%     plei.tex  =  sed-definitions  +  blei.tex   
%
%     abgeschlossene Wurzeln  \wu  ,  genau dann wenn  \gdw
%       = mit Doppelpunkt     \gll  \glr 
%     Halbpfeil ueber         \vc  ,  Punkt(e) ueber   \p \pp  
%     Punkt ueber Halbpfeil ueber  \pvc  
%     Zwei Punkte ueber Halbpfeil  \ppvc 
%     Halbpfeil-Buchstaben "small"        \vcsm
%     Halbpfeil ueber Schlange, kleine    \vcts   
%              bzw. grosse Buchstabem     \vctl
%     Gabel-Psi  \gps ,  Kurzer downarrow ueber  \apf
%     Lange Doppelpfeile  \lpfr \lpfl \lpfu \lpfd
%     Integral mit Kringel  \klint (in $ $)  \grint (in $$ $$)  
%     Anfuehrungsstriche unten und oben      \anfu \anfo
%     Stilisiertes Gross-A  \biga  \smala  , \ende . 
%
%     Abkuerzungen vorhandener Befehle :
%
\typeout{sqrt.sty --> (c) by H. Schulz (verbessert von Michael Schroeter)}
\def\nz{\par \noindent}  % 'neue Zeile' (ohne Einrueckung)
\def\schl#1{ \widetilde{#1} }
%  Klammern :
   \def\({\left(} \def\){\right)}  
   \def\lk{\,\left[ \,} \def\rk{\,\right] \,}
   \def\lb{\left\{} \def\rb{\right\}}  
   \def\lw{\left\langle} \def\rw{\right\rangle}
%  
\def\dis{ \displaystyle }    
\def\lsim{\,\lower 4pt\hbox{$\sim\!\!\!\!\!$}\raise 2pt\hbox{$<$}\,}
\def\gsim{\,\lower 4pt\hbox{$\sim\!\!\!\!\!$}\raise 2pt\hbox{$>$}\,}
\def\be{ \begin{equation} }  \def\bea{ \begin{eqnarray} }
\def\ee{ \end{equation} }    \def\eea{ \end{eqnarray} }
\def\sgn{\,\mbox{sgn}\,}    
%  ! !  :
\def\6{\partial }
%
%    das alte blei.tex  : 
%
   \def\wu#1{\sqrt{{#1} \,}^{ \hbox to0.19pt{\hss$ 
          \vrule height 2.7pt width 0.4pt depth -0.1pt $} \;\! } }
   \def\gdw{\leftharpoonup \hbox to-1pt{\hss $\rightharpoondown$} \;}
          \font\dick=cmbx10  \font\duenn=cmbx8
   \def\dop{\duenn \raise0.9pt\hbox to 0.2pt{: \hss}}
   \def\dep{\duenn \raise0.9pt\hbox to 0.3pt{\hss :}}
   \def\gll{\; \dop =}   \def\glr{= \dep \;}
   \def\pbox{\dick _{\hbox{.}} }  \def\ppbox{\dick _{\hbox{..}} }
   \def\pfeil{_\rightharpoonup}  \def\leer{\phantom{a}}
   \def\opf{\buildrel \pfeil \over \leer}
   \def\jvv{j \lower0.4pt\hbox to 2pt{\hss $\opf$}} 
   \def\jv{j \lower0.2pt\hbox to 1.4pt{\hss $\opf$}} 
   \def\ivv{i \lower0.4pt\hbox to 2pt{\hss $\opf$}} 
   \def\iv{i \lower0.2pt\hbox to 1.4pt{\hss $\opf$}} 
   \def\hq{h \raise0.2pt\hbox to 0.4pt{\hss $^-$}}   
   \def\vk#1{\hbox{$\buildrel           \pfeil \over #1$}}
   \def\vkk#1{\hbox{$\buildrel   \;     \pfeil \over #1$}}
   \def\vkkk#1{\hbox{$\buildrel  \, \;  \pfeil \over #1$}}
   \def\grpf{\displaystyle  _\rightharpoonup}
   \def\vg#1{\hbox{$\buildrel       \grpf \over #1$}}
   \def\vgg#1{\hbox{$\buildrel  \;  \grpf \over #1$}}
\def\fzz{f} \def\bzz{b} \def\dzz{d} \def\gzz{g} \def\hzz{h} \def\jzz{j} 
\def\kzz{k} \def\lzz{l} \def\mzz{m} \def\wzz{w} \def\tzz{t} \def\izz{i} 
\def\bezz{\beta} \def\dezz{\delta} \def\xizz{\xi} \def\pszz{\psi} 
\def\vthzz{\vartheta}
\def\uph{ \! \mathop{\vphantom{a}} } \def\dph{ \vphantom{a} }
\def\vc#1{\def\tast{\noexpand#1} \def\test{#1}
\ifcat\tast\bzz 
\ifx\test\fzz \vkkk f \uph \else   \ifx\test\bzz \vkk b \uph \else
\ifx\test\dzz \vkkk d \uph \else   \ifx\test\gzz \vkk g \dph \else
\ifx\test\hzz \vkk h \uph \else    \ifx\test\izz \ivv \dph \else 
\ifx\test\jzz \jvv \dph \else      \ifx\test\kzz \vkk k \uph \else
\ifx\test\lzz \vkk l \uph \else    \ifx\test\tzz \vkk t \uph \else
\ifx\test\mzz \vg m \dph \else     \ifx\test\wzz \vg w \dph \else 
\ifnum \lq#1<91 \vgg #1 \uph \else \vk #1 \dph 
  \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi   \else
\ifx\test\bezz \vkk \beta \uph \else  \ifx\test\pszz \vkk \psi \dph \else 
\ifx\test\dezz \vkk \delta \uph \else \ifx\test\xizz \vkk \xi \uph \else
\ifx\test\vthzz \vkk \vartheta \uph \else \vk #1 \dph
  \fi \fi \fi \fi \fi \fi }
\def\abst#1{\def\tast{\noexpand#1} \ifcat\tast\bzz 
    \ifnum \lq#1<91 \; \else \, \fi      \else \, \fi}
\def\absv#1{\def\tast{\noexpand#1} \def\test{#1}
\ifcat\tast\bzz \ifx\test\fzz \, \; \else  \ifx\test\dzz \, \; \else
\ifx\test\bzz \, \else \ifx\test\gzz \, \else \ifx\test\hzz \, \else
\ifx\test\kzz \, \else \ifx\test\lzz \, \else \ifx\test\tzz \, \else 
\ifnum \lq#1<91 \; \else   
  \fi \fi \fi \fi \fi \fi \fi \fi \fi \else
\ifx\test\bezz \, \else \ifx\test\pszz \, \else \ifx\test\dezz \, \else
\ifx\test\xizz \, \else \ifx\test\vthzz \, \else 
   \fi \fi \fi \fi \fi \fi }
\def\vphan#1{\def\tast{\noexpand#1} \def\test{#1}
\ifcat\tast\bzz \ifx\test\fzz  \uph \else \ifx\test\bzz  \uph \else
\ifx\test\dzz  \uph \else   \ifx\test\hzz  \uph \else
\ifx\test\kzz  \uph \else   \ifx\test\lzz  \uph \else
\ifx\test\tzz  \uph \else   \ifnum \lq#1<91  \uph \else \dph 
  \fi \fi \fi \fi \fi \fi \fi \fi \else
\ifx\test\bezz  \uph \else  \ifx\test\dezz  \uph \else
\ifx\test\xizz  \uph \else  \ifx\test\vthzz  \uph \else \dph
  \fi \fi \fi \fi \fi }
\def\p#1{{\buildrel \abst #1 \pbox \over #1} \vphan #1 }
\def\pp#1{{\buildrel \abst #1 \ppbox \over #1} \vphan #1 }
\def\pvc#1{{\buildrel \absv #1 \pbox \over {\vc #1}} \vphan #1 }
\def\ppvc#1{{\buildrel \absv #1 \ppbox \over {\vc #1}} \vphan #1 }
\def\vcsm#1{ \def\sm{\raise 1.6pt\hbox to 5pt{\hss $_#1$}} 
             {\buildrel \pfeil \over \sm} \>\!\! }
\def\vcts#1{\buildrel \absv #1 \pfeil \over {\schl #1} }
\def\vctl#1{\buildrel \absv #1 \grpf \over {\schl #1} }
\def\sinh{ {\rm sh} } \def\cosh{ {\rm ch} } \def\tanh{ {\rm th} } 
\def\cotanh{ {\rm cth} } \def\coth{ {\rm cth} } \def\sh{ {\rm sh} } 
\def\ch{ {\rm ch} }  \def\th{ {\rm th} }  \def\cth{ {\rm cth} } 
\def\gps{ \; \lower 2.6pt\hbox{$^\vert$} % 2.6
           \raise 1.4pt\hbox to 2.2pt{\hss $\cup$} \,} %1.6
\def\abpfeil{ \raise 1pt\hbox{ $_\vee$ \hskip -7.6pt
           \vrule depth 0.7pt height 4.7pt width 0.3pt} \;\; }
\def\apf#1{ \buildrel \abpfeil \over {#1} }
\def\lpfr{\hbox{$\, =\!\!\!=\!\!\!=\!\!\!\Longrightarrow \,$} }
\def\lpfl{\hbox{$\, \Longleftarrow\!\!\!=\!\!\!=\!\!\!= \,$} } 
\def\lpfu{\vbox to 15pt{\hbox{$\, \,\Uparrow \,$} \vss 
                        \hbox{$\, \>\Vert \,$} \vss}}
\def\lpfd{\vbox to 15pt{\vss \hbox{$\, \>\Vert \,$} \vss
                             \hbox{$\, \,\Downarrow \,$}}}
\def\biga{ \raise 2pt\hbox{$ \bigcap \!\!\!\!\!\!\> $} \hbox{$-$}  } 
\def\smala{ \hbox{$ \cap \!\!\!\!\!\!\; $} \lower 0.7pt\hbox{$-$}  } 
\font\gital=cmti10 scaled \magstep4   \def\Vau{\hbox{{\gital v$\!\>$}}}
\def\ende{ \hskip 5.64cm \vrule depth -2pt width 3cm height 2.5pt  
           \hskip -1.55cm $\bullet$ \nz }
%  ENDE           -1.55               -2               height 2.1

