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    %                                                               %
    %          tkz-func.sty      encodage : utf8                    %
    %                                                               %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %                                                               %
    %           Créé par Alain Matthes le 07-07-2007.               %
    %                                                               %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 14/09/2007 twoptoff --->off
%% Objet :  fonctions numériques en 2D
% 3.1 correction no need  real of calc
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\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{tkz-fct}[2008/02/05 v3.1 function ]
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%                          Initialisation
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\RequirePackage{tkz-base}
\FPmessagesfalse% 

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%            Tools
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%<–––––––– code from TeX in Practice ––––––––>
\newif\if@TestSubString
\def\SubStringConditional #1#2{%
    TT\fi
    \edef\@MainString{#1}%
    \edef\@SubStringConditionalTemp{{#1}{#2}}%
    \expandafter\@SubStringConditional\@SubStringConditionalTemp
}
\def\@SubStringConditional #1#2{% 
    \def\@TestSubS ##1#2##2\\{% 
        \def\@TestTemp{##1}% 
    }% 
    \@TestSubS #1#2\\
    \ifx\@MainString\@TestTemp
        \@TestSubStringfalse
    \else
        \@TestSubStringtrue
    \fi
    \if@TestSubString
}

\def\RecursionMacroEnd #1#2#3{% 
    #1\relax
        \def\@RecursionMacroEndNext{#2}% 
    \else
        \def\@RecursionMacroEndNext{#3}% 
    \fi
    \@RecursionMacroEndNext
}

\def\ReplaceSubStrings #1#2#3#4{%
    \def\@ReplaceResult{#1}%
    \edef\@ReplaceMain{#2}%
    \edef\@ReplaceSub{#3}%
    \edef\@ReplaceSubRep{#4}%
    \@ReplaceSubStrings
}
\def\@ReplaceSubStrings{% 
    \RecursionMacroEnd
        {\if\SubStringConditional{\@ReplaceMain}{\@ReplaceSub}}%
      {\@ReplaceSubStringsDo}{\expandafter\edef\@ReplaceResult{\@ReplaceMain}}%
}
\def\@ReplaceSubStringsDoX{%
    \def\@ReplaceSubStringsDoA ##1%
}%
\def\@ReplaceSubStringsDo{% 
    \expandafter\@ReplaceSubStringsDoX \@ReplaceSub
                                    ##2\@EndReplaceSubStrings{%
        \edef\@ReplaceMain{##1\@ReplaceSubRep ##2}%
    }%
    \expandafter\@ReplaceSubStringsDoA\@ReplaceMain
        \@EndReplaceSubStrings
    \@ReplaceSubStrings
}   
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               tkzfonct 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\define@cmdkey  [TKZ] {tkzf}{samples}{}
\define@cmdkey  [TKZ] {tkzf}{label}{}
\define@cmdkey  [TKZ] {tkzf}{lw}{}
\define@cmdkey  [TKZ] {tkzf}{style}{}
\define@cmdkey  [TKZ] {tkzf}{color}{}
\presetkeys     [TKZ] {tkzf}{%
                       samples   = 100,%
                       label     = {},%
                       color     = black,%
                       lw        = 0.8pt,%
                       style     = solid%
                       }{}

\newcommand*{\tkzFct}[1][]{\tkz@fct[#1]}% 

\def\tkz@fct[#1](#2..#3)#4{%
\setkeys[TKZ]{tkzf}{#1}%
  \ifTKZ@tkzInit@NO%
     \FPdiv{\xdelta}{\cmdTKZ@tkzInit@xorigine}{\cmdTKZ@tkzInit@xstep}%
     \FPdiv{\ydelta}{\cmdTKZ@tkzInit@yorigine}{\cmdTKZ@tkzInit@ystep}%
  \else        
     \FPset{\xdelta}{0}
     \FPset{\ydelta}{0}%
  \fi%
  \stepcounter{cmdTKZ@tkzf@fct}
  \expandafter\def\csname tkzFctgnu\alph{cmdTKZ@tkzf@fct}\endcsname{#4}%
  \def\x{(x*\cmdTKZ@tkzInit@xstep)}
  \FPeval\tkz@min{(#2)}  
  \FPeval\tkz@max{(#3)}  
  \FPdiv\tkz@ba{\tkz@min}{\cmdTKZ@tkzInit@xstep}
  \FPdiv\tkz@bb{\tkz@max}{\cmdTKZ@tkzInit@xstep} 

  \begin{scope}
    \clip (\tkz@xa,\tkz@ya) rectangle (\tkz@xb,\tkz@yb);
    \draw [xshift     = -\xdelta cm,%
           yshift     = -\ydelta cm,%
           line width = \cmdTKZ@tkzf@lw,%
           color      = \cmdTKZ@tkzf@color,\cmdTKZ@tkzf@style]%
     plot [id         = tkzfonct,%
           domain     = \tkz@ba:\tkz@bb,%
           samples    = \cmdTKZ@tkzf@samples]%
          function{(#4)/\cmdTKZ@tkzInit@ystep}%
     node[above left =6pt] {\cmdTKZ@tkzf@label};
  \end{scope}
  \ReplaceSubStrings{\tkz@tempa}{#4}{log}{ln}
  \ReplaceSubStrings{\tkz@tempb}{\tkz@tempa}{**}{^}
  \ReplaceSubStrings{\tkz@tempc}{\tkz@tempb}{\x}{x}
  \expandafter\edef\csname tkzFct\alph{cmdTKZ@tkzf@fct}\endcsname{\tkz@tempc}%
}

\newcommand*{\tkzFctPar}[1][]{\tkz@fctp[#1]}% 

\def\tkz@fctp[#1](#2..#3)#4#5{%
\setkeys[TKZ]{tkzf}{#1}%
  \ifTKZ@tkzInit@NO%
     \FPdiv{\xdelta}{\cmdTKZ@tkzInit@xorigine}{\cmdTKZ@tkzInit@xstep}%
     \FPdiv{\ydelta}{\cmdTKZ@tkzInit@yorigine}{\cmdTKZ@tkzInit@ystep}%
  \else        
     \FPset{\xdelta}{0}
     \FPset{\ydelta}{0}%
  \fi%
  \stepcounter{cmdTKZ@tkzf@fct}
  \def\t{(t*\cmdTKZ@tkzInit@xstep)} 
  \FPeval\tkz@min{(#2)}  
  \FPeval\tkz@max{(#3)}  
  \FPdiv\tkz@ba{\tkz@min}{\cmdTKZ@tkzInit@xstep}
  \FPdiv\tkz@bb{\tkz@max}{\cmdTKZ@tkzInit@xstep} 

  \begin{scope}
	\twoptoff
    \clip (\tkz@xa,\tkz@ya) rectangle (\tkz@xb,\tkz@yb);
    \draw [xshift     = -\xdelta cm,%
           yshift     = -\ydelta cm,%
           line width = \cmdTKZ@tkzf@lw,%
           color      = \cmdTKZ@tkzf@color,\cmdTKZ@tkzf@style]%
     plot [parametric,%
           id         = tkzfonct,%
           domain     = \tkz@ba:\tkz@bb,%
           samples    = \cmdTKZ@tkzf@samples]%
         function {(#4)/\cmdTKZ@tkzInit@ystep,(#5)/\cmdTKZ@tkzInit@ystep}
     node[above left =6pt] {\cmdTKZ@tkzf@label};
\twopton
  \end{scope}
}

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                                  tangente 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\tikzstyle{StyleTan}=[->,>=latex]
\define@cmdkey [TKZ] {tan} {color}{}
\define@cmdkey [TKZ] {tan} {lw}{}
\define@cmdkey [TKZ] {tan} {style}{}
\define@cmdkey [TKZ] {tan} {kr}{}
\define@cmdkey [TKZ] {tan} {kl}{}
\define@cmdkey [TKZ] {tan} {pos}{}
\define@cmdkey [TKZ] {tan} {mark}{}
\define@cmdkey [TKZ] {tan} {size}{}
\define@cmdkey [TKZ] {tan} {colorpt}{}
\define@boolkey[TKZ] {tan} {nopoint}[true]{}  
\define@boolkey[TKZ] {tan} {noname}[true]{}
\define@boolkey[TKZ] {tan} {coord}[true]{}  
\presetkeys    [TKZ] {tan} {%
                   style     = solid,%
                   lw        = .8pt,%
                   color     = blue,%
                   kr        = 1,%
                   kl        = 1,%
                   mark      = *,% 
                   size      = 1pt,%
                   colorpt   = black,%
                   pos       = below right,%
                   nopoint   = false,%
                   coord     = false,% 
                   noname    = false}{}%

\newcommand*{\tkzTan}[1][]{\tkz@Tan[#1]}%
\def\tkz@Tan[#1]#2(#3)#{
  \setkeys[TKZ]{tan}{#1}%
  \FPeval\x{(#3)}%
  \FPeval\img{#2}
  \let\y #2%
  \let\xx\x%
  \let\ydeltah\img
  \tkz@@Tan
}
\def\tkz@@Tan#1{%
  \tkz@ptStar(\x,\img){#1}
  \FPdiv{\krx}{\cmdTKZ@tan@kr}{\cmdTKZ@tkzInit@xstep}
  \FPdiv{\kry}{\cmdTKZ@tan@kr}{\cmdTKZ@tkzInit@ystep}
  \FPdiv{\klx}{\cmdTKZ@tan@kl}{\cmdTKZ@tkzInit@xstep}
  \FPdiv{\kly}{\cmdTKZ@tan@kl}{\cmdTKZ@tkzInit@ystep}
   % demi tgt--> droite
  \FPifzero{\cmdTKZ@tan@kr} \else%
  \FPadd{\x}{\xx}{0.000001}
  \FPeval\img{\y}% 
  \FPadd{\deltay}{\ydeltah}{-\img}
  \FPmul{\tkz@pente}{\deltay}{1000000}
  \draw[StyleTan,%
        color      = \cmdTKZ@tan@color,%
        line width = \cmdTKZ@tan@lw]%
        (#1.center)--++(\krx cm,%
                           -\kry * \tkz@pente cm );\fi%
  % demi tgt --> gauche
  \FPifzero{\cmdTKZ@tan@kl} \else%
  \FPadd{\x}{\xx}{-0.000001} 
  \FPeval\img{\y}% 
  \FPadd{\deltay}{\ydeltah}{-\img}
  \FPmul{\tkz@pente}{\deltay}{-1000000}
  \draw[StyleTan,%
        color      = \cmdTKZ@tan@color,%
        line width = \cmdTKZ@tan@lw]%
        (#1.center)--++(-\klx cm,%
                        \kly * \tkz@pente cm );\fi%
   \presetkeys  [TKZ] {pt}{%
                   mark     = \cmdTKZ@tan@mark,% 
                   size     = \cmdTKZ@tan@size,%
                   color    = \cmdTKZ@tan@colorpt,% 
                   pos      = \cmdTKZ@tan@pos}{}

\ifTKZ@tan@nopoint \else%
  \ifTKZ@tan@noname \presetkeys[TKZ]{pt}{noname = true}{}%
         \else%
              \presetkeys[TKZ]{pt}{noname = false}{}%
           \fi%
  \ifTKZ@tan@coord \presetkeys[TKZ]{pt}{coord = true}{}%
         \else%
              \presetkeys[TKZ]{pt}{coord = false}{}%
         \fi% 

\tkzDrawPoint(#1) \fi   
}  

%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                            point d'une courbe 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\tkzFctPt}[1][]{\tkz@fctpt[#1]}%
\def\tkz@fctpt[#1]#2(#3)#{
  \setkeys[TKZ]{pt}{#1}%
  \FPeval\x{(#3)}%
  \FPeval\y{#2}
   \tkz@defpoint
}
\def\tkz@defpoint#1{
  \tkz@ptStar(\x,\y){#1}%
  \tkz@DrawPoint{#1}%
} 


%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                               tkzAera 
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>% pb avec les unités
\define@cmdkey [TKZ] {aire}{color}{}
\define@cmdkey [TKZ] {aire}{opacity}{}
\define@cmdkey [TKZ] {aire}{samples}{}
\define@cmdkey [TKZ] {aire}{style}{} %18/03
\presetkeys    [TKZ] {aire}{%
                     color   = lightgray,
                     opacity = 0.5,
                     style   = {},
                     samples = 200%
                     }{}

\newcommand*{\tkzAera}[1][]{\tkz@aire[#1]}%
\def\tkz@aire[#1](#2..#3){%
   \setkeys[TKZ]{aire}{#1}%
   \ifTKZ@tkzInit@NO%
      \FPdiv{\xdelta}{\cmdTKZ@tkzInit@xorigine}{\cmdTKZ@tkzInit@xstep}%
      \FPdiv{\ydelta}{\cmdTKZ@tkzInit@yorigine}{\cmdTKZ@tkzInit@ystep}%
   \else        
      \FPset{\xdelta}{0}
      \FPset{\ydelta}{0}%
   \fi%
   % essai du test sur xstep
  \def\x{(x*\cmdTKZ@tkzInit@xstep)}
  \FPeval\tkz@min{(#2)}  
  \FPeval\tkz@max{(#3)}  
  \FPdiv\tkz@ba{\tkz@min}{\cmdTKZ@tkzInit@xstep}
  \FPdiv\tkz@bb{\tkz@max}{\cmdTKZ@tkzInit@xstep} 

   \begin{scope} 
   \protected@edef\@tempa{%
   \noexpand  \fill[color        = \cmdTKZ@aire@color,%
                    fill opacity = \cmdTKZ@aire@opacity,%
                    \cmdTKZ@aire@style]%18/03/07
     (\tkz@ba,0)--plot [id          = tkzfonct,%
                        domain     = \tkz@ba:\tkz@bb,%
                        samples    = \cmdTKZ@tkzf@samples]%
       function{(\tkzFctgnua)/\cmdTKZ@tkzInit@ystep}--(\tkz@bb,0);}\@tempa
   \end{scope}
}
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
%                             tkzAerafg
%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––>
\newcommand*{\tkzAerafg}[1][]{\tkz@airefg[#1]}%
\def\tkz@airefg[#1](#2..#3)#4#5{%
\setkeys[TKZ]{aire}{#1}%
\ifTKZ@tkzInit@NO%
   \FPdiv{\xdelta}{\cmdTKZ@tkzInit@xorigine}{\cmdTKZ@tkzInit@xstep}%
   \FPdiv{\ydelta}{\cmdTKZ@tkzInit@yorigine}{\cmdTKZ@tkzInit@xstep}%
\else        
   \FPset{\xdelta}{0}
   \FPset{\ydelta}{0}%
\fi%
% essai du test sur xstep
\def\x{(x*\cmdTKZ@tkzInit@xstep)}
  \FPeval\tkz@min{(#2)}  
  \FPeval\tkz@max{(#3)}  
  \FPdiv\tkz@ba{\tkz@min}{\cmdTKZ@tkzInit@xstep}
  \FPdiv\tkz@bb{\tkz@max}{\cmdTKZ@tkzInit@xstep} 
  \begin{scope} 
    \clip (\tkz@ba,\tkz@ya)--plot[id=tkzfonct,%
          domain = \tkz@ba:\tkz@bb,samples=\cmdTKZ@aire@samples]%
          function{(#4)/\cmdTKZ@tkzInit@ystep}--(\tkz@bb,\tkz@ya);%
    \clip (\tkz@ba,\tkz@yb)--plot[id=tkzfonct,%
          domain = \tkz@ba:\tkz@bb,samples=\cmdTKZ@aire@samples]%
          function{(#5)/\cmdTKZ@tkzInit@ystep}--(\tkz@bb,\tkz@yb);
   \protected@edef\@tempa{%
      \noexpand%
      \fill[color=\cmdTKZ@aire@color,%
            fill opacity=0.4,%
            \cmdTKZ@aire@style]%
         (\tkz@ba,\tkz@ya) rectangle (\tkz@bb,\tkz@yb);}\@tempa
  \end{scope}
}


%<––––––––––––––––––––––––––––––– fin –––––––––––––––––––––––––––––––––––––––>
\endinput