% Macros von Thomas Keilen

%\usepackage{graphicx}    % dient dem Einbinden von Graphikfiles
%\usepackage{epsfig}            % dient dem Einbinden von Graphikfiles
\usepackage{amsmath}
\usepackage{amssymb} 
\usepackage{amsthm}
\usepackage{latexsym}
\usepackage{bbm}
\usepackage{oldgerm}
\usepackage{texdraw}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Zu verwendende Regelsaetze 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Bei Nummerierung vom Typ swapped soll abweichend vom Standard
%%% "5.12. Satz" erscheinen als "5.12 Satz", das heisst ohne
%%% zusaetzlichen Punkt.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\swappedhead#1#2#3{%
  \thmnumber{#2}\thmname{\@ifnotempty{#2}{ }#1}%
  \thmnote{ {\the\thm@notefont(#3)}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Neue Theoremstile
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newtheoremstyle{standard}% name
  {}%      Space above, empty = `usual value'
  {}%      Space below
  {\normalfont}% Body font
  {}%         Indent amount (empty = no indent, \parindent = para indent)
  {\bfseries}% Thm head font
  {:}%        Punctuation after thm head
  {0.5em}% Space after thm head: \newline = linebreak
  {}%         Thm head 
\newtheoremstyle{break-italic}% name
  {}%      Space above, empty = `usual value'
  {}%      Space below
  {\itshape}% Body font
  {0cm}%         Indent amount (empty = no indent, \parindent = para indent)
  {\bfseries}% Thm head font
  {}%        Punctuation after thm head
  {\newline}% Space after thm head: \newline = linebreak
  {}%         Thm head 
\newtheoremstyle{break-roman}% name
  {}%      Space above, empty = `usual value'
  {}%      Space below
  {\normalfont}% Body font
  {}%         Indent amount (empty = no indent, \parindent = para indent)
  {\bfseries}% Thm head font
  {}%        Punctuation after thm head
  {\newline}% Space after thm head: \newline = linebreak
  {}%         Thm head spec
\newtheoremstyle{varthm-roman}% name
  {}%      Space above, empty = `usual value'
  {0.5ex}%      Space below
  {\normalfont}% Body font
  {}%         Indent amount (empty = no indent, \parindent = para indent)
  {\bfseries}% Thm head font
  {:}%        Punctuation after thm head 
  {.5em}%     Space after thm head: " " = normal interword space;
        %       \newline = linebreak
  {\thmnote{#3}}% Thm head spec
\newtheoremstyle{varthm-roman-no-punctuation}% name
  {}%      Space above, empty = `usual value'
  {}%      Space below
  {\normalfont}% Body font
  {}%         Indent amount (empty = no indent, \parindent = para indent)
  {\bfseries}% Thm head font
  {}%        Punctuation after thm head 
  {.5em}%     Space after thm head: " " = normal interword space;
        %       \newline = linebreak
  {\thmnote{#3}}% Thm head spec
\newtheoremstyle{varthm-roman-break}% name
  {}%      Space above, empty = `usual value'
  {}%      Space below
  {\normalfont}% Body font
  {}%         Indent amount (empty = no indent, \parindent = para indent)
  {\bfseries}% Thm head font
  {}%        Punctuation after thm head
  {\newline}%     Space after thm head: " " = normal interword space;
        %       \newline = linebreak
  {\thmnote{#3}}% Thm head spec
\newtheoremstyle{varthm-italic}% name
  {}%      Space above, empty = `usual value'
  {}%      Space below
  {\itshape}% Body font
  {}%         Indent amount (empty = no indent, \parindent = para indent)
  {\bfseries}% Thm head font
  {:}%        Punctuation after thm head 
  {.5em}%     Space after thm head: " " = normal interword space;
        %       \newline = linebreak
  {\thmnote{#3}}% Thm head spec
\newtheoremstyle{varthm-italic-no-punctuation}% name
  {}%      Space above, empty = `usual value'
  {}%      Space below
  {\itshape}% Body font
  {}%         Indent amount (empty = no indent, \parindent = para indent)
  {\bfseries}% Thm head font
  {}%        Punctuation after thm head 
  {.5em}%     Space after thm head: " " = normal interword space;
        %       \newline = linebreak
  {\thmnote{#3}}% Thm head spec
\newtheoremstyle{varthm-italic-break}% name
  {}%      Space above, empty = `usual value'
  {}%      Space below
  {\itshape}% Body font
  {}%         Indent amount (empty = no indent, \parindent = para indent)
  {\bfseries}% Thm head font
  {}%        Punctuation after thm head
  {\newline}%     Space after thm head: " " = normal interword space;
        %       \newline = linebreak
  {\thmnote{#3}}% Thm head spec

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Neue Regelsätze mit Nummerierung "5.12 Satz" etc.
%%% Durch Setzen der Variablen \theoremnumberstyle wird der Stil
%%% ausgewaehlt.
%%% plain         = Satz 12
%%% change        = 12 Satz 
%%% section       = Satz 5.12
%%% changesection = 5.12 Satz
%%% chapter       = Satz V.12
%%% changechapter = V.12 Satz
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\thmsection{section}
\def\thmchangesection{changesection}
\def\thmchapter{chapter}
\def\thmchangechapter{changechapter}
\def\thmchange{change}
\def\thmplain{plain}
%\def\yes{yes}
%\def\no{no}
\ifx\theoremnumberstyle\thmplain
  \theoremstyle{break-italic} 
  \newtheorem{satz}{Satz} 
\else
  \ifx\theoremnumberstyle\thmsection
    \theoremstyle{break-italic} 
    \newtheorem{satz}{Satz}[section]
  \else
    \ifx\theoremnumberstyle\thmchange
      \swapnumbers
      \theoremstyle{break-italic} 
      \newtheorem{satz}{Satz}
    \else
      \ifx\theoremnumberstyle\thmchangesection
         \swapnumbers
         \theoremstyle{break-italic} 
         \newtheorem{satz}{Satz}[section]
      \else
        \ifx\theoremnumberstyle\thmchangechapter
           \swapnumbers
           \theoremstyle{break-italic} 
           \newtheorem{satz}{Satz}[chapter]
        \else
          \ifx\theoremnumberstyle\thmsection
             \theoremstyle{break-italic} 
             \newtheorem{satz}{Satz}[section]
          \else
            %% Wenn \theoremnumberstyle nicht gesetzt ist, dann immer plain.
            \theoremstyle{break-italic} 
            \newtheorem{satz}{Satz}[section]
          \fi
        \fi
      \fi
    \fi
  \fi
\fi

\theoremstyle{break-italic} 
\newtheorem{theorem}[satz]{Theorem}
\newtheorem{lemma}[satz]{Lemma}
\newtheorem{folgerung}[satz]{Folgerung}
\newtheorem{korollar}[satz]{Korollar}
\newtheorem{corollary}[satz]{Corollary}
\newtheorem{proposition}[satz]{Proposition}
\newtheorem{axiom}[satz]{Axiom}

\theoremstyle{break-roman} 
\newtheorem{definition}[satz]{Definition}
\newtheorem{exercise}[satz]{Exercise}
\newtheorem{aufgabe}[satz]{Aufgabe}
\newtheorem{loesung}[satz]{L\"osung zu Aufgabe}
\newtheorem{beispiel}[satz]{Beispiel}
\newtheorem{example}[satz]{Example}
\newtheorem{bemerkung}[satz]{Bemerkung}
\newtheorem{remark}[satz]{Remark}
\newtheorem{notation}[satz]{Notation}
\newtheorem{algorithmus}[satz]{Algorithmus}
\newtheorem{hinweise}[satz]{Allgemeine Hinweise}
\newtheorem{generalvoraussetzung}[satz]{Generalvoraussetzung}
\newtheorem{definitionsatz}[satz]{Definition und Satz}
\newtheorem{definitiontheorem}[satz]{Definition and Theorem}
\newtheorem{definitionbemerkung}[satz]{Definition und Bemerkung}
\newtheorem{definitionremark}[satz]{Definition and Remark}

\theoremstyle{standard} 
\newtheorem*{behauptung}{Behauptung}
\newtheorem*{claim}{Claim}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Regelsaetze, deren Bezeichner noch frei gewaehlt werden kann;
%%% z.B. Generalvoraussetzung, Notation, Hinweis, ...
%%% Beispiel mit angepasster Nummerierung:
%%%    \stepcounter{satz}
%%%    \begin{varthm-roman-break}[\arabic{section}.\arabic{satz} Hinweis]
%%%    \end{varthm-roman-break}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\theoremstyle{varthm-roman}
\newtheorem*{varthm-roman}{}% all text supplied in the note
\theoremstyle{varthm-italic}
\newtheorem*{varthm-italic}{}% all text supplied in the note
\theoremstyle{varthm-roman-break}
\newtheorem*{varthm-roman-break}{}% all text supplied in the note
\theoremstyle{varthm-italic-break}
\newtheorem*{varthm-italic-break}{}% all text supplied in the note
\theoremstyle{varthm-roman-no-punctuation}
\newtheorem{varthm-roman-no-punctuation-numbered}[satz]{}% all text supplied in the note
\theoremstyle{varthm-italic-no-punctuation}
\newtheorem{varthm-italic-no-punctuation-numbered}[satz]{}% all text supplied in the note

\newenvironment{varthm-roman-numbered}[1]{
  \begin{varthm-roman-no-punctuation-numbered}
    \mbox{\rm\textbf{#1}}
  }{\end{varthm-roman-no-punctuation-numbered}}
\newenvironment{varthm-italic-numbered}[1]{
  \begin{varthm-italic-no-punctuation-numbered}
    \mbox{\rm\textbf{#1}}
  }{\end{varthm-italic-no-punctuation-numbered}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Eigendefinition f\"ur Proof-Umgebung (amsthm-package) muss geladen sein)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewenvironment{proof}[1][\proofname]{\par
  \normalfont
  \topsep6\p@\@plus6\p@ \trivlist
  \item[\hskip\labelsep\bfseries
    #1\@addpunct{:}]\ignorespaces\parindent0cm
}{%
  \qed\endtrivlist
}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Auflistung mit Formelnummern als Nummerierungssymbolen
%%% Der optionale Parameter von \item gibt den Labeleintrag an.
%%%     z.B. \begin{equationlist} \item[eq:drei] ... \end{equationlist} 
%%%          .... (\ref{eq:drei}) ...
%%% Benoetigt den Befehl \mylabel.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newenvironment{equationlist}{
  \begin{list}{}
    {\renewcommand{\makelabel}[1]{\stepcounter{equation}\mbox{\rm(\theequation)}%
        \if##1\empty\else\mylabel{##1}{\theequation}\fi}
     \leftmargin3.5cm \itemindent-1cm\labelwidth1.5cm \parsep6pt \topsep6pt\labelsep0.8cm}
    }
  {\end{list}
  }
\newenvironment{tequationlist}{
  \begin{list}{}
    {\renewcommand{\makelabel}[1]{\stepcounter{equation}\mbox{\rm(\theequation)}%
        \if##1\empty\else\tmylabel{##1}{\theequation}\fi}
     \leftmargin3.5cm \itemindent-1cm\labelwidth1.5cm \parsep6pt \topsep6pt\labelsep0.8cm}
    }
  {\end{list}
  }

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Auflistung mit 
%%% Der optionale Parameter von \item gibt den Labeleintrag an.
%%%     z.B. \begin{equationlist} \item[eq:drei] ... \end{equationlist} 
%%%          .... (\ref{eq:drei}) ...
%%% Benoetigt den Befehl \mylabel.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newenvironment{wideitemize}{
  \begin{list}{}{\leftmargin1.1cm \labelwidth1cm}
  }
  {\end{list}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Aenderung von ref und label, so dass Kapitelnummer bei ref mit zitiert
%%% wird, falls der Aufruf in einem anderen Kapitel erfolgt!
%%% 
%%% Hierzu werden von label nicht nur {Gliederungsnummer}{Seitennummer} 
%%% in \newlabel{name}{{Gliederungsnummer}{Seitennummer}} abgespeichert,
%%% sondern {\CHAPTER@LABEL{Kapitelnummer}{Gliederungsnummer}}{Seitennummer}.
%%% \CHAPTER@LABEL sorgt dafuer, dass ein Satz im gleichen Kapitel
%%% ohne vorangestellte Kapitelnummer referiert wird, sonst mit
%%% vorangestellter Kapitelnummer.
%%%
%%% Dies baut auf den ref und label-Befehlen in latex.ltx auf!
%%%
%%% Die Befehle vertragen sich nicht mit dem Paket babel. ???
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\catcode`@=11%%% Sorgt daruer, dass @ in Marconamen verwendet werden kann
\def\label#1{\@bsphack
  \protected@write\@auxout{}%
  {\string\newlabel{#1}{{\@currentlabel}{\thepage}}}%
  \@esphack}
\def\thechapter{}
\renewcommand\thechapter{\Roman{chapter}}  %%% Kapitel mit roemischen Ziffern numerieren
\newcounter{refhilfszaehler}
\newcommand{\CHAPTER@LABEL}[2]{%
  \setcounter{refhilfszaehler}{\number#1}%
  \ifnum\value{refhilfszaehler}=\value{chapter}{#2}%
  \else\ifnum\value{refhilfszaehler}=0{#2}% Der Anhang hat Kapitelnummer 0.
  \else\Roman{refhilfszaehler}.#2\fi\fi%
  }
\newcommand{\tlabel}[1]{\@bsphack
  \protected@write\@auxout{}%
  {\string\newlabel{#1}{{\string\CHAPTER@LABEL{\arabic{chapter}}{\@currentlabel}}{\thepage}}}%
  \@esphack}
%%% Erste, schlechte Version von Labeln, die Kapitel mitfuehren. %%%%%%%%%
%\long\def\@firstofthree#1#2#3{#1}
%\long\def\@secondofthree#1#2#3{#2}
%\long\def\@thirdofthree#1#2#3{#3}
%\newcounter{refhilfszaehler}  %%% Ein Hilfszaehler, fuer die Kapitelnummer  
%\def\tref#1{\def\EI@NS{\expandafter\@setref\csname r@#1\endcsname\@firstofthree{#1}}%%%erster Eintrag aus \newlabel
%  \def\DR@EI{\expandafter\@setref\csname r@#1\endcsname\@thirdofthree{#1}}%%%dritter Eintrag aus \newlabel
%  \setcounter{refhilfszaehler}{\number\DR@EI}%%% Hilfszaehler wird Kapitelnummer
%  \ifnum\value{refhilfszaehler}=\value{chapter}\EI@NS\else\Roman{refhilfszaehler}.\EI@NS\fi}
%\def\tlabel#1{\@bsphack
%  \protected@write\@auxout{}%
%  {\string\newlabel{#1}{{\@currentlabel}{\thepage}{\arabic{chapter}}}}%
%  \@esphack}
%\def\tpageref#1{\expandafter\@setref\csname r@#1\endcsname\@secondofthree{#1}}
%%% Ende: Erste, schlechte ...
\newenvironment{tequation}{%
  \@beginparpenalty\predisplaypenalty
  \@endparpenalty\postdisplaypenalty
  \refstepcounter{equation}%
  \@topsep\abovedisplayskip \trivlist
  \item[]\leavevmode
    \hbox to\linewidth\bgroup\hfil$\displaystyle
    }{%
    \m@th$\hfil \displaywidth\linewidth \hbox{\@eqnnum}\egroup
    \endtrivlist
  }%
\catcode`@=\active%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Eigene Befehle
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % Label an beliebiger Stelle mit beliebigem Symbol setzen
  % \mylabel{labelname}{(*)} liefert (*) nach \ref{labelname}
\catcode`@=11%%% Sorgt daruer, dass @ in Marconamen verwendet werden kann
\newcommand{\mylabel}[2]{\@bsphack
  \protected@write\@auxout{}%
  {\string\newlabel{#1}{{#2}{\thepage}}}%
  \@esphack}
\newcommand{\tmylabel}[2]{\@bsphack
  \protected@write\@auxout{}%
  {\string\newlabel{#1}{{#2}{\thepage}{\arabic{chapter}}}}%
  \@esphack}
\catcode`@=\active%
%%%% Die urspruengliche Fassung funktioniert aus irgendeinem Grund nicht mehr.
%\newcommand{\mylabel}[2]{\protect\immediate\write\@mainaux{\string\newlabel{#1}{{#2}{\thepage}}}}

%%% Erzeugt an der Stelle des Aufrufs einen nicht sichtbaren Punkt.
\newcommand{\leererpunkt}{
  \drawdim pt
  \begin{texdraw}
    \setgray 1
    \lcir r:0.01       
  \end{texdraw}
  }



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Eigene Zeichen 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % maximale Untergruppe / Normalteiler / Ideal
\newcommand{\lemax}{\mbox{$<\hspace{-4pt}\cdot\hspace{2pt}$}}
\newcommand{\lhdmax}{\mbox{$\lhd\cdot$}}
  % zweizeilige Matrix
\newcommand{\mymatrix}[2]{\mbox{\footnotesize $\left(\begin{array}{#1} #2\end{array}\right)$}}
  % Wurzelfunktion
%\newcommand{\sqrtn}[2]{\hspace*{2pt}^#1\hspace{-4pt}\sqrt{#2}}
\newcommand{\sqrtn}[2]{\sqrt[#1]{#2}}
  % Zeichen fuer transvers
\newcommand{\transvers}{\mbox{$\,\cap\hspace{-9pt}\mid\;$}} 
 % Option für MakeIndex
\newcommand{\uu}[1]{\underline{#1}}
 % Paragraph-Zeichen
\newcommand{\§}{\S}
 % Projektiver Raum ueber den komplexen Zahlen
\newcommand{\PC}{\P_{\!\!\scriptscriptstyle\C}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Bold-Zeichensatz fuer natuerliche Zahlen, etc.
%%% with amsmath package
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\newcommand{\N}{{\mathbbm N}}
%\newcommand{\A}{{\mathbbm A}}
%\newcommand{\Z}{{\mathbbm Z}}
%\newcommand{\R}{{\mathbbm R}}
%\newcommand{\C}{{\mathbbm C}}
%\newcommand{\Q}{{\mathbbm Q}}
%\renewcommand{\P}{{\mathbbm P}}
%\newcommand{\D}{{\mathbbm D}}
%\newcommand{\F}{{\mathbbm F}}
%\newcommand{\E}{{\mathbbm E}}
%\newcommand{\G}{{\mathbbm G}}
%\newcommand{\K}{{\mathbbm K}}
%\newcommand{\V}{{\mathbbm V}}
%\renewcommand{\H}{{\mathbbm H}}
\DeclareMathAlphabet{\mathds}{U}{dsrom}{m}{n}
\newcommand{\N}{{\mathds N}}
\newcommand{\A}{{\mathbbm A}}
\newcommand{\Z}{{\mathds Z}}
\newcommand{\R}{{\mathds R}}
\newcommand{\C}{{\mathds C}}
\newcommand{\Q}{{\mathds Q}}
\renewcommand{\P}{{\mathds P}}
\newcommand{\D}{{\mathds D}}
\newcommand{\F}{{\mathds F}}
\newcommand{\E}{{\mathds E}}
\newcommand{\G}{{\mathds G}}
\newcommand{\K}{{\mathds K}}
\newcommand{\V}{{\mathds V}}
\renewcommand{\H}{{\mathds H}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% new commands for fraktur charakters with oldgerm
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \newcommand{\m}{\textswab{m}} 
\newcommand{\m}{\mathfrak{m}} 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% new commands for calligraphic characters with amsmath 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\ka}{{\mathcal A}}
\newcommand{\kb}{{\mathcal B}}
\newcommand{\kc}{{\mathcal C}}
\newcommand{\kd}{{\mathcal D}}
\newcommand{\ke}{{\mathcal E}}
\newcommand{\kf}{{\mathcal F}}
\newcommand{\kg}{{\mathcal G}}
\newcommand{\kh}{{\mathcal H}}
\newcommand{\ki}{{\mathcal I}}
\newcommand{\kj}{{\mathcal J}}
\newcommand{\kk}{{\mathcal K}}
\newcommand{\kl}{{\mathcal L}}
\newcommand{\km}{{\mathcal M}}
\newcommand{\kn}{{\mathcal N}}
\newcommand{\ko}{{\mathcal O}}
\newcommand{\kp}{{\mathcal P}}
\newcommand{\kq}{{\mathcal Q}}
\newcommand{\kr}{{\mathcal R}}
\newcommand{\ks}{{\mathcal S}}
\newcommand{\kt}{{\mathcal T}}
\newcommand{\ku}{{\mathcal U}}
\newcommand{\kv}{{\mathcal V}}
\newcommand{\kw}{{\mathcal W}}
\newcommand{\kx}{{\mathcal X}}
\newcommand{\ky}{{\mathcal Y}}
\newcommand{\kz}{{\mathcal Z}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Postscript Schriftarten benutzen 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\DeclareFixedFont{\AdobeZapfChancery}{T1}{pzc}{m}{it}{10}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Mathematische Operatoren
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\DeclareMathOperator{\ann}{ann}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\Baselocus}{Baselocus}
\DeclareMathOperator{\Bil}{Bil}
\DeclareMathOperator{\Bl}{Bl}
\DeclareMathOperator{\Char}{char}
\DeclareMathOperator{\Cl}{\kc\!\!\;\ell\!\:}
\DeclareMathOperator{\codim}{codim}
\DeclareMathOperator{\Cok}{Cok}
\DeclareMathOperator{\coker}{coker}
\DeclareMathOperator{\Def}{Def}
\DeclareMathOperator{\Der}{Der}
\DeclareMathOperator{\Div}{Div}
\DeclareMathOperator{\Eig}{Eig}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\Exp}{Exp}
\DeclareMathOperator{\Ext}{Ext}
\DeclareMathOperator{\Fix}{Fix}
\DeclareMathOperator{\Gal}{Gal}
%\DeclareMathOperator{\gcd}{gcd}
\DeclareMathOperator{\GF}{GF}
\DeclareMathOperator{\ggT}{ggT}
\DeclareMathOperator{\Gl}{Gl}
\DeclareMathOperator{\height}{height}
\DeclareMathOperator{\Hau}{Hau}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\Hilb}{Hilb}
% Hom-Garbe - die Variable gibt die Schriftgroesse an
\newcommand{\HOM}[1]{\mbox{\DeclareFixedFont{\AZC}{T1}{pzc}{m}{it}{#1}\AZC Hom\,}}
\DeclareMathOperator{\Ker}{Ker}
\DeclareMathOperator{\kgV}{kgV}
\DeclareMathOperator{\length}{length}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\im}{Im}
\DeclareMathOperator{\ind}{ind}
\DeclareMathOperator{\Inn}{Inn}
\DeclareMathOperator{\jet}{jet}
\DeclareMathOperator{\Mat}{Mat}
\renewcommand{\mod}{\mbox{\rm mod }}
%\DeclareMathOperator{\mod}{mod}
\DeclareMathOperator{\modality}{mod}
\DeclareMathOperator{\Mor}{Mor}
\DeclareMathOperator{\mSpec}{\textswab{m}-Spec}
\DeclareMathOperator{\mult}{mult}
\DeclareMathOperator{\NS}{NS}
\DeclareMathOperator{\Num}{Num}
\DeclareMathOperator{\ord}{ord}
\DeclareMathOperator{\OO}{O}
\DeclareMathOperator{\Pic}{Pic}
\DeclareMathOperator{\pr}{pr}
\DeclareMathOperator{\Preshv}{Preshv}
\DeclareMathOperator{\Proj}{Proj}
\DeclareMathOperator{\PSL}{PSL}
\DeclareMathOperator{\Quot}{Quot}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\re}{Re}
\DeclareMathOperator{\Res}{Res}
\DeclareMathOperator{\Sec}{Sec}
\DeclareMathOperator{\Sing}{Sing}
\DeclareMathOperator{\Shv}{Shv}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\Sl}{Sl}
\DeclareMathOperator{\SO}{SO}
\DeclareMathOperator{\Spec}{Spec}
\DeclareMathOperator{\Spur}{Spur}
\DeclareMathOperator{\SU}{SU}
\DeclareMathOperator{\Syl}{Syl}
\DeclareMathOperator{\Sym}{Sym}
\DeclareMathOperator{\supp}{supp}
\DeclareMathOperator{\Tor}{Tor}
\DeclareMathOperator{\UU}{U}
\DeclareMathOperator{\ZFK}{ZFK}





















