\NeedsTeXFormat{LaTeX2e}[1996/06/01]
\ProvidesPackage{mathe}


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% Xenia Rendtel
% 02.10.2007
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Äquivalenzpfeile mit verschiedenen Abständen
% sowie weitere Pfeile
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\same}{\ensuremath{\Leftrightarrow}}
\newcommand{\qsame}{\quad\same\quad}
\newcommand{\lsame}{\ensuremath{\Longleftrightarrow}}
\newcommand{\qlsame}{\quad\lsame\quad}
\newcommand{\dsame}{\ensuremath{:\Leftrightarrow}}
\newcommand{\qdsame}{\quad\dsame\quad}
\newcommand{\ldsame}{\ensuremath{:\Longleftrightarrow}}
\newcommand{\qldsame}{\quad\ldsame\quad}
\newcommand{\samedef}{\ensuremath{\us {\text{def}} \Leftrightarrow}}
\newcommand{\qsamedef}{\quad\samedef\quad}
\newcommand{\lsamedef}{\ensuremath{\us {\text{def}} \Longleftrightarrow}}
\newcommand{\qlsamedef}{\quad\lsamedef\quad}
\newcommand{\lto}{\longrightarrow}
\newcommand{\qTo}{\quad\To\quad}
\newcommand{\sTo}{\ \To\ }
\newcommand{\To}{\ensuremath{\Rightarrow}}


%%
% Mengendefinitionen
%%

\newcommand{\N}{\ensuremath{\mathbb {N}}}
\newcommand{\Z}{\ensuremath{\mathbb {Z}}}
\newcommand{\Q}{\ensuremath{\mathbb {Q}}}
\newcommand{\R}{\ensuremath{\mathbb {R}}}
\newcommand{\C}{\ensuremath{\mathbb {C}}}
\renewcommand{\S}{\ensuremath{\mathbb {S}}}
\newcommand{\Prim}{\ensuremath{{\mathbb P}}}
\newcommand{\0}{\ensuremath{\emptyset}}
\renewcommand{\Re}{\ensuremath{\operatorname{Re}}}
\renewcommand{\Im}{\ensuremath{\operatorname{Im}}}


%%
% Logisches Und und Oder
%%

\newcommand{\sand}{\ensuremath{\; \land \;}}
\newcommand{\sor}{\ensuremath{\; \lor \;}}
\renewcommand{\*}{\ensuremath{\cdot}}
\newcommand{\od}{\vee}
\newcommand{\n}{\neg}
\newcommand{\un}{\wedge}


%%
% nicht Element von
%%

\newcommand{\nin}{\not\in}



%%
% Bei Integral, Summe,... die Grenzen über bzw. 
% unter das Zeichen
%%

\newcommand{\I}{\int\limits}
\newcommand{\Sum}{\sum\limits}
\newcommand{\Prod}{\prod\limits}
\newcommand{\Min}{\min\limits}
\newcommand{\Max}{\max\limits}
\newcommand{\Lim}{\lim\limits}
\newcommand{\Inf}{\inf\limits}
\newcommand{\Sup}{\sup\limits}
\newcommand{\Liminf}{\liminf\limits}
\newcommand{\Limsup}{\limsup\limits}
%\renewcommand{\Cup}{\bigcup\limits}
%\renewcommand{\Cap}{\bigcap\limits}
\newcommand{\Otimes}{\bigotimes\limits}
\newcommand{\Oplus}{\bigoplus\limits}




%%
% den Beweis schick machen
%%


% Ende des Beweises
\newcommand{\qed}{\mbox{}\hfill\ensuremath{\Box}}



\newcommand{\operp}{
  \settowidth{\length}{\ensuremath{\bigcirc}}
  \text{\makebox[\length]{
      \makebox[0pt]{\ensuremath{\bigcirc}}
      \makebox[0pt]{\ensuremath{\perp}}
}}}




%%
% Arcus Cotangens, Logarithmus
%%

\newcommand{\arcsinh}{\operatorname{arcsinh}}
\newcommand{\arccosh}{\operatorname{arccosh}}
\newcommand{\arctanh}{\operatorname{arctanh}}
\newcommand{\arccot}{\operatorname{arccot}}
\newcommand{\arccoth}{\operatorname{arccoth}}
\newcommand{\Log}{\operatorname{Log}}


%%
% Griechische Buchstaben
%%

\newcommand{\e}{\ensuremath{\varepsilon}}
%\renewcommand{\phi}{\varphi}
\renewcommand{\l}{\lambda}
\renewcommand{\t}{\tau}



%%
% Bezeichnungen
%%


\newcommand{\Rgn}{\R_{>0}} % R größer Null
\newcommand{\Rad}{\operatorname{Rad}}   % Radikal
\newcommand{\KGV}{\operatorname{KGV}}   % Kleinster gemeinsame Vielfache
\newcommand{\kgV}{\operatorname{kgV}}   % Kleinster gemeinsame Vielfache
\newcommand{\GGT}{\operatorname{GGT}}   % Größter gemeinsame Teiler
\newcommand{\ggT}{\operatorname{ggT}}   % Größter gemeinsame Teiler
\newcommand{\winkel}{\sphericalangle}          % Winkelsymbol
\newcommand{\dt}{\operatorname{dt}}   % Determinante
\newcommand{\dx}{\operatorname{dx}}   % Determinante
\newcommand{\dy}{\operatorname{dy}}   % Determinante
\newcommand{\dz}{\operatorname{dz}}   % Determinante
\newcommand{\vek}[1]{\overrightarrow{#1}}