQ}{\mathbb{Q}}
\newcommand{\ZZ}{\mathbb{Z}}

\newcommand{\ti}{TI-\emph{n}{\bf spire CAS} \,}
\makeatletter
\newenvironment{tablehere}{\def\@captype{table}}{}
\newenvironment{figurehere}{\bigskip \def\@captype{figure}}{}
\makeatother

\newcolumntype{C}[1]{>{\centering\arraybackslash}p{#1}}

\def\toc_dotfill{ }
\def\trademark{{\ooalign{\hfil\raise.07ex\hbox{\scriptsize R}\hfil\crcr\mathhexbox20D}}}

%%%%    Hyphenations

\hyphenation{sys-tem} \hyphenation{Sys-temmodul}
\hyphenation{Work-sheet}

%%%%    Layout, Abschnitte

%%    Abschnitte

\newcommand{\Abschnitt}[3]{{
 %\vspace*{5mm}\mbox{\textsc{primes}}
     \section*{\Large\bf\hrule\vspace{1mm}
      \centerline{#1}}\vspace{-2.5mm}\hrule}
   \label{#3}
  \addcontentsline{toc}{section}{\normalsize \bf #2 }
   \vspace*{4mm}
 }

\newcommand{\UnterAbschnitt}[3]{
  \vspace{5mm}
\subsection*{\Large \bf #1}\label{#3}
  \addcontentsline{toc}{subsection}{\normalsize \sl #2}
\vspace{4mm}}

\makeatletter

\def\@hdrwidths#1,#2\@@{%
  \edef\@rest{#2}%
  \ifx\@rest\empty
    \def\@wtitle{120mm}\def\@wfotos{55mm}
  \else
    \def\@wtitle{100mm}\def\@wfotos{75mm}%
  \fi}

\newcommand{\Aufsatz}[7]{%
  \gdef\title{#1}
  \gdef\titlefortoc{#2}
  \gdef\author{#3}
  \gdef\authorlabel{#4}
  \gdef\authorwithaddress{#5}
  \gdef\images{#6}
  \gdef\emails{#7}
  \@hdrwidths#3,\@@
  \vspace{3mm}
  \begin{center}
    \begin{minipage}[b]{\@wtitle}
      {\Large\bfseries\title}  \\[1em]
      {\bfseries\authorwithaddress}  \\[1em]
      \@for\email:=\emails\do{\href{mailto:\email}{\texttt{\email}}\\}
    \end{minipage}%
    \begin{minipage}[b]{\@wfotos}
      \flushright
      \@for\image:=\images\do{ \includegraphics[height=45mm]{\image}}
    \end{minipage}
  \end{center}
  \addcontentsline{toc}{subsection}{\normalsize\sl\titlefortoc\ \upshape (\author)}
  \label{\authorlabel}
  \setcounter{satz}{0}%
}

\newcommand{\AufsatzOhneFoto}[6]{%
  \gdef\title{#1}
  \gdef\titlefortoc{#2}
  \gdef\author{#3}
  \gdef\authorlabel{#4}
  \gdef\authorwithaddress{#5}
  \gdef\emails{#6}
  \@hdrwidths#3,\@@
  \vspace{3mm}\noindent
   {\Large\bfseries\title}  \\[1em]
      {\bfseries\authorwithaddress}  \\[1em]
      \@for\email:=\emails\do{\href{mailto:\email}{\texttt{\email}}\\}
  \addcontentsline{toc}{subsection}{\normalsize\sl\titlefortoc\ \upshape (\author)}
  \label{\authorlabel}
  \setcounter{satz}{0}%
}


\newcommand{\AufsatzDrei}[7]{%
  \gdef\title{#1}
  \gdef\titlefortoc{#2}
  \gdef\author{#3}
  \gdef\authorlabel{#4}
  \gdef\authorwithaddress{#5}
  \gdef\images{#6}
  \gdef\emails{#7}
  \@hdrwidths#3,\@@
  \vspace{3mm}
  \begin{center}
    \begin{minipage}[b]{\@wtitle}
      {\Large\bfseries\title}  \\[1em]
      {\bfseries\authorwithaddress}  \\[1em]
      \@for\email:=\emails\do{\href{mailto:\email}{\texttt{\email}}\\}
    \end{minipage}%
    \begin{minipage}[b]{\@wfotos}
      \flushright
      \@for\image:=\images\do{ \includegraphics[height=32mm]{\image}}
    \end{minipage}
  \end{center}
  \addcontentsline{toc}{subsection}{\normalsize\sl\titlefortoc\ \upshape (\author)}
  \label{\authorlabel}
  \setcounter{satz}{0}%
}


\newcommand{\AufsatzFuenf}[7]{%
  \gdef\title{#1}
  \gdef\titlefortoc{#2}
  \gdef\author{#3}
  \gdef\authorlabel{#4}
  \gdef\authorwithaddress{#5}
  \gdef\images{#6}
  \gdef\emails{#7}
  \@hdrwidths#3,\@@
  \vspace{3mm}
  \begin{center}
    \begin{minipage}[b]{\@wtitle}
      {\Large\bfseries\title}  \\[1em]
      {\bfseries\authorwithaddress}  \\[1em]
      \@for\email:=\emails\do{\href{mailto:\email}{\texttt{\email}}\\}
    \end{minipage}%
    \begin{minipage}[b]{\@wfotos}
      \flushright
      \@for\image:=\images\do{ \includegraphics[height=30mm]{\image}}
    \end{minipage}
  \end{center}
  \addcontentsline{toc}{subsection}{\normalsize\sl\titlefortoc\ \upshape (\author)}
  \label{\authorlabel}
  \setcounter{satz}{0}%
}



\newcommand{\ImpressumItem}[2]{
\begin{minipage}[b]{75mm}
  \parbox{17mm}{\includegraphics[width=17mm]{#2}}
  \parbox{50mm}{
  #1
  }
\end{minipage}}

\newcommand{\konfhinwitem}[3]{\item{\bf \normalsize #1}

 #2

{\footnotesize #3}}

\newcommand{\konfhinwitemhttp}[3]{\item{\bf \normalsize #1}

 #2

{\footnotesize \href{http://#3}{{\tt #3}}}}

\newcommand{\konfhinwitemhttps}[3]{\item{\bf \normalsize #1}

 #2

{\footnotesize \href{https://#3}{{\tt #3}}}}


\newcommand{\konfhinwitemhttptwo}[4]{\item{\bf \normalsize #1}

 #2

{\footnotesize \href{http://#3}{{\tt #3}}}\\
{\footnotesize \href{http://#4}{{\tt #4}}}}


\newcommand{\konfhinwitemhttpstwo}[4]{\item{\bf \normalsize #1}

 #2

{\footnotesize \href{https://#3}{{\tt #3}}}\\
{\footnotesize \href{https://#4}{{\tt #4}}}}

\newcommand{\konfhinwitemnourl}[2]{\item{\bf \normalsize #1}

 #2
}


%%  Ueberschrift (vom Autor einzusetzen)

\makeatletter

\newcommand{\Ueberschrift}[2]{\bigskip\bigskip\vspace*{-6mm}%
\noindent\begin{minipage}[t]{\columnwidth}
\Large\bfseries\hrule\vspace{1.5mm}%
\begin{center}{#1}\end{center}%
\vspace{-2.8mm}\hrule
\end{minipage}\label{#2}\medskip\par
\@afterheading\ignorespaces}

\newcommand{\Ueberschriftu}[1]{\bigskip
\noindent{\bfseries #1}\\
\@afterheading\ignorespaces}

\makeatother

%%%% Theorem.sty

\usepackage{ntheorem}

\theoremseparator{}
\theoremheaderfont{\bfseries}
\theorembodyfont{\itshape}
\newtheorem{satz}{Satz}[section]
%\newtheorem{lemma}[satz]{Lemma}
%\newtheorem{kor}[satz]{Korollar}
%\newtheorem{theo}[satz]{Theorem}
%
\theorembodyfont{\rmfamily}
\newtheorem{bsp}[satz]{Beispiel}
%\newtheorem{bem}[satz]{Bemerkung}
%\newtheorem{bemerkung}[satz]{Bemerkung}
%\newtheorem{bemerkungen}[satz]{Bemerkungen}
\newtheorem{defi}[satz]{Definition}
\newtheorem{ford}{Forderung}
\newtheorem{notation}[satz]{Notation}
\newtheorem{notationen}[satz]{Notationen}

\renewcommand{\thesatz}{\arabic{satz}}

%%%% Gestaltungselemente

\newlength{\picwidth}
\definecolor{headgray}{gray}{0.1}
\definecolor{backgray}{gray}{0.9}
\long\def\backbox#1{\colorbox[gray]{0.1}{\color[gray]{1}#1}}

\newenvironment{btext}%
    {\setlength\fboxsep{10pt}%
    \setlength{\picwidth}{\linewidth}%
    \addtolength{\picwidth}{-2\fboxsep}%
    \noindent\Sbox\minipage{\picwidth}\footnotesize}%
    {\endminipage\endSbox\colorbox{backgray}{\TheSbox}}

\def\linedhead#1{{\color[gray]{0.1}
\setlength\fboxsep{3pt}%
\centering{\hfil{\hbox{\normalsize\bfseries \hfil #1\hfil}}\hfil}
\vskip4pt\hrule height \fboxrule
\medskip}}

\newcommand{\CBox}[1]{\begin{center}
  \cornersize{0.1}\ovalbox{~\parbox[c]{0.925\columnwidth}{\vspace*{0.25em}
   \footnotesize #1\vspace*{0.25em}}~}
\end{center}}

\newcommand{\CBoxP}[2]{\begin{center}
  \cornersize{0.1}\ovalbox{~\parbox[c]{0.925\columnwidth}{\vspace*{0.25em}
   \footnotesize #1\vspace*{0.25em}}~}\vspace*{#2}
\end{center}}

\newcommand{\negskip}{\vspace*{-1.25em}\smallskip}

%%  Bilder

\newcommand{\Bild}[3]{\begin{center}\begin{minipage}[c]{\columnwidth}
    \begin{center}
    \includegraphics[width=#2]{#1}
    \end{center}
    \vspace*{-2em}
    \begin{flushright}
    {\em\small #3}
    \end{flushright}
\end{minipage}\end{center}}

\newcommand{\BildX}[2]{\begin{center}\begin{minipage}[c]{\columnwidth}
    \begin{center}
    \includegraphics[width=#2]{#1}
    \end{center}
\end{minipage}\end{center}}

\newcommand{\Bilder}[4]{\begin{center}\begin{minipage}[c]{\columnwidth}
    \begin{center}
    \includegraphics[width=#3]{#1}\hspace*{0.5em}\includegraphics[width=#3]{#2}
    \end{center}
    \vspace*{-2em}
    \begin{flushright}
    {\em\small #4}
    \end{flushright}
\end{minipage}\end{center}}

\newcommand{\BilderX}[3]{\begin{center}\begin{minipage}[c]{\columnwidth}
    \begin{center}
    \includegraphics[width=#3]{#1}\hspace*{0.5em}\includegraphics[width=#3]{#2}
    \end{center}
\end{minipage}\end{center}}

\newcommand{\VierBilder}[6]{\begin{center}\begin{minipage}[c]{\columnwidth}
    \begin{center}
    \includegraphics[width=#1]{#2}\includegraphics[width=#1]{#3}\includegraphics[width=#1]{#4}\includegraphics[width=#1]{#5}
    \end{center}
    \vspace*{-2em}
    \begin{flushright}
    {\em\small #6}
    \end{flushright}
\end{minipage}\end{center}}

%% Fonts

\font\courir=pcrb at 8pt
\font\courirsmall=pcrb at 7pt
