pst-func (18apr17)

git-svn-id: svn://tug.org/texlive/trunk@43912 c570f23f-e606-0410-a88d-b1316a301751

3 files changed, 276 insertions, 21 deletions

diff --git a/Master/texmf-dist/doc/generic/pst-func/Changes b/Master/texmf-dist/doc/generic/pst-func/Changes
index b2c4046fbfc..a430f165a07 100644
--- a/Master/texmf-dist/doc/generic/pst-func/Changes
+++ b/Master/texmf-dist/doc/generic/pst-func/Changes
@@ -1,4 +1,5 @@
 ..... pst-func.tex
+0.85  2017-04-18  - allow framing of function values (ts)
 0.84  2017-03-11  - some more modifications to the binomial distributions (ts)
 0.83  2017-03-07  - added some more macros for binomial distributions (ts)
 0.82  2016-05-01  - psk@PontName->\psk@func@PointName (same name in pst-eucl)
diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
index eb54d3153d8..c366b9a9dc5 100644
--- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
+++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
index 2c508068253..e5c5fc0aa5d 100644
--- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
+++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
@@ -25,7 +25,17 @@
 
 
 \lstset{language=PSTricks,
-    morekeywords={psGammaDist,psChiIIDist,psTDist,psFDist,psBetaDist,psPlotImpl},basicstyle=\footnotesize\ttfamily}
+    morekeywords={psGammaDist,psChiIIDist,psTDist,psFDist,psBetaDist,psPlotImpl},basicstyle=\footnotesize\ttfamily,
+  literate=%
+    {Ö}{{\"O}}1
+    {Ä}{{\"A}}1
+    {Ü}{{\"U}}1
+    {ß}{{\ss}}1
+    {ü}{{\"u}}1
+    {ä}{{\"a}}1
+    {ö}{{\"o}}1
+    {~}{{\textasciitilde}}1
+}
 %
 \psset{labelFontSize=\scriptstyle}% for mathmode
 %\def\pshlabel#1{\footnotesize#1}
@@ -63,6 +73,7 @@ Thanks to \\
     Leon Free,
     Attila Gati, 
     Horst Gierhardt,  
+    Jürgen Gilg,
     Christophe Jorssen,
     Lars Kotthoff, 
     Buddy Ledger,
@@ -600,7 +611,7 @@ which plots the envelope curve instead of the Bernstein polynomial.
 \Lcs{psZero}\OptArgs\Largr{$x_0,x_1$}\Largb{functionA}\OptArg{functionB}\Largb{node name}
 \end{BDef}
 
-If the second function is not given the macro calculates and displays the zeros of 
+If the second function is not given the macro calculates and displays the zeros of
 the first function. If the second function is defined too, then the macro calculates the
 intermediate point of the two functions. The intervall is defined as $[x_0,x_1]$.
 Possible optional arguments are
@@ -608,28 +619,69 @@ Possible optional arguments are
 
 \medskip
 \begin{tabularx}{\linewidth}{ @{} l >{\ttfamily}l X @{} }\toprule
-\emph{Name} & \emph{Default} & \emph{Meaning} \\\midrule
-\Lkeyword{markZeros}    & false & Mark the zeros/intermediate points with a symbol.\\
-\Lkeyword{Newton} & false & Use Newton method instead of the bisector one.\\
-\Lkeyword{PrintCoord}  & false & Print the pair of coordinate of the zero/intermediate point.\\
-\Lkeyword{onlyNode}    & false & Calculate only the node, do not print anything.\\
-\Lkeyword{onlyYVal}     & false & Print only the value.\\
-\Lkeyword{originV}      & false & Put the values without an offset.\\
-\Lkeyword{PointName}    & I      & The printed prefix for the calculated Points.\\
-\Lkeyword{decimals}     & 2      & The decimals for the $x$ value.\\
-\Lkeyword{ydecimals}    & 2      & The decimals for the $y$ value.\\
-\Lkeyword{xShift}    & 0      & $x$ move for the printed value.\\
-\Lkeyword{yShift}    & 0      & $y$ move for the printed value.\\\bottomrule
+\emph{Name}           & \emph{Default} & \emph{Meaning} \\\midrule
+\Lkeyword{markZeros}  & false          & Mark the zeros/intermediate points with a symbol.\\
+\Lkeyword{Newton}     & false          & Use Newton method instead of the bisector one.\\
+\Lkeyword{PrintCoord} & false          & Print the pair of coordinates of the zero/intermediate point, like $P(x|y)$.\\
+\Lkeyword{onlyNode}   & false          & Calculate only the node, do not print anything, if markZeros $=$ false.\\
+\Lkeyword{onlyYVal}   & false          & Print only the $y$-value.\\
+\Lkeyword{xory}       & false          & Print $x=$ $x$-Value or, if onlyYVal $=$  true, $y=$ $y$-value.\\
+\Lkeyword{approx}     & true           & Change the $=$, if xory $=$ true to $\approx$.\\
+\Lkeyword{originV}    & false          & Put the values without an offset.\\
+\Lkeyword{Framed}     & false          & Show a filled frame in backround, framesep, fillcolor, opacity or 
+				    linestyle are options to show different frames.\\
+\Lkeyword{PointName}  & I              & The printed prefix for the calculated Points.\\
+\Lkeyword{decimals}   & 2              & The decimals for the $x$ value.\\
+\Lkeyword{ydecimals}  & 2              & The decimals for the $y$ value.\\
+\Lkeyword{xShift}     & 0              & $x$ move for the printed value.\\
+\Lkeyword{yShift}     & 0              & $y$ move for the printed value.\\
+\bottomrule
 \end{tabularx}
 
 \medskip
-The following example was done by Thomas Söll.
+The following examples where done by Jürgen Gilg and Thomas Söll.
 
 \bigskip
 \definecolor{BeigeTS}{rgb}{0.98,0.95,0.87}
 \definecolor{CornBlauTS}{rgb}{0.39,0.59,0.93}
 \definecolor{SandBraun}{rgb}{0.96,0.64,0.38}
-\psset{yunit=1.25cm,arrowinset=0.02,arrowlength=2,linewidth=0.5pt,saveNodeCoors,NodeCoorPrefix=n}
+\psset{yunit=1.25cm,arrowinset=0.02,arrowlength=2,linewidth=0.5pt,saveNodeCoors,NodeCoorPrefix=n,comma}
+\def\funkf{2*sqrt(x)*cos(ln(x))*sin(x)}
+\begin{pspicture}[plotpoints=500,algebraic,fontscale=5,markZeros,
+  PointName=N,dotscale=0.7](-0.5,-3)(10,2.5)
+\psStep[fillstyle=solid,fillcolor=BeigeTS,opacity=0.7,linewidth=0.3pt,
+       linecolor=SandBraun!50](0.001,9.5){40}{\funkf}
+\psStep[StepType=Riemann,fillstyle=solid,opacity=0.3,fillcolor=CornBlauTS,
+       linecolor=CornBlauTS,linewidth=0.3pt](0.001,9.5){40}{\funkf}
+\psaxes[labelFontSize=\scriptstyle,ticksize=-0.1 0]{->}(0,0)(0,-2.75)(10,2.5)
+\psplot[linecolor=BeigeTS!60,linewidth=0.8pt]{0.001}{9.75}{\funkf}
+\psplotTangent[linecolor=blue,Derive={Derive(1,\funkf)}]{1.29}{1.5}{\funkf}
+\uput[90](6,1.2){$f(x)=2\cdot\sqrt{x}\cdot\cos{(\ln{x})}\cdot\sin{x}$}
+{\psset{dotscale=1.5,linecolor=blue!50!black!90,ydecimals=0,Framed,opacity=0.8,decimals=1,PrintCoord}
+ \psZero[xShift=-0.2,yShift=0.15,postString=1,Newton](0.5,1){\funkf}{N1}
+ \psZero[xShift=-0.05,yShift=0.15,postString=2](2,4){\funkf}{N2}
+ \psZero[xShift=-0.45,yShift=0.15,postString=3](4,6){\funkf}{N3}
+ \psZero[xShift=-0.45,yShift=0.15,postString=4](6,7){\funkf}{N4}
+ \psZero[xShift=-0.25,yShift=0.15,PointName=x,postString=5,xory,PrintCoord=false,linestyle=none,fillcolor=green,opacity=0.6](9,11){\funkf}{N5}
+ \psZero[xShift=-0.95,yShift=0,PointName=M,decimals=0,linestyle=none,fillcolor=SandBraun,
+  ydecimals=1,opacity=0.8,postString={m=1}](0.5,2){Derive(1,\funkf)-1+\funkf}[\funkf]{M}%
+}
+\pcline{->}(0.5,-1)(M)
+\nbput[nrot=:U,labelsep=0.3,npos=0.2]{%
+  \scriptsize \psZero[originV=true,xory=true,onlyYVal=true,PointName=f(x),postString={m=1},Framed,
+  opacity=0.8,linestyle=none,markZeros=false,fontscale=10](0.5,2){Derive(1,\funkf)-1+\funkf}[\funkf]{R}}
+\psdot[linecolor=green,strokeopacity=0.8](M)
+\uput{0.5}[40](M){\psZero[originV=true,approx=false,xory=true,onlyYVal=true,
+ PointName=m,postString={m=1},markZeros=false,fontscale=8](0.5,2){Derive(1,\funkf)-1}[1]{R}}
+\end{pspicture}
+
+
+%\begin{LTXexample}[pos=t]
+\begin{lstlisting}
+\definecolor{BeigeTS}{rgb}{0.98,0.95,0.87}
+\definecolor{CornBlauTS}{rgb}{0.39,0.59,0.93}
+\definecolor{SandBraun}{rgb}{0.96,0.64,0.38}
+\psset{yunit=1.25cm,arrowinset=0.02,arrowlength=2,linewidth=0.5pt,saveNodeCoors,NodeCoorPrefix=n,comma}
 \def\funkf{2*sqrt(x)*cos(ln(x))*sin(x)}
 \begin{pspicture}[plotpoints=500,algebraic,fontscale=5,markZeros,PrintCoord,
   PointName=N,dotscale=0.7](-0.5,-3)(10,2.5)
@@ -641,23 +693,225 @@ The following example was done by Thomas Söll.
 \psplot[linecolor=BeigeTS!60,linewidth=0.8pt]{0.001}{9.75}{\funkf}
 \psplotTangent[linecolor=blue,Derive={Derive(1,\funkf)}]{1.29}{1.5}{\funkf}
 \uput[90](6,1.2){$f(x)=2\cdot\sqrt{x}\cdot\cos{(\ln{x})}\cdot\sin{x}$}
-{\psset{dotscale=1.5,linecolor=blue!50!black!90,ydecimals=0}
+{\psset{dotscale=1.5,linecolor=blue!50!black!90,ydecimals=0,Framed,opacity=0.8,decimals=1}
  \psZero[xShift=-0.2,yShift=0.15,postString=1,Newton](0.5,1){\funkf}{N1}
  \psZero[xShift=-0.05,yShift=0.15,postString=2](2,4){\funkf}{N2}
  \psZero[xShift=-0.45,yShift=0.15,postString=3](4,6){\funkf}{N3}
  \psZero[xShift=-0.45,yShift=0.15,postString=4](6,7){\funkf}{N4}
  \psZero[xShift=-0.45,yShift=0.15,postString=5](9,11){\funkf}{N5}
- \psZero[xShift=-1.15,yShift=0,PointName=M,
-   postString={m=1}](0.5,2){Derive(1,\funkf)-1+\funkf}[\funkf]{M}%
+ \psZero[xShift=-1.15,yShift=0,PointName=M,decimals=0,linestyle=none,fillcolor=SandBraun,
+  opacity=0.8,postString={m=1}](0.5,2){Derive(1,\funkf)-1+\funkf}[\funkf]{M}%
 }
 \pcline{->}(0.5,-1)(M)
 \nbput[nrot=:U,labelsep=0.01]{%
-  \scriptsize Steigung ist hier 
+  \scriptsize Steigung ist hier\phantom{i}
     \psPrintValueNew[PSfont=Palatino-Roman,decimals=0,round,fontscale=7]{nMx,{Derive(1,\funkf)}}}
 \psdot[linecolor=green,strokeopacity=0.8](*{nMx} {\funkf})
-\uput[90](*{nMx} {\funkf}){$m=$ 
+\uput[90](*{nMx} {\funkf}){$m=$
   \psPrintValueNew[PSfont=Palatino-Roman,decimals=0,round,fontscale=8]{nMx,{Derive(1,\funkf)}}}
 \end{pspicture}
+\end{lstlisting}
+%\end{LTXexample}
+
+{\psset{yunit=0.8,comma,decimals=2,algebraic=true,markZeros=true,plotpoints=500,saveNodeCoors,NodeCoorPrefix=n}
+%----------------- FUNKTIONSDEFINITIONEN in "algebraic"  -----------------
+\def\funkf{0.75*x^4-3*x^2-2}
+\def\funkg{0.25*x+1}
+
+\begin{pspicture}(-6.5,-5.5)(6.5,8.5)
+%------ Gitter im Hintergrund (CLIPPED) -----------------
+\begin{psclip}%
+{\psframe[linestyle=none](-6.4,-5.4)(6.4,7.4)}
+\psgrid[subgriddiv=2,gridlabels=0,gridwidth=0.3pt,gridcolor=black!50,subgridwidth=0.2pt,subgridcolor=black!30](-6.5,-7.5)(6.5,8.5)
+\end{psclip}
+%--------- Achsen ------------
+\psaxes[xDecimals=0, yDecimals=0,labelFontSize=\scriptstyle,arrowscale=1.3,arrowinset=0.05,arrowlength=1.9, Dy=1,dy=1,dx=1,Dx=1,subticks=0,comma,tickwidth=0.5pt]{->}(0,0)(-6.5,-5.5)(6.5,7.5)[$x$,-90][$y$,180]% Achsen
+%----- Funktionsgraphen plotten (Clippen, damit sie nicht aus dem Gitter ragen) -----------------
+\begin{psclip}%
+{\psframe[linestyle=none](-6.5,-5.4)(6.5,7.4)}
+\psplot[linewidth=1pt,linecolor=Gray]{-6.5}{6.5}{\funkf}%
+\psplot[linewidth=1pt,linecolor=BrickRed]{-6.5}{6.5}{\funkg}%
+\end{psclip}
+%----------------- SPEZIELLE PUNKTE -----------------
+{\psset{fontscale=8,PrintCoord=true,linestyle=none,opacity=0.8,Framed=true,fillcolor=cyan!10}
+%----------------- NULLSTELLEN -----------------
+\psZero[xShift=-0.9,yShift=0.15,PointName={N},postString={1},ydecimals=0](-3,-2){\funkf}[0]{N1}
+\psZero[xShift=-0.9,yShift=0.15,PointName={N},postString={2},ydecimals=0](2,3){\funkf}[0]{N2}
+%----------------- EXTREMWERTE -----------------
+\psZero[xShift=-0.9,yShift=-0.25,PointName={T},postString={1}](-2,0){Derive(1,\funkf)+\funkf}[\funkf]{T1}
+\psZero[xShift=-0.9,yShift=0.25,PointName={H},postString={}](-1,1){Derive(1,\funkf)+\funkf}[\funkf]{H}
+\psZero[xShift=-0.9,yShift=-0.25,PointName={T},postString={2}](0,2.5){Derive(1,\funkf)+\funkf}[\funkf]{T2}
+%----------------- WENDEPUNKTE -----------------
+\psZero[xShift=-1.2,yShift=-0.25,PointName={W},postString={1}](-1.5,-0.5){Derive(2,\funkf)+\funkf}[\funkf]{W1}
+\psZero[xShift=-0.6,yShift=-0.25,PointName={W},postString={2}](0.5,1.5){Derive(2,\funkf)+\funkf}[\funkf]{W2}
+\psZero[onlyNode=true,markZeros=false](-1.5,-0.5){Derive(2,\funkf)+Derive(1,\funkf)}[Derive(1,\funkf)]{mW1}%Steigung Wendepunkt 1 ist "nmW1y"
+}
+%----------------- GLEICHUNG WENDETANGENTE -----------------
+\def\funkWende{nmW1y*(x-nW1x)+nW1y}
+%----------------- GLEICHUNG WENDENORMALE -----------------
+\def\funkNormal{-1/nmW1y*(x-nW1x)+nW1y} %m_n=-1/m_t
+%----------------- Tangente und Normale in W1 plotten ------------------
+\psplot[linewidth=1pt,linecolor=blue]{-1.3}{2.55}{\funkWende}%
+\psplot[linewidth=1pt,linecolor=Green]{-6.5}{5}{\funkNormal}%
+%----------------- Punkte und Werte NICHT anzeigen
+{\psset{onlyNode=true,markZeros=false}
+%----------------- Schnittpunkt: Wendetangente in W1 mit f -------------
+\psZero(0,4){\funkWende}[\funkf]{WS1}
+%----------------- Schnittpunkte: Wendenormale in W1 mit f -------------
+\psZero(-4,0){\funkNormal}[\funkf]{WN1}
+\psZero(0,1.5){\funkNormal}[\funkf]{WN2}
+\psZero(1.5,3){\funkNormal}[\funkf]{WN3}
+%----------------- NULLSTELLE von g -----------------
+\psZero(-3,3){\funkg}[0]{Ng1}
+%----------------- SCHNITTPUNKTE f und g -----------------
+\psZero(0,3){\funkg}[\funkf]{S1}
+\psZero(-3,0){\funkg}[\funkf]{S2}
+}
+%----------------- FLÄCHE mit x-ACHSE -----------------
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=gray,linestyle=none]{%
+\psplot{nN1x}{nW1x}{\funkf}
+\lineto(!nW1x 0)
+\closepath
+}
+%----------------- FLÄCHE ZWISCHEN WENDETANGENTE UND KURVE f -----------------
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=blue,linestyle=none]{%
+\psplot{nW1x}{nWS1x}{\funkWende}
+\psplot{nWS1x}{nW1x}{\funkf}
+\closepath
+}
+%----------------- FLÄCHE ZWISCHEN WENDENORMALE UND KURVE f (Zwei FlÄchenstücke!!!) ----
+%----------------- linke FLÄCHE -----------------
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=green,linestyle=none]{%
+\psplot{nWN1x}{nW1x}{\funkNormal}
+\psplot{nW1x}{nWN1x}{\funkf}
+\closepath
+}
+%----------------- rechte FLÄCHE -----------------
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=green,linestyle=none]{%
+\psplot{nWN2x}{nWN3x}{\funkNormal}
+\psplot{nWN3x}{nWN2x}{\funkf}
+\closepath
+}
+%----------------- FLÄCHE zwischen den KURVEN f und g und beiden KOORDINATEN-ACHSEN -----
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=yellow,linestyle=none]{%
+\psplot{0}{nS1x}{\funkg}
+\psplot{nS1x}{nN2x}{\funkf}
+\lineto(0,0)
+\closepath
+}
+% SPIELEREI: FLÄCHE mit f und PARALLELEN ZUR x-ACHSE
+% Punkte und Werte NICHT anzeigen
+{\psset{onlyNode=true,markZeros=false}
+\psZero(-3,-2){\funkf}[2]{M1}
+\psZero(-3,-2){\funkf}[4]{M2}
+}
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=magenta,linestyle=none]{%
+\psplot{nM1x}{nM2x}{\funkf}
+\lineto(0,4)
+\lineto(0,2)
+\closepath
+}
+\end{pspicture}}
+
+\begin{lstlisting}
+\psset{yunit=0.8,comma,decimals=2,algebraic=true,markZeros=true,plotpoints=500,saveNodeCoors,NodeCoorPrefix=n}
+%----------------- FUNKTIONSDEFINITIONEN in "algebraic"  -----------------
+\def\funkf{0.75*x^4-3*x^2-2}
+\def\funkg{0.25*x+1}
+
+\begin{pspicture}(-6.5,-5.5)(6.5,8.5)
+%------ Gitter im Hintergrund (CLIPPED) -----------------
+\begin{psclip}%
+{\psframe[linestyle=none](-6.4,-5.4)(6.4,7.4)}
+\psgrid[subgriddiv=2,gridlabels=0,gridwidth=0.3pt,gridcolor=black!50,subgridwidth=0.2pt,subgridcolor=black!30](-6.5,-7.5)(6.5,8.5)
+\end{psclip}
+%--------- Achsen ------------
+\psaxes[xDecimals=0, yDecimals=0,labelFontSize=\scriptstyle,arrowscale=1.3,arrowinset=0.05,arrowlength=1.9, Dy=1,dy=1,dx=1,Dx=1,subticks=0,comma,tickwidth=0.5pt]{->}(0,0)(-6.5,-5.5)(6.5,7.5)[$x$,-90][$y$,180]% Achsen
+%----- Funktionsgraphen plotten (Clippen, damit sie nicht aus dem Gitter ragen) -----------------
+\begin{psclip}%
+{\psframe[linestyle=none](-6.5,-5.4)(6.5,7.4)}
+\psplot[linewidth=1pt,linecolor=Gray]{-6.5}{6.5}{\funkf}%
+\psplot[linewidth=1pt,linecolor=BrickRed]{-6.5}{6.5}{\funkg}%
+\end{psclip}
+%----------------- SPEZIELLE PUNKTE -----------------
+{\psset{fontscale=8,PrintCoord=true,linestyle=none,opacity=0.8,Framed=true,fillcolor=cyan!10}
+%----------------- NULLSTELLEN -----------------
+\psZero[xShift=-0.9,yShift=0.15,PointName={N},postString={1},ydecimals=0](-3,-2){\funkf}[0]{N1}
+\psZero[xShift=-0.9,yShift=0.15,PointName={N},postString={2},ydecimals=0](2,3){\funkf}[0]{N2}
+%----------------- EXTREMWERTE -----------------
+\psZero[xShift=-0.9,yShift=-0.25,PointName={T},postString={1}](-2,0){Derive(1,\funkf)+\funkf}[\funkf]{T1}
+\psZero[xShift=-0.9,yShift=0.25,PointName={H},postString={}](-1,1){Derive(1,\funkf)+\funkf}[\funkf]{H}
+\psZero[xShift=-0.9,yShift=-0.25,PointName={T},postString={2}](0,2.5){Derive(1,\funkf)+\funkf}[\funkf]{T2}
+%----------------- WENDEPUNKTE -----------------
+\psZero[xShift=-1.2,yShift=-0.25,PointName={W},postString={1}](-1.5,-0.5){Derive(2,\funkf)+\funkf}[\funkf]{W1}
+\psZero[xShift=-0.6,yShift=-0.25,PointName={W},postString={2}](0.5,1.5){Derive(2,\funkf)+\funkf}[\funkf]{W2}
+\psZero[onlyNode=true,markZeros=false](-1.5,-0.5){Derive(2,\funkf)+Derive(1,\funkf)}[Derive(1,\funkf)]{mW1}%Steigung Wendepunkt 1 ist "nmW1y"
+}
+%----------------- GLEICHUNG WENDETANGENTE -----------------
+\def\funkWende{nmW1y*(x-nW1x)+nW1y}
+%----------------- GLEICHUNG WENDETANGENTE -----------------
+\def\funkNormal{-1/nmW1y*(x-nW1x)+nW1y} %m_n=-1/m_t
+%----------------- Tangente und Normale in W1 plotten ------------------
+\psplot[linewidth=1pt,linecolor=blue]{-1.3}{2.55}{\funkWende}%
+\psplot[linewidth=1pt,linecolor=Green]{-6.5}{5}{\funkNormal}%
+%----------------- Punkte und Werte NICHT anzeigen
+{\psset{onlyNode=true,markZeros=false}
+%----------------- Schnittpunkt: Wendetangente in W1 mit f -------------
+\psZero(0,4){\funkWende}[\funkf]{WS1}
+%----------------- Schnittpunkte: Wendenormale in W1 mit f -------------
+\psZero(-4,0){\funkNormal}[\funkf]{WN1}
+\psZero(0,1.5){\funkNormal}[\funkf]{WN2}
+\psZero(1.5,3){\funkNormal}[\funkf]{WN3}
+%----------------- NULLSTELLE von g -----------------
+\psZero(-3,3){\funkg}[0]{Ng1}
+%----------------- SCHNITTPUNKTE f und g -----------------
+\psZero(0,3){\funkg}[\funkf]{S1}
+\psZero(-3,0){\funkg}[\funkf]{S2}
+}
+%----------------- FLÄCHE mit x-ACHSE -----------------
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=gray,linestyle=none]{%
+\psplot{nN1x}{nW1x}{\funkf}
+\lineto(!nW1x 0)
+\closepath
+}
+%----------------- FLÄCHE ZWISCHEN WENDETANGENTE UND KURVE f -----------------
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=blue,linestyle=none]{%
+\psplot{nW1x}{nWS1x}{\funkWende}
+\psplot{nWS1x}{nW1x}{\funkf}
+\closepath
+}
+%----------------- FLÄCHE ZWISCHEN WENDENORMALE UND KURVE f (Zwei FlÄchenstücke!!!) ----
+%----------------- linke FLÄCHE -----------------
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=green,linestyle=none]{%
+\psplot{nWN1x}{nW1x}{\funkNormal}
+\psplot{nW1x}{nWN1x}{\funkf}
+\closepath
+}
+%----------------- rechte FLÄCHE -----------------
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=green,linestyle=none]{%
+\psplot{nWN2x}{nWN3x}{\funkNormal}
+\psplot{nWN3x}{nWN2x}{\funkf}
+\closepath
+}
+%----------------- FLÄCHE zwischen den KURVEN f und g und beiden KOORDINATEN-ACHSEN -----
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=yellow,linestyle=none]{%
+  \psplot{0}{nS1x}{\funkg}
+  \psplot{nS1x}{nN2x}{\funkf}
+  \lineto(0,0)
+  \closepath}
+% SPIELEREI: FLÄCHE mit f und PARALLELEN ZUR x-ACHSE
+% Punkte und Werte NICHT anzeigen
+{\psset{onlyNode=true,markZeros=false}
+\psZero(-3,-2){\funkf}[2]{M1}
+\psZero(-3,-2){\funkf}[4]{M2}}
+\pscustom[fillstyle=solid,opacity=0.3,fillcolor=magenta,linestyle=none]{%
+  \psplot{nM1x}{nM2x}{\funkf}
+  \lineto(0,4)
+  \lineto(0,2)
+  \closepath}
+\end{pspicture}
+\end{lstlisting}
+
 
 
 %\begin{LTXexample}[pos=t]