new graphics package tkz-fct (5jun11)

git-svn-id: svn://tug.org/texlive/trunk@22831 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 714 insertions, 0 deletions

diff --git a/Master/texmf-dist/tex/latex/tkz-fct/tkz-fct.sty b/Master/texmf-dist/tex/latex/tkz-fct/tkz-fct.sty
new file mode 100644
index 00000000000..86aa260a027
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+++ b/Master/texmf-dist/tex/latex/tkz-fct/tkz-fct.sty
@@ -0,0 +1,714 @@
+% Copyright 2011 by Alain Matthes
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.   
+%
+    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+    %                                                               %
+    %          tkz-fct.sty      encodage : utf8                     %
+    %                                                               %
+    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+    %                                                               %
+    %           Créé par Alain Matthes le 16-01-2011                %
+    %                                                               %
+    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Objet :  fonctions numériques en 2D with gnuplot 
+
+% constants from tkz-base 
+% \tkz@init@xstep
+% \tkz@init@ystep
+%<--------------------------------------------------------------------------->
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{tkz-fct}[2011/06/01 1.16 c function ] 
+\newcount\tkz@tkzf@fct
+\edef\tkzTWOPTCode{\the\catcode`\:} 
+\tkz@tkzf@fct=0 % 
+\def\tkzfctloaded{} 
+%<--------------------------------------------------------------------------->
+%                          Initialisation
+%<--------------------------------------------------------------------------->
+\RequirePackage{tkz-base}
+% % Code from Christian Tellechea 2009 % modified by AM
+% modified \FP@pow from fp.sty
+\def\FP@pow#1#2#3{%
+ \FP@beginmessage{POW}%
+ {\def\FP@beginmessage##1{}%
+ \def\FP@endmessage##1{}%
+ \FPifzero{#2}%
+     \expandafter\@firstoftwo
+ \else
+     \expandafter\@secondoftwo
+ \fi
+ {\FP@pow@zero{#3}}%
+ {\FPifint{#3}%
+     \expandafter\@firstoftwo
+ \else
+    \expandafter\@secondoftwo
+ \fi  
+{\FPifneg{#2}%
+ \FPneg\FP@tmpd{#2}%
+ \FPln\FP@tmpd\FP@tmpd
+ \FPmul\FP@tmpd\FP@tmpd{#3}%
+ \FPexp\FP@tmpd\FP@tmpd
+ \FPtrunc\FP@tmp{#3}0%
+ \ifodd\FP@tmp
+     \FPneg\FP@tmp\FP@tmpd
+ \else
+     \let\FP@tmp\FP@tmpd
+ \fi
+\else
+ \FPln\FP@tmpd{#2}%
+ \FPmul\FP@tmpd\FP@tmpd{#3}%
+ \FPexp\FP@tmp\FP@tmpd
+\fi
+}% 
+{\FPln\FP@tmpd{#2}%
+ \FPmul\FP@tmpd\FP@tmpd{#3}%
+ \FPexp\FP@tmp\FP@tmpd}%
+}%
+\global\let\FP@tmp\FP@tmp}%
+\FP@endmessage{}%
+\let#1\FP@tmp}
+%<--------------------------------------------------------------------------->
+%                               Styles 
+%<--------------------------------------------------------------------------->
+\def\tkzfctset#1{\pgfkeys{/tkztan/.cd,#1}}
+
+\tkzfctset{tan style/.style={->,>=latex}}                %<--------------------------------------------------------------------------->
+%                               tkzFct 
+%<--------------------------------------------------------------------------->
+\newif\iftkz@draw 
+\newif\iftkz@fp
+\def\tkz@dmin{-5}\def\tkz@dmax{5} 
+\pgfkeys{%
+/tkzfct/.cd,
+domain/.code args={#1:#2} {\FPeval\tkz@min{(#1)}
+                           \FPeval\tkz@max{(#2)}}, 
+samples/.code          =  {\edef\tkz@fct@samples{#1}}, 
+id/.code               =  {\edef\tkz@fct@id{#1}},
+fp/.is          if     = tkz@fp,
+fp/.default            = false,  
+/tkzfct/.unknown/.code =  {\let\searchname=\pgfkeyscurrentname
+                           \pgfkeysalso{\searchname/.try=#1,
+                           /tikz/\searchname/.retry=#1}}}  
+
+\def\tkzFct{\pgfutil@ifnextchar[{\tkzActivOff\tkz@fct}{\tkz@fct[]}} 
+\def\tkz@fct[#1]#2{%
+\pgfkeys{/tkzfct/.cd,
+domain      = \@xa:\@xb,
+samples     = 200,
+fp          = true,
+id          = tkzfct}
+\pgfqkeys{/tkzfct}{#1}%
+\iftkz@init@NO%
+  \FPdiv{\tkz@x@delta}{\tkz@init@xorigine}{\tkz@init@xstep}%
+  \FPdiv{\tkz@y@delta}{\tkz@init@yorigine}{\tkz@init@ystep}%
+\else
+  \FPset{\tkz@x@delta}{0}%
+  \FPset{\tkz@y@delta}{0}%
+\fi% 
+% stockage
+\advance\tkz@tkzf@fct by  1 %
+\FPdiv\tkz@ba{\tkz@min}{\tkz@init@xstep}%
+\FPdiv\tkz@bb{\tkz@max}{\tkz@init@xstep}%
+\def\x{(x*\tkz@init@xstep)}%
+\expandafter\edef\csname tkzFctgnu\@alph\tkz@tkzf@fct \endcsname{#2}%
+\expandafter\edef\csname tkzFctgnuLast\endcsname{#2}     
+\begin{scope}[samples    = \tkz@fct@samples,#1]
+ \clip (\tkz@xa,\tkz@ya) rectangle (\tkz@xb,\tkz@yb);
+ \draw[xshift  = -\tkz@x@delta cm,yshift  = -\tkz@y@delta cm,/tkzfct/.cd]%
+ plot[id=\tkz@fct@id,domain= \tkz@ba:\tkz@bb]%
+ function{(#2)/\tkz@init@ystep};%
+\end{scope} 
+   \let\tkz@tmp@xstep\tkz@init@xstep
+   \def\tkz@init@xstep{1}
+\iftkz@fp%       
+   \ReplaceSubStrings{\tkz@tempa}{#2}{log}{ln}
+   \ReplaceSubStrings{\tkz@tempb}{\tkz@tempa}{**}{^}
+   \ReplaceSubStrings{\tkz@tempa}{\tkz@tempb}{\x}{x}
+   \ReplaceSubStrings{\tkz@tempb}{\tkz@tempa}{asin}{arcsin}
+   \ReplaceSubStrings{\tkz@tempa}{\tkz@tempb}{acos}{arccos}
+   \ReplaceSubStrings{\tkz@tempb}{\tkz@tempa}{atan}{arctan} 
+  \expandafter\edef\csname tkzFct\@alph\tkz@tkzf@fct\endcsname{\tkz@tempb}%
+  \expandafter\edef\csname tkzFctLast\endcsname{\tkz@tempb}%
+ \fi 
+  \let\tkz@init@xstep\tkz@tmp@xstep 
+ \catcode`\:=\tkzTWOPTCode\relax   
+}%
+%<--------------------------------------------------------------------------->
+%                            point d'une courbe (new method)
+%<--------------------------------------------------------------------------->
+\pgfkeys{%
+/tkzfctpt/.cd, 
+draw/.is if   = tkz@draw,
+draw/.default = true,
+with/.code    = \global\def\tkz@fct@used{#1},
+ref/.code     = \global\def\tkz@fct@ref{#1}}
+                           
+\def\tkzDefPointByFct{\pgfutil@ifnextchar[{\tkz@fctpoint}{\tkz@fctpoint[]}}   
+\def\tkz@fctpoint[#1](#2){%
+\pgfkeys{/tkzfctpt/.cd,
+         draw  = false,
+         with  = {},
+         ref   = {}}
+\pgfqkeys{/tkzfctpt}{#1}
+
+  \FPeval\x{(#2)}%
+   \ifx\tkzutil@empty\tkz@fct@used
+       \FPeval\tkz@fx{\tkzFctLast}  
+   \else 
+      \edef\tkz@fct{\csname tkzFct\tkz@fct@used\endcsname}
+         \FPeval\tkz@fx{\tkz@fct}
+    \fi   
+  \tkzDefPoint(\x,\tkz@fx){tkzPointResult}%
+       \iftkz@draw
+     \tkzDrawPoint(tkzPointResult)
+     \fi
+\ifx\tkzutil@empty\tkz@fct@ref 
+\else
+  \tkzGetPoint{\tkz@fct@ref}
+\fi
+}%
+%<--------------------------------------------------------------------------->
+%                                  tangente \tkzDrawTangentLine
+%<--------------------------------------------------------------------------->
+\pgfkeys{%
+/tkztan/.cd,
+draw/.is if            = tkz@draw,
+draw/.default          = true,
+with/.code             = \global\def\tkz@fct@used{#1},
+kr/.code               = {\edef\tkz@tan@kr{#1}},
+kl/.code               = {\edef\tkz@tan@kl{#1}},
+/tkztan/.unknown/.code = {\let\searchname=\pgfkeyscurrentname
+                          \pgfkeysalso{\searchname/.try=#1,
+                          /tikz/\searchname/.retry=#1}}
+}%
+%<--------------------------------------------------------------------------->
+\def\tkzDrawTangentLine{\pgfutil@ifnextchar[{\tkz@DrawTangentLine}{%
+                                             \tkz@DrawTangentLine[]}} 
+\def\tkz@DrawTangentLine[#1](#2){%
+\begingroup
+\pgfkeys{/tkztan/.cd,
+         draw  = false,
+         with  = {},   
+         kr    = 1,
+         kl    = 1}
+\pgfqkeys{/tkztan}{#1}
+\FPeval\x{(#2)}%
+\ifx\tkzutil@empty\tkz@fct@used
+    \FPeval\tkz@img{\tkzFctLast}
+    \let\tkz@fct\tkzFctLast  
+\else 
+   \edef\tkz@fct{\csname tkzFct\tkz@fct@used\endcsname}
+      \FPeval\tkz@img{\tkz@fct}
+ \fi
+\let\tkz@old@img\tkz@img
+\let\tkz@old@x\x
+\tkzDefPoint(\tkz@old@x,\tkz@old@img){tkzPointResult}  
+\FPdiv{\tkz@krx}{\tkz@tan@kr}{\tkz@init@xstep}
+\FPdiv{\tkz@kry}{\tkz@tan@kr}{\tkz@init@ystep}
+\FPdiv{\tkz@klx}{\tkz@tan@kl}{\tkz@init@xstep}
+\FPdiv{\tkz@kly}{\tkz@tan@kl}{\tkz@init@ystep}
+ % demi tgt--> droite
+\FPifzero{\tkz@tan@kr}%
+\else
+\FPadd{\x}{\tkz@old@x}{0.000001}%
+\FPeval\tkz@img{\tkz@fct}% 
+\FPadd{\tkz@deltay}{\tkz@old@img}{-\tkz@img}%
+\FPmul{\tkz@slope}{\tkz@deltay}{1000000}%
+\protected@edef\tkz@temp{%
+\noexpand\draw[/tkztan/tan style,/tkztan/.cd,#1]}\tkz@temp%
+      (tkzPointResult)--++(\tkz@krx,-\tkz@kry*\tkz@slope);
+\fi
+% demi tgt --> gauche
+\FPifzero{\tkz@tan@kl}%
+ \else
+\FPadd{\x}{\tkz@old@x}{-0.000001} 
+\FPeval\tkz@img{\tkz@fct}% 
+\FPadd{\tkz@deltay}{\tkz@old@img}{-\tkz@img}
+\FPmul{\tkz@slope}{\tkz@deltay}{-1000000}
+\protected@edef\tkz@temp{%
+\noexpand\draw[/tkztan/tan style,/tkztan/.cd,#1]}\tkz@temp%
+     (tkzPointResult)--++(-\tkz@klx,\tkz@kly*\tkz@slope);
+  \fi
+     \iftkz@draw
+     \tkzDrawPoint(tkzPointResult)
+     \fi  
+\endgroup 
+}
+%<--------------------------------------------------------------------------->
+%                               tkzArea 
+%<--------------------------------------------------------------------------->
+\pgfkeys{%
+/tkzarea/.cd,
+domain/.code args={#1:#2}     {\FPeval\tkz@min{(#1)}
+                               \FPeval\tkz@max{(#2)}}, 
+opacity/.code              =  {\edef\tkz@fct@opacity{#1}},
+id/.code                   =  {\edef\tkz@fct@id{#1}},
+color/.code                =  {\edef\tkz@fct@color{#1}},
+samples/.code              =  {\edef\tkz@fct@samples{#1}},
+/tkzarea/.unknown/.code    =  {\let\searchname=\pgfkeyscurrentname
+                                 \pgfkeysalso{\searchname/.try=#1,
+                                   /tikz/\searchname/.retry=#1}}}
+\def\tkzArea{\pgfutil@ifnextchar[{\catcode`\:=12 \tkz@aire}{\tkz@aire[]}}
+\def\tkz@aire[#1]{%
+\begingroup
+\pgfkeys{%
+/tkzarea/.cd,
+domain     = -5:5,   
+color      =  \tkz@otherlinecolor,
+samples    =  200,
+id         =  tkzfonct,
+opacity    =  .5}    
+\pgfqkeys{/tkzarea}{#1}
+\iftkz@init@NO
+   \FPdiv{\tkz@x@delta}{\tkz@init@xorigine}{\tkz@init@xstep}%
+   \FPdiv{\tkz@y@delta}{\tkz@init@yorigine}{\tkz@init@ystep}%
+\else        
+   \FPset{\tkz@x@delta}{0}
+   \FPset{\tkz@y@delta}{0}%
+\fi%
+\def\x{(x*\tkz@init@xstep)}
+\FPdiv\tkz@ba{\tkz@min}{\tkz@init@xstep}%
+\FPdiv\tkz@bb{\tkz@max}{\tkz@init@xstep}%
+\begin{scope}[] 
+  \path[ fill,  
+         xshift       = -\tkz@x@delta cm,
+         yshift       = -\tkz@y@delta cm,
+         color        = \tkz@fct@color,%
+         fill opacity = \tkz@fct@opacity,#1,
+         domain       = \tkz@ba:\tkz@bb,
+         samples      = \tkz@fct@samples]%
+        (\tkz@ba,0)--plot [id = \tkz@fct@id]%
+       function{(\tkzFctgnuLast)/\tkz@init@ystep}--(\tkz@bb,0);
+   \end{scope}
+\endgroup
+}
+\let\tkzDrawArea\tkzArea 
+%<--------------------------------------------------------------------------->
+%                             tkzAreafg
+%<--------------------------------------------------------------------------->
+\pgfkeys{/tkzareafg/.cd,
+domain/.code args={#1:#2} {\FPeval\tkz@min{(#1)}
+                           \FPeval\tkz@max{(#2)}},  
+between/.code args={#1 and #2}{\def\tkz@below{#1}
+                               \def\tkz@above{#2}},
+opacity/.code             =  {\edef\tkz@fct@opacity{#1}},
+id/.code                  =  {\edef\tkz@fct@id{#1}},
+color/.code               =  {\edef\tkz@fct@color{#1}},
+samples/.code             =  {\edef\tkz@fct@samples{#1}},
+/tkzareafg/.unknown/.code =  {\let\searchname=\pgfkeyscurrentname
+                                 \pgfkeysalso{\searchname/.try=#1,
+                                   /tikz/\searchname/.retry=#1}}} 
+\def\tkzAreafg{\pgfutil@ifnextchar[{\tkz@airefg}{\tkz@airefg[]}} 
+\def\tkz@airefg[#1]{%
+\begingroup
+\pgfkeys{/tkzareafg/.cd,
+domain     = -5:5, 
+between    = a and b,
+color      =  lightgray,
+samples    =  200,
+id         =  tkzfonct,
+opacity    =  .5
+}     
+\pgfqkeys{/tkzareafg}{#1}
+\def\tkz@fctsup{\csname tkzFctgnu\tkz@below\endcsname}
+\def\tkz@fctinf{\csname tkzFctgnu\tkz@above\endcsname}
+\iftkz@init@NO%
+   \FPdiv{\tkz@x@delta}{\tkz@init@xorigine}{\tkz@init@xstep}%
+   \FPdiv{\tkz@y@delta}{\tkz@init@yorigine}{\tkz@init@xstep}%
+\else        
+   \FPset{\tkz@x@delta}{0}
+   \FPset{\tkz@y@delta}{0}%
+\fi%
+% essai du test sur xstep
+\def\x{(x*\tkz@init@xstep)}
+\FPdiv\tkz@ba{\tkz@min}{\tkz@init@xstep}
+\FPdiv\tkz@bb{\tkz@max}{\tkz@init@xstep}
+\begin{scope}[domain  = \tkz@ba:\tkz@bb,
+              samples = \tkz@fct@samples,
+              id      = \tkz@fct@id] 
+ \clip (\tkz@ba,\tkz@ya)--plot function{(\tkz@fctsup)/\tkz@init@ystep}%
+                        --(\tkz@bb,\tkz@ya);%
+ \clip (\tkz@ba,\tkz@yb)--plot function{(\tkz@fctinf)/\tkz@init@ystep}%
+                        --(\tkz@bb,\tkz@yb);
+  \fill [color        = \tkz@fct@color,
+         fill opacity = \tkz@fct@opacity,
+         /tkzareafg/.cd,
+         #1]%
+        (\tkz@ba,\tkz@ya) rectangle (\tkz@bb,\tkz@yb);
+\end{scope}
+\endgroup
+} 
+\let\tkzDrawAreafg\tkzAreafg 
+\def\tkz@pamin{-5}\def\tkz@pamax{5} 
+%<--------------------------------------------------------------------------->
+%                               tkzFctPar 
+%<--------------------------------------------------------------------------->
+\def\tkzFctPar{\pgfutil@ifnextchar[{\catcode`\:=12 \tkz@fctp}{\tkz@fctp[]}} 
+\def\tkz@fctp[#1]#2#3{%
+\begingroup
+\pgfkeys{%
+/tkzfct/.cd,
+domain      = \tkz@pamin:\tkz@pamax,
+samples     = 200,
+fp          = true, 
+id          = tkzfct}
+\pgfqkeys{/tkzfct}{#1}  
+  \iftkz@init@NO%
+     \FPdiv{\tkz@x@delta}{\tkz@init@xorigine}{\tkz@init@xstep}%
+     \FPdiv{\tkz@y@delta}{\tkz@init@yorigine}{\tkz@init@ystep}%
+  \else
+     \FPset{\tkz@x@delta}{0}
+     \FPset{\tkz@y@delta}{0}%
+  \fi%
+ \begin{scope}[samples    = \tkz@fct@samples]
+  \tkzActivOff
+    \clip (\tkz@xa,\tkz@ya) rectangle (\tkz@xb,\tkz@yb);
+    \draw [xshift     = -\tkz@x@delta cm,%
+           yshift     = -\tkz@y@delta cm,
+           /tkzfct/.cd, #1]%
+     plot [parametric,domain     = \tkz@min:\tkz@max,%
+           id         = tkzparfct]%
+         function {(#2)/\tkz@init@xstep,(#3)/\tkz@init@ystep};
+  \tkzActivOn
+  \end{scope}
+\endgroup
+} 
+%<--------------------------------------------------------------------------->
+%                               tkzFctPolar 
+%<--------------------------------------------------------------------------->
+\def\tkz@pomin{0}\def\tkz@pomax{2*pi}  
+\def\tkzFctPolar{\pgfutil@ifnextchar[{%
+                 \catcode`\:=12 \tkz@FctPolar}{\tkz@FctPolar[]}} 
+\def\tkz@FctPolar[#1]#2{%
+\begingroup
+\pgfkeys{%
+/tkzfct/.cd,
+domain      = \tkz@pomin:\tkz@pomax,
+fp          = true, 
+samples     = 200,
+id          = tkzfctpolar}
+\pgfqkeys{/tkzfct}{#1}  
+  \iftkz@init@NO%
+     \FPdiv{\tkz@x@delta}{\tkz@init@xorigine}{\tkz@init@xstep}%
+     \FPdiv{\tkz@y@delta}{\tkz@init@yorigine}{\tkz@init@ystep}%
+  \else
+     \FPset{\tkz@x@delta}{0}
+     \FPset{\tkz@y@delta}{0}%
+  \fi%
+  
+  \begin{scope}
+  \tkzActivOff
+    \draw [xshift     = -\tkz@x@delta cm,%
+           yshift     = -\tkz@y@delta cm,
+           /tkzfct/.cd, #1]%
+     plot [raw gnuplot,id = tkzpolarfct]%
+         function { set polar;set samples \tkz@fct@samples ; set trange  [\tkz@min:\tkz@max]; plot (#2)/\tkz@init@xstep};
+  \tkzActivOn
+  \end{scope}
+\endgroup
+} 
+%<--------------------------------------------------------------------------->
+%                               tkzDrawRiemannSum 
+%<--------------------------------------------------------------------------->
+\pgfkeys{/tkzriemann/.cd,
+interval/.code args={#1:#2} {\FPeval\tkz@min{(#1)}
+                             \FPeval\tkz@max{(#2)}},
+number/.code                =  {\edef\tkz@fct@nb{#1}},   
+opacity/.code               =  {\edef\tkz@fct@opacity{#1}},
+color/.code                 =  {\edef\tkz@fct@color{#1}},
+/tkzriemann/.unknown/.code  =  {\let\searchname=\pgfkeyscurrentname
+                                 \pgfkeysalso{\searchname/.try=#1,
+                                   /tikz/\searchname/.retry=#1}}} \def\tkzDrawRiemannSum{\pgfutil@ifnextchar[{%
+                 \catcode`\:=12 \tkz@DrawRiemannSum}{\tkz@DrawRiemannSum[]}} 
+\def\tkz@DrawRiemannSum[#1]{%
+\begingroup
+\pgfkeys{%
+/tkzriemann/.cd,
+interval        = 1:2,
+number          = 10,
+opacity         = 0.5,
+line width      = 1pt}
+\pgfqkeys{/tkzriemann}{#1}  
+  \iftkz@init@NO%
+     \FPdiv{\tkz@x@delta}{\tkz@init@xorigine}{\tkz@init@xstep}%
+     \FPdiv{\tkz@y@delta}{\tkz@init@yorigine}{\tkz@init@ystep}%
+  \else
+     \FPset{\tkz@x@delta}{0}
+     \FPset{\tkz@y@delta}{0}%
+  \fi%
+\FPadd\tkz@intwd{\tkz@max}{-\tkz@min}
+\FPdiv\tkz@delta{\tkz@intwd}{\tkz@fct@nb}
+\FPadd\tkz@fct@nb{\tkz@fct@nb}{-1}   
+ \begin{scope}
+\foreach \i in {0,1,...,\tkz@fct@nb}{%
+  \FPeval\x{(\tkz@min+i*\tkz@delta)}
+  \FPeval\tkz@fx{\tkzFcta}
+  \FPadd\tkz@next{\x}{\tkz@delta}
+ \draw[color=\tkz@fct@color,opacity=\tkz@fct@opacity,/tkzriemann/.cd,#1] (\x ,0 ) rectangle (\tkz@next , \tkz@fx/\tkz@init@ystep );  
+   }    
+   \end{scope}  
+\endgroup
+} 
+%<--------------------------------------------------------------------------->
+%                               tkzDrawRiemannSumInf 
+%<--------------------------------------------------------------------------->
+\pgfkeys{/tkzriemann/.cd,
+interval/.code args={#1:#2} {\FPeval\tkz@min{(#1)}
+                             \FPeval\tkz@max{(#2)}},
+number/.code                =  {\edef\tkz@fct@nb{#1}},   
+opacity/.code               =  {\edef\tkz@fct@opacity{#1}},
+color/.code                 =  {\edef\tkz@fct@color{#1}},
+/tkzriemann/.unknown/.code  =  {\let\searchname=\pgfkeyscurrentname
+                                 \pgfkeysalso{\searchname/.try=#1,
+                                   /tikz/\searchname/.retry=#1}}} \def\tkzDrawRiemannSumInf{\pgfutil@ifnextchar[{%
+                 \catcode`\:=12 \tkz@DrawRiemannSumInf}{\tkz@DrawRiemannSumInf[]}} 
+\def\tkz@DrawRiemannSumInf[#1]{%
+\begingroup
+\pgfkeys{%
+/tkzriemann/.cd,
+interval        = 1:2,
+number          = 10,
+opacity         = 0.5,
+line width      = 1pt}
+\pgfqkeys{/tkzriemann}{#1}  
+  \iftkz@init@NO%
+     \FPdiv{\tkz@x@delta}{\tkz@init@xorigine}{\tkz@init@xstep}%
+     \FPdiv{\tkz@y@delta}{\tkz@init@yorigine}{\tkz@init@ystep}%
+  \else
+     \FPset{\tkz@x@delta}{0}
+     \FPset{\tkz@y@delta}{0}%
+  \fi%
+\FPadd\tkz@intwd{\tkz@max}{-\tkz@min}
+\FPdiv\tkz@delta{\tkz@intwd}{\tkz@fct@nb}
+\FPadd\tkz@fct@nb{\tkz@fct@nb}{-1}   
+ 
+\begin{scope}
+\foreach \i in {0,1,...,\tkz@fct@nb}{%
+  \FPeval\x{(\tkz@min+i*\tkz@delta)}
+  \FPeval\tkz@fx{\tkzFcta}
+   \let\tkz@firstimg\tkz@fx
+    \let\tkz@firstx\x 
+  \FPadd\tkz@next{\x}{\tkz@delta}
+  \let\tkzFctTmp\tkzFcta
+  \FPset\x{\tkz@next}
+  \FPeval\tkz@fxnext{\tkzFcta}
+\ifdim \tkz@fx pt < \tkz@fxnext pt\relax
+ \draw[opacity=\tkz@fct@opacity,/tkzriemann/.cd,#1] (\tkz@firstx ,0 ) rectangle (\tkz@next , \tkz@firstimg/\tkz@init@ystep );
+\else 
+\draw[opacity=\tkz@fct@opacity,/tkzriemann/.cd,#1] (\tkz@firstx ,0 ) rectangle (\tkz@next , \tkz@fxnext/\tkz@init@ystep );
+ \fi  
+   }    
+   \end{scope}  
+\endgroup
+} 
+%<--------------------------------------------------------------------------->
+%                               tkzDrawRiemannSumSup 
+%<--------------------------------------------------------------------------->
+
+\def\tkzDrawRiemannSumSup{\pgfutil@ifnextchar[{%
+                 \catcode`\:=12 \tkz@DrawRiemannSumSup}{\tkz@DrawRiemannSumSup[]}} 
+\def\tkz@DrawRiemannSumSup[#1]{%
+\begingroup
+\pgfkeys{%
+/tkzriemann/.cd,
+interval        = 1:2,
+number          = 10,
+opacity         = 0.5,
+line width      = 1pt}
+\pgfqkeys{/tkzriemann}{#1}  
+  \iftkz@init@NO%
+     \FPdiv{\tkz@x@delta}{\tkz@init@xorigine}{\tkz@init@xstep}%
+     \FPdiv{\tkz@y@delta}{\tkz@init@yorigine}{\tkz@init@ystep}%
+  \else
+     \FPset{\tkz@x@delta}{0}
+     \FPset{\tkz@y@delta}{0}%
+  \fi%
+\FPadd\tkz@intwd{\tkz@max}{-\tkz@min}
+\FPdiv\tkz@delta{\tkz@intwd}{\tkz@fct@nb}
+\FPadd\tkz@fct@nb{\tkz@fct@nb}{-1}   
+ 
+\begin{scope}
+\foreach \i in {0,1,...,\tkz@fct@nb}{%
+  \FPeval\x{(\tkz@min+i*\tkz@delta)}
+  \FPeval\tkz@fx{\tkzFcta}
+   \let\tkz@firstimg\tkz@fx
+    \let\tkz@firstx\x 
+  \FPadd\tkz@next{\x}{\tkz@delta}
+  \let\tkzFctTmp\tkzFcta
+  \FPset\x{\tkz@next}
+  \FPeval\tkz@fxnext{\tkzFcta}
+\ifdim \tkz@fx pt > \tkz@fxnext pt\relax
+ \draw[opacity=\tkz@fct@opacity,/tkzriemann/.cd,#1] (\tkz@firstx ,0 ) rectangle (\tkz@next , \tkz@firstimg/\tkz@init@ystep );
+\else 
+\draw[opacity=\tkz@fct@opacity,/tkzriemann/.cd,#1] (\tkz@firstx ,0 ) rectangle (\tkz@next , \tkz@fxnext/\tkz@init@ystep );
+ \fi  
+   }    
+   \end{scope}  
+\endgroup
+}
+%<--------------------------------------------------------------------------->
+%                               tkzDrawRiemannSumMid 
+%<--------------------------------------------------------------------------->
+
+\def\tkzDrawRiemannSumMid{\pgfutil@ifnextchar[{%
+                 \catcode`\:=12 \tkz@DrawRiemannSumMid}{\tkz@DrawRiemannSumMid[]}} 
+\def\tkz@DrawRiemannSumMid[#1]{%
+\begingroup
+\pgfkeys{%
+/tkzriemann/.cd,
+interval        = 1:2,
+number          = 10,
+opacity         = 0.5,
+line width      = 1pt}
+\pgfqkeys{/tkzriemann}{#1}  
+  \iftkz@init@NO%
+     \FPdiv{\tkz@x@delta}{\tkz@init@xorigine}{\tkz@init@xstep}%
+     \FPdiv{\tkz@y@delta}{\tkz@init@yorigine}{\tkz@init@ystep}%
+  \else
+     \FPset{\tkz@x@delta}{0}
+     \FPset{\tkz@y@delta}{0}%
+  \fi%
+\FPadd\tkz@intwd{\tkz@max}{-\tkz@min}
+\FPdiv\tkz@delta{\tkz@intwd}{\tkz@fct@nb}
+\FPadd\tkz@fct@nb{\tkz@fct@nb}{-1}   
+ 
+\begin{scope}
+\foreach \i in {0,1,...,\tkz@fct@nb}{%
+  \FPeval\x{(\tkz@min+i*\tkz@delta)}
+  \FPeval\tkz@fx{\tkzFcta}
+   \let\tkz@firstimg\tkz@fx
+    \let\tkz@firstx\x 
+  \FPadd\tkz@next{\x}{\tkz@delta}
+  \FPset\x{\tkz@next}
+  \FPeval\tkz@fxnext{\tkzFcta}
+  \FPeval\tkz@midimg{(\tkz@firstimg+\tkz@fxnext)/2}
+
+ \draw[opacity=\tkz@fct@opacity,/tkzriemann/.cd,#1] (\tkz@firstx ,0 ) rectangle (\tkz@next , \tkz@midimg/\tkz@init@ystep ); 
+   }    
+   \end{scope}  
+\endgroup
+}  
+  
+%<--------------------------------------------------------------------------–>
+%                 tkzXH      F rien T et [ ou ]
+%<--------------------------------------------------------------------------–>
+\def\tkz@ComT{v}  % need
+
+\pgfkeys{
+  tkzxh/.cd,
+  posgrad/.code  = {\def\tkz@tkzXh@posgrad{#1}},
+  left/.code     = {\def\tkz@tkzXh@left{#1}},
+  right/.code    = {\def\tkz@tkzXh@right{#1}},
+  color/.code    = {\def\tkz@tkzXh@color{#1}},
+  } 
+\def\tkzXH{\pgfutil@ifnextchar[{\tkz@xh}{\tkz@xh[]}}   
+\def\tkz@xh[#1]#2{%
+\pgfkeys{/tkzxh/.cd,
+         posgrad = {below=6 pt},
+         color   = \tkz@mainlinecolor,
+         left    = {},
+         right   = {}
+}  
+ \pgfqkeys{/tkzxh}{#1}  
+\begingroup
+\foreach \xA/\RA/\sA/\xB/\RB/\sB in {#2}{%
+       \tkzDefPoint(\xA,0){deb}\tkzDefPoint(\xB,0){fin}
+       \begin{scope}[decoration={border,angle=-45,
+                    amplitude=0.3cm,segment length=2mm,raise=0.1cm}]
+         \draw[decorate,\tkz@tkzXh@color,thick] (deb) -- (fin);
+         \node at (deb) {\Large\textbf{\sA}};
+         \node at (fin) {\Large\textbf{\sB}};
+\ifx\RA\tkz@ComT
+ \protected@edef\tkz@temp{%
+  \noexpand\node[\tkz@tkzXh@posgrad]}\tkz@temp at (deb){%
+ \tkz@showgrad{\xA}$\numprint{\tkz@result}$};\fi
+
+\ifx\RB\tkz@ComT 
+  \protected@edef\tkz@temp{\noexpand\node[\tkz@tkzXh@posgrad]}\tkz@temp%
+          at (fin){%
+   \tkz@showgrad{\xB}$\numprint{\tkz@result}$};\fi
+
+\protected@edef\tkz@temp{%
+          \noexpand\node[\tkz@tkzXh@posgrad]}\tkz@temp at (\tkz@xa,0) {\tkz@tkzXh@left};%
+\protected@edef\tkz@temp{\noexpand\node[\tkz@tkzXh@posgrad]}\tkz@temp%
+ at (\tkz@xb,0) {\tkz@tkzXh@right};
+\end{scope}
+}%
+\endgroup
+}%
+%<--------------------------------------------------------------------------->
+%                                  tangente  obsolete
+%<--------------------------------------------------------------------------->
+\def\tkzTan{\pgfutil@ifnextchar[{\tkz@Tan}{\tkz@Tan[]}} 
+
+\def\tkz@Tan[#1]#2(#3)#{
+\pgfkeys{/tkztan/.cd,
+draw = false,
+with={},
+kr   = 1,
+kl   = 1}
+\pgfqkeys{/tkztan}{#1}  
+ \global\edef\tkz@opttan{#1}   
+  \FPeval\x{(#3)}%
+  \FPeval\tkz@img{#2}
+  \let\tkz@yy #2%
+  \let\tkz@xx\x%
+  \let\tkz@old@img\tkz@img
+  \tkz@@Tan
+}
+\def\tkz@@Tan#1{%
+\FPdiv{\tkz@old@x}{\x}{1}
+\let\tkz@nexpty\tkz@img
+\tkz@ptStar[](\tkz@old@x,\tkz@nexpty){#1}
+\FPdiv{\tkz@krx}{\tkz@tan@kr}{\tkz@tmp@xstep}
+\FPdiv{\tkz@kry}{\tkz@tan@kr}{\tkz@init@ystep}
+\FPdiv{\tkz@klx}{\tkz@tan@kl}{\tkz@tmp@xstep}
+\FPdiv{\tkz@kly}{\tkz@tan@kl}{\tkz@init@ystep}
+ % demi tgt--> droite
+\FPifzero{\tkz@tan@kr}%
+\else
+\FPadd{\x}{\tkz@xx}{0.000001}%
+\FPeval\tkz@img{\tkz@yy}% 
+\FPadd{\tkz@deltay}{\tkz@old@img}{-\tkz@img}%
+\FPmul{\tkz@slope}{\tkz@deltay}{1000000}%
+\protected@edef\tkz@temp{
+   \noexpand\draw[tan style,/tkztan/.cd,\tkz@opttan,-]}\tkz@temp%
+       (#1)--++(\tkz@krx,-\tkz@kry*\tkz@slope);
+\fi
+% demi tgt --> gauche
+\FPifzero{\tkz@tan@kl}%
+ \else
+\FPadd{\x}{\tkz@xx}{-0.000001} 
+\FPeval\tkz@img{\tkz@yy}% 
+\FPadd{\tkz@deltay}{\tkz@old@img}{-\tkz@img}
+\FPmul{\tkz@slope}{\tkz@deltay}{-1000000}
+  \protected@edef\tkz@temp{
+    \noexpand  
+\draw[tan style,/tkztan/.cd,\tkz@opttan,-]}\tkz@temp%
+       (#1)--++(-\tkz@klx,\tkz@kly*\tkz@slope);
+  \fi
+}
+%<--------------------------------------------------------------------------->
+%                            point d'une courbe   obsolete
+%<--------------------------------------------------------------------------->
+\def\tkzFctPt{\pgfutil@ifnextchar[{\tkz@fctpt}{\tkz@fctpt[]}} 
+\def\tkz@fctpt[#1]#2(#3)#{%
+ \global\edef\tkz@optptfct{#1} 
+  \FPeval\x{(#3)}%
+  \FPeval\tkz@y{#2}
+  \tkz@defpoint
+}
+\def\tkz@defpoint#1{
+  \tkzDefPoint(\x,\tkz@y){#1}
+\protected@edef\tkz@temp{
+   \noexpand  \tkzDrawPoint[\tkz@optptfct](#1)}\tkz@temp
+  \let\tkz@init@xstep\tkz@tmp@xstep
+}  
+%<--------------------------  the end --------------------------------------->
+\endinput 
+
+ 
\ No newline at end of file