tablor 4.0 (8oct08)

git-svn-id: svn://tug.org/texlive/trunk@10915 c570f23f-e606-0410-a88d-b1316a301751
author: Karl Berry <karl@freefriends.org> 2008-10-10 23:15:06 +0000
committer: Karl Berry <karl@freefriends.org> 2008-10-10 23:15:06 +0000
commit: 41977cc6e6769af289a96d6846be398bdd94d133 (patch)
tree: e05fceb93f97d08ebc333e21ddc1f1f27c39200e /Master
parent: a4e7b650b36655b60114b5bcf614496a9dfcfc31 (diff)
57 files changed, 9117 insertions, 7784 deletions
diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp b/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp
index d0549eeb9cf..0f84f2a3c09 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp
@@ -4,12 +4,12 @@ newLigneVariables(btex $ {x}$ etex);
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-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3x+2}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3 x+2}$ etex);
                               moins;
                                 valBarre(btex 0 etex);plus;barre;
                               plus;barre;plus;
                               
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5x^{2}-1}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5 x^{2}-1}$ etex);
                               plus;barre;
                               plus;
                                 valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.0 b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.0
index ffbec24f4c8..ae6786f19dc 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.0
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.0
@@ -1,18 +1,22 @@
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diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.1 b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.1
index eb7d268cb39..ae6786f19dc 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.1
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.1
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diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.9 b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.9
index 9db7e1ac706..6c89a54adba 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.9
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@@ -1,15 +1,17 @@
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diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
index 5797a66cf34..fa53635eeb2 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
@@ -8,7 +8,39 @@ verbatimtex
 \renewcommand\cdot{ } % idem pour les cdot
 \begin{document}
 etex
-beginTableau(0) newLigneVariables(btex $x$ etex);val(btex $-5$ etex);
+beginTableau(0) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
+val(btex $-1$ etex);
+val(btex $0$ etex);
+val(btex $1$ etex);
+val(btex $+\infty $ etex);
+
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex); plus; nonDefBarre;plus;valBarre(btex 0 etex);moins;nonDefBarre;moins;
+newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex
+                                    $+\infty $
+                                    etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex          $0$
+                                            etex,1);limGauche(btex
+                                    $-\infty$
+                                    etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0);
+
+endTableau;
+
+beginTableau(1) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
+val(btex $-1$ etex);
+val(btex $0$ etex);
+val(btex $1$ etex);
+val(btex $+\infty $ etex);
+
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex); plus; nonDefBarre;plus;valBarre(btex 0 etex);moins;nonDefBarre;moins;
+newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex
+                                    $+\infty $
+                                    etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex          $0$
+                                            etex,1);limGauche(btex
+                                    $-\infty$
+                                    etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0);
+
+endTableau;
+
+beginTableau(2) newLigneVariables(btex $x$ etex);val(btex $-5$ etex);
 val(btex $0$ etex);
 val(btex $7$ etex);
 
@@ -17,7 +49,7 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);va
 valPos(btex $49$ etex,1);
 endTableau;
 
-beginTableau(1) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(3) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
 val(btex $0$ etex);
 val(btex $+\infty $ etex);
 
@@ -29,14 +61,14 @@ endTableau;
 
 
 
-beginTableau(2) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
 val(btex $0$ etex);
 val(btex $+\infty $ etex);
 
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; valBarre(btex 0 etex);plus;
 endTableau;
 
-beginTableau(3) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
+beginTableau(5) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
 val(btex $-1$ etex);
 val(btex $0$ etex);
 val(btex $1$ etex);
@@ -52,7 +84,20 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);va
 
 endTableau;
 
-beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(6) newLigneVariables(btex $t$ etex);val(btex $-\pi $ etex);
+val(btex $\frac{(-\pi )}{2}$ etex);
+val(btex $\frac{\pi }{2}$ etex);
+val(btex $\pi $ etex);
+
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex); moins; valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;
+newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);valPos(btex $\frac{1}{2}$ etex,1); valPos(btex          $\frac{-1}{2}$
+                                            etex,0);
+valPos(btex          $\frac{3}{2}$
+                                            etex,1);valPos(btex $\frac{1}{2}$ etex,0);
+
+endTableau;
+
+beginTableau(7) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
 val(btex $-1$ etex);
 val(btex $1$ etex);
 val(btex $+\infty $ etex);
@@ -61,7 +106,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $0$ etex,0);debutNonDef;finNonDef;limDroite(btex $0$ etex,0);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(5) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(8) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
 val(btex $-1$ etex);
 val(btex $1$ etex);
 val(btex $\frac{5}{2}$ etex);
@@ -73,7 +118,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $-\infty$ etex,0);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex$\ln\left(\frac{441}{16}\right)$etex,1);limGauche(btex $-\infty$ etex,0);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(6) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $\alpha_1$ etex);val(btex $-1$ etex);val(btex $0$ etex);val(btex $1$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
+beginTableau(9) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $\alpha_1$ etex);val(btex $-1$ etex);val(btex $0$ etex);val(btex $1$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
 
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$  $ etex);plus; nonDefBarre;plus;valBarre(btex 0 etex);moins;nonDefBarre;moins;valBarre(btex $  $ etex);moins;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
@@ -83,7 +128,7 @@ valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); limGauche(bte
                                                                  valPos(btex $1$ etex,0);
 endTableau;
 
-beginTableau(7) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);val(btex $+\infty $ etex);
+beginTableau(10) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);val(btex $+\infty $ etex);
 
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;  nonDefBarre;plus;valBarre(btex $  $ etex);plus;valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins;nonDefBarre;moins;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
@@ -95,7 +140,7 @@ valPos(btex $\frac{100}{99}$ etex,0);  limGauche(btex $+\infty $ etex,1);nonDefB
                                                                  limGauche(btex $-\infty$ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0);
 endTableau;
 
-beginTableau(9) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(12) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
 val(btex $     0.212584$ etex);
 val(btex $     0.584635$ etex);
 val(btex $+\infty $ etex);
@@ -107,27 +152,27 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);no
 valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(10) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
-val(btex $\frac{1}{8} \times \pi $ etex);
-val(btex $\frac{1}{3} \times \pi $ etex);
-val(btex $\frac{3}{8} \times \pi $ etex);
+beginTableau(13) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+val(btex $\frac{\pi }{8}$ etex);
+val(btex $\frac{\pi }{3}$ etex);
+val(btex $\frac{3 \pi }{8}$ etex);
 val(btex $\frac{\pi }{2}$ etex);
 
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3\sin\left(\frac{3\pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3\sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex);
-newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex          $\cos\left(\frac{3\pi }{8}\right)$
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3 \sin\left(\frac{3 \pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3 \sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex);
+newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex          $\cos\left(\frac{3 \pi }{8}\right)$
                                             etex,0.5);valPos(btex          $-1$
                                             etex,0);
 valPos(btex          $-\left(\cos\left(\frac{\pi }{8}\right)\right)$
                                             etex,0.5);valPos(btex $0$ etex,1);
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex);valBarre(btex $4$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-2$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $4$ etex);
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle y}$ etex);valPos(btex $0$ etex,0);valPos(btex          $1$
-                                            etex,1);valPos(btex          $-\left(\frac{1}{2} \times \sqrt{3}\right)$
+                                            etex,1);valPos(btex          $\frac{(-\left(\sqrt{3}\right))}{2}$
                                             etex,0.5);valPos(btex          $-1$
                                             etex,0);
 valPos(btex $0$ etex,1);
 endTableau;
 
-beginTableau(11) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
+beginTableau(14) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
 val(btex $-4$ etex);
 val(btex $-1$ etex);
 val(btex $0$ etex);
@@ -155,7 +200,7 @@ valPos(btex          $\frac{16}{3}$
 endTableau;
 
 
-          beginTableau(12)
+          beginTableau(15)
    newLigneVariables(btex $ {x}$ etex);
    val(btex $-\infty$ etex);val(btex $\frac{3}{2}$ etex);
 val(btex $5$etex);
@@ -165,7 +210,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2x+3}$ etex);plus;val
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -x+5}$ etex);plus;barre;plus;valBarre(btex 0 etex);moins;
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle {(-2x+3)(-x+5)}}$ etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
 endTableau;
-  beginTableau(13)
+  beginTableau(16)
 newLigneVariables(btex $ {x}$ etex);
    val(btex $-\infty $ etex);val(btex $-\left(\sqrt{2}\right)$ etex);
 val(btex $-1$ etex);
@@ -173,7 +218,7 @@ val(btex $1$ etex);
 val(btex $\sqrt{2}$ etex);
 val(btex $\frac{3}{2}$ etex);
 val(btex $+\infty $ etex); 
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex);
                               plus;barre;
                               plus;barre;
                               plus;barre;
@@ -214,7 +259,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle P(x)}$ etex);
                               
 endTableau;
 
-   beginTableau(14)
+   beginTableau(17)
 newLigneVariables(btex $ {x}$ etex);
    val(btex $-15$ etex);val(btex $-10$ etex);
 val(btex $10$ etex); 
@@ -231,7 +276,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f(x)}$ etex);
 endTableau;
 
  
-beginTableau(15)
+beginTableau(18)
 newLigneVariables(btex $ {x}$ etex);
    val(btex $-\infty $ etex);val(btex $-4$ etex);
 val(btex $\frac{5}{4}$ etex);
@@ -239,14 +284,14 @@ val(btex $\frac{3}{2}$ etex);
 val(btex $2$ etex);
 val(btex $4$ etex);
 val(btex $+\infty $ etex); 
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex);
                               plus;barre;
                               plus;barre;
                               plus;
                                 valBarre(btex 0 etex);moins;barre;
                               moins;barre;moins;
      
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(4x\right)+5}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(4 x\right)+5}$ etex);
                               plus;barre;
                               plus;
                                 valBarre(btex 0 etex);moins;barre;
@@ -266,32 +311,16 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-2}$ etex);
                               moins;
                                 valBarre(btex 0 etex);plus;barre;plus; 
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex);
-                              moins;nonDefBarre; plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;nonDefBarre;plus; 
-endTableau;
-
-
-beginTableau(16)
-newLigneVariables(btex $ {x}$ etex);
-   val(btex $-\infty $ etex);val(btex $-10$ etex);
-val(btex $10$ etex); 
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-10}$ etex);
-                              moins;barre;moins;
-    
-                                valBarre(btex 0 etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+10}$ etex);
-                              moins;valBarre(btex 0 etex);plus; 
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex);
-                              plus;nonDefBarre; moins;
-                                valBarre(btex 0 etex);
+                              moins;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;valBarre(btex 0 etex);plus; 
 endTableau;
 
 
 
-beginTableau(17)
+beginTableau(19)
 newLigneVariables(btex $\displaystyle  {x}$ etex);
    val(btex $-10$ etex);val(btex $-5$ etex);
 val(btex $10$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10)(x+5)}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+5)}$ etex);
                               plus;valBarre(btex 0 etex); moins;valBarre(btex 0 etex);
 endTableau;
 
@@ -301,12 +330,12 @@ newLigneVariables(btex $ {x}$ etex);
 val(btex $-\frac{\sqrt{5}}{5}$ etex);
 val(btex $\frac{\sqrt{5}}{5}$ etex);
 val(btex $50$ etex); 
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3x+2}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3 x+2}$ etex);
                               moins;
                                 valBarre(btex 0 etex);plus;barre;
                               plus;barre;plus;
                               
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5x^{2}-1}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5 x^{2}-1}$ etex);
                               plus;barre;
                               plus;
                                 valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
@@ -316,7 +345,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle F(x)}$ etex);
                               
 endTableau;
 
- beginTableau(18) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
+ beginTableau(20) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;moins;valBarre(btex$  $ etex);moins; valBarre(btex 0 etex);plus;valBarre(btex $  $ etex);plus;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
 nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPos(btex          $-1$
@@ -324,7 +353,7 @@ nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPo
                                             $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(19) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(21) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins;  valBarre(btex 0 etex);plus;valBarre(btex $  $ etex);plus;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
 valPos(btex $\frac{1}{4}$ etex,1);  valPos(btex          $0$
@@ -332,13 +361,13 @@ valPos(btex $\frac{1}{4}$ etex,1);  valPos(btex          $0$
                                             $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(20) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(22) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus;valBarre(btex$  $ etex);plus;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
 nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(22) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
+beginTableau(24) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
 val(btex $+\infty $ etex);
 
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins;
@@ -346,7 +375,7 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);va
 
 endTableau;
 
-beginTableau(23) newLigneVariables(btex $x$ etex);val(btex $-\pi $ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $\pi $ etex);
+beginTableau(25) newLigneVariables(btex $x$ etex);val(btex $-\pi $ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $\pi $ etex);
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);valBarre(btex 0 etex);moins;valBarre(btex$  $ etex);moins; valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
 valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex          $1$
@@ -354,9 +383,9 @@ valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex          $1$
                                             $ 1/2 $ etex,0.5);valPos(btex $-1$ etex,0);
 endTableau;
 
-beginTableau(24) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(26) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
 val(btex $\pi $ etex);
-val(btex $2\pi $ etex);
+val(btex $2 \pi $ etex);
 
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);valBarre(btex 0 etex);moins; valBarre(btex 0 etex);plus;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $1$ etex,1); valPos(btex          $-1$
@@ -364,22 +393,22 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);va
 valPos(btex $1$ etex,1);
 endTableau;
 
-beginTableau(25) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex);
+beginTableau(27) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex);
 
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle h'(t)}$ etex); plus;valBarre(btex$  $ etex);plus; nonDefBarre;plus;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle h}$ etex);
 valPos(btex $0$ etex,0);valPos(btex $ 7 $ etex,0.5); limGauche(btex $+\infty $ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $0$ etex,1);
 endTableau;
 
-beginTableau(26) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);
+beginTableau(28) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$  $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
-valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex          $\frac{3}{4} \times \sqrt{3}$
+valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex          $\frac{3 \sqrt{3}}{4}$
                                             etex,1);valPos(btex
                                             $ 1 $ etex,0.5);valPos(btex $0$ etex,0);
 endTableau;
 
-beginTableau(27) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
+beginTableau(29) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
 val(btex $0$ etex);
 val(btex $+\infty $ etex);
 
@@ -389,15 +418,15 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);no
 
 endTableau;
 
-  beginTableau(28)
+  beginTableau(30)
 newLigneVariables(btex $ {x}$ etex);
-   val(btex $-10$ etex);val(btex $-\left(\frac{1}{2} \times \sqrt{5}\right)+\frac{-3}{2}$ etex);
+   val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex);
 val(btex $-1$ etex);
-val(btex $\frac{1}{2} \times \sqrt{5}+\frac{-3}{2}$ etex);
+val(btex $\frac{(\sqrt{5}-3)}{2}$ etex);
 val(btex $1$ etex);
 val(btex $\frac{3}{2}$ etex);
 val(btex $+\infty $ etex); 
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex);
                               plus;barre;
                               plus;barre;
                               plus;barre;
@@ -419,7 +448,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+1}$ etex);
                               plus;barre;
                               plus;barre;plus;
                               
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+3x+1}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+3 x+1}$ etex);
                               plus;
                                 valBarre(btex 0 etex);moins;barre;
                               moins;
@@ -431,7 +460,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex);
                               
 endTableau;
 
- beginTableau(29) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+ beginTableau(31) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins;  valBarre(btex 0 etex);plus;valBarre(btex $  $ etex);plus;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
 valPos(btex $-1$ etex,1);  valPos(btex          $-\left(e^{-4}\right)-1$
@@ -439,7 +468,7 @@ valPos(btex $-1$ etex,1);  valPos(btex          $-\left(e^{-4}\right)-1$
                                             $ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(30) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(32) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);plus;  valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
 valPos(btex $1$ etex,0);  valPos(btex          $2$
@@ -447,7 +476,7 @@ valPos(btex $1$ etex,0);  valPos(btex          $2$
                                             $ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0);
 endTableau;
 
-beginTableau(32) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(34) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
 val(btex $1$ etex);
 val(btex $+\infty $ etex);
 
@@ -457,13 +486,13 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);va
 
 endTableau;
 
-beginTableau(33) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex);
+beginTableau(35) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex);
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins;valBarre(btex$  $ etex);moins;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
 valPos(btex $1$ etex,1);valPos(btex $ 0 $ etex,0.5);valPos(btex $-\pi -1$ etex,0);
 endTableau;
 
-beginTableau(34) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $e^{\frac{1}{2}}$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
+beginTableau(36) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $e^{\frac{1}{2}}$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus;valBarre(btex$  $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);
 nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ -1 $ etex,0.5); valPos(btex          $\frac{1}{4}$
@@ -473,15 +502,15 @@ endTableau;
 
 
 
-beginTableau(35)
+beginTableau(37)
 newLigneVariables(btex $\displaystyle  {x}$ etex);
    val(btex $-10$ etex);val(btex $10$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10)(x+10)}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+10)}$ etex);
                                 valBarre(btex 0 etex);plus; 
                                 valBarre(btex 0 etex);
 endTableau;
 
-beginTableau(36) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(38) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
 val(btex $-\left(\sqrt{2}\right)$ etex);
 val(btex $-1$ etex);
 val(btex $1$ etex);
@@ -492,7 +521,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; v
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); valPos(btex$-2$etex,0);limGauche(btex $0$ etex,1);debutNonDef;finNonDef;limDroite(btex $0$ etex,1);valPos(btex$-2$etex,0);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(37) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(39) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
 val(btex $-1$ etex);
 val(btex $1$ etex);
 val(btex $+\infty $ etex);
@@ -501,38 +530,38 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $-\infty$ etex,0);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(38) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
-val(btex $\frac{1}{8} \times \pi $ etex);
-val(btex $\frac{1}{3} \times \pi $ etex);
-val(btex $\frac{3}{8} \times \pi $ etex);
+beginTableau(40) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+val(btex $\frac{\pi }{8}$ etex);
+val(btex $\frac{\pi }{3}$ etex);
+val(btex $\frac{3 \pi }{8}$ etex);
 val(btex $\frac{\pi }{2}$ etex);
 
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3\sin\left(\frac{3\pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3\sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex);
-newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex          $\cos\left(\frac{3\pi }{8}\right)$
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3 \sin\left(\frac{3 \pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3 \sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex);
+newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex          $\cos\left(\frac{3 \pi }{8}\right)$
                                             etex,0.5);valPos(btex          $-1$
                                             etex,0);
 valPos(btex          $-\left(\cos\left(\frac{\pi }{8}\right)\right)$
                                             etex,0.5);valPos(btex $0$ etex,1);
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex);valBarre(btex $4$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-2$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $4$ etex);
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle y}$ etex);valPos(btex $0$ etex,0);valPos(btex          $1$
-                                            etex,1);valPos(btex          $-\left(\frac{1}{2} \times \sqrt{3}\right)$
+                                            etex,1);valPos(btex          $\frac{(-\left(\sqrt{3}\right))}{2}$
                                             etex,0.5);valPos(btex          $-1$
                                             etex,0);
 valPos(btex $0$ etex,1);
 endTableau;
 
-beginTableau(39) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
-val(btex $\frac{1}{3} \times \pi $ etex);
+beginTableau(41) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+val(btex $\frac{\pi }{3}$ etex);
 val(btex $\pi $ etex);
-val(btex $\frac{5}{3} \times \pi $ etex);
-val(btex $2\pi $ etex);
+val(btex $\frac{5 \pi }{3}$ etex);
+val(btex $2 \pi $ etex);
 
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $-1$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-1$ etex);
-newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle x}$ etex);valPos(btex $0$ etex,1);valPos(btex          $-\left(\sqrt{3}\right)-\left(\frac{1}{-3} \times \pi \right)$
+newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle x}$ etex);valPos(btex $0$ etex,1);valPos(btex          $\frac{(\pi +-3 \sqrt{3})}{3}$
                                             etex,0);
 valPos(btex          $\pi $
-                                            etex,0.5);valPos(btex          $\sqrt{3}+\frac{5}{3} \times \pi $
-                                            etex,1);valPos(btex $2\pi $ etex,0);
+                                            etex,0.5);valPos(btex          $\frac{(5 \pi +3 \sqrt{3})}{3}$
+                                            etex,1);valPos(btex $2 \pi $ etex,0);
 
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(\sqrt{3}\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $\sqrt{3}$ etex);plus;valBarre(btex $0$ etex);
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle y}$ etex);valPos(btex $1$ etex,1);valPos(btex          $0$
@@ -542,7 +571,7 @@ valPos(btex          $0$
                                             etex,0.5);valPos(btex $1$ etex,1);
 endTableau;
 
-beginTableau(40) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
 val(btex $-1$ etex);
 val(btex $1$ etex);
 val(btex $\frac{5}{2}$ etex);
@@ -554,75 +583,51 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $\sqrt{35}$ etex,0);debutNonDef;finNonDef;limDroite(btex $\sqrt{15}$ etex,0);valPos(btex$\sqrt{21}$etex,1);limGauche(btex $\sqrt{15}$ etex,0);debutNonDef;finNonDef;limDroite(btex $\sqrt{35}$ etex,0);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(41) newLigneVariables(btex $x$ etex);val(btex $-5$ etex);
-val(btex $\frac{2}{5}$ etex);
-val(btex $10$ etex);
-
-newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $\frac{169}{2}$ etex,1); valPos(btex          $\frac{58}{5}$
-                                            etex,0);
-valPos(btex $242$ etex,1);
-endTableau;
-
-beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-20$ etex);
-val(btex $-\left(\frac{1}{9} \times \sqrt{7}\right)+\frac{5}{9}$ etex);
-val(btex $\frac{1}{9} \times \sqrt{7}+\frac{5}{9}$ etex);
-val(btex $20$ etex);
-
-newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-26047$ etex,0); valPos(btex          $\frac{14}{243} \times \sqrt{7}+\frac{-1681}{243}$
-                                            etex,1);valPos(btex          $-\left(\frac{14}{243} \times \sqrt{7}\right)+\frac{-1681}{243}$
-                                            etex,0);
-valPos(btex $22033$ etex,1);
-endTableau;
+beginTableau(43) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+val(btex $\frac{\pi }{8}$ etex);
+val(btex $\frac{\pi }{6}$ etex);
+val(btex $\frac{3 \pi }{8}$ etex);
+val(btex $\frac{\pi }{2}$ etex);
 
-beginTableau(43) newLigneVariables(btex $x$ etex);val(btex $-20$ etex);
-val(btex $-\left(\frac{1}{9} \times \sqrt{7}\right)+\frac{5}{9}$ etex);
-val(btex $\frac{1}{9} \times \sqrt{7}+\frac{5}{9}$ etex);
-val(btex $20$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(t)}$ etex);valBarre(btex $3$ etex);plus;valBarre(btex $3 \cos\left(\frac{3 \pi }{8}\right)$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3 \cos\left(\frac{\pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);
+newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $0$ etex,0);valPos(btex          $\sin\left(\frac{3 \pi }{8}\right)$
+                                            etex,0.5);valPos(btex          $1$
+                                            etex,1);valPos(btex          $-\left(\sin\left(\frac{\pi }{8}\right)\right)$
+                                            etex,0.5);valPos(btex $-1$ etex,0);
 
-newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $26047$ etex,1); valPos(btex          $-\left(\frac{14}{243} \times \sqrt{7}\right)+\frac{1681}{243}$
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex);valBarre(btex $4$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-2$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $4$ etex);
+newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);valPos(btex $0$ etex,0);valPos(btex          $1$
+                                            etex,1);valPos(btex          $\frac{\sqrt{3}}{2}$
+                                            etex,0.5);valPos(btex          $-1$
                                             etex,0);
-valPos(btex          $\frac{14}{243} \times \sqrt{7}+\frac{1681}{243}$
-                                            etex,1);valPos(btex $-22033$ etex,0);
-
+valPos(btex $0$ etex,1);
 endTableau;
 
-
-
-beginTableau(44)
-newLigneVariables(btex $\displaystyle  {x}$ etex);
-   val(btex $-20$ etex);val(btex $     1.942052$ etex);
-val(btex $20$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(3x^{3}\right)+5x^{2}-\left(2x\right)+7}$ etex);
-                              plus;valBarre(btex 0 etex); moins;
+  beginTableau(44)
+newLigneVariables(btex $ {x}$ etex);
+   val(btex $0$ etex);val(btex $\frac{\pi }{3}$ etex);
+val(btex $\frac{\pi }{3}$ etex);
+val(btex $\frac{7 \pi }{6}$ etex);
+val(btex $\frac{5 \pi }{3}$ etex);
+val(btex $\frac{11 \pi }{6}$ etex);
+val(btex $2 \pi $ etex); 
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \cos\left(x\right)+\frac{1}{-2}}$ etex);
+                              plus;
+                                valBarre(btex 0 etex);plus;
+                                valBarre(btex 0 etex);moins;barre;
+                              moins;
+                                valBarre(btex 0 etex);plus;barre;plus;
                               
-endTableau;
-
-
-
-beginTableau(45)
-newLigneVariables(btex $\displaystyle  {x}$ etex);
-   val(btex $-20$ etex);val(btex $     1.942052$ etex);
-val(btex $20$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3x^{3}-\left(5x^{2}\right)+2x-7}$ etex);
-                              moins;valBarre(btex 0 etex); plus;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \sin\left(x\right)+\frac{1}{2}}$ etex);
+                              plus;barre;
+                              plus;barre;
+                              plus;
+                                valBarre(btex 0 etex);moins;barre;
+                              moins;valBarre(btex 0 etex);plus;
+                              
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle  f (x)}$ etex);
+                              plus;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
                               
 endTableau;
 
-beginTableau(46) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $     0.000000$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f''(x)}$ etex);plus;  valBarre(btex 0 etex);moins;valBarre(btex $  $ etex);moins;
-newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f'}$ etex);
-valPos(btex $\frac{1}{2}$ etex,0);  valPos(btex          $     1.000000$
-                                            etex,1);valPos(btex
-                                            $ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0);
-endTableau;
-
-beginTableau(47) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
-val(btex $     0.639232$ etex);
-val(btex $+\infty $ etex);
-
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);plus; valBarre(btex 0 etex);moins;
-newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-\infty$ etex,0); valPos(btex          $     0.967397$
-                                            etex,1);valPos(btex $-\infty$ etex,0);
-
-endTableau;
-
+ 
+\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.pdf b/Master/texmf-dist/doc/latex/tablor/tablor.pdf
index db5ac600269..e79dbbf0274 100644
--- a/Master/texmf-dist/doc/latex/tablor/tablor.pdf
+++ b/Master/texmf-dist/doc/latex/tablor/tablor.pdf
diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.tex b/Master/texmf-dist/doc/latex/tablor/tablor.tex
index dcc593424ab..fd514f0f77e 100644
--- a/Master/texmf-dist/doc/latex/tablor/tablor.tex
+++ b/Master/texmf-dist/doc/latex/tablor/tablor.tex
@@ -48,11 +48,11 @@ keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,com
 % petits environnements bclogo
 
 \newenvironment{DANGER}[1]{%
-\begin{bclogo}{\attention}{#1}{0.9white}{0.1}}
+\begin{bclogo}{\attention}{#1}{0.9white}{0.1}{0}}
 {\end{bclogo}}
 
 \newenvironment{Idee}[1]{%
-\begin{bclogo}{\coeur}{#1}{0.9white}{0.1}}
+\begin{bclogo}{\coeur}{#1}{0.9white}{0.1}{0}}
 {\end{bclogo}}
 
 
@@ -72,24 +72,6 @@ keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,com
 
 
 
-%%%% Macros pour un Vrai-Faux
-
-\usepackage{pifont}
-
-\newcommand{\Q}{\mbox{\ding{114}\hspace{-.7em}\raisebox{.2ex}[1ex]{\ding{51}}}}
-
-\newcommand{\VF}{%
-	\hfill\makebox[1cm][s]{\bf V\hfill F}
-	}
-	
-\newcommand{\Rep}[1][]{%
-	\ifthenelse{\equal{#1}{v}}{%
-		\hfill\makebox[1cm][s]{\Q\hfill \ding{114}}}{%
-		\ifthenelse{\equal{#1}{f}}{%
-			\hfill\makebox[1cm][s]{\ding{114} \hfill\Q}}{%
-			\hfill\makebox[1cm][s]{\ding{114} \hfill\ding{114}}}}}
-
-
 % titre
 
 \title{\texttt{tablor.sty} \\La machine � cr�er des tableaux de signes et de variations }
@@ -98,7 +80,7 @@ keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,com
 avec l'efficace participation de Jean-Michel \textsc{Boucart}\\
 Forum d'aide ~:~\href{http://gconnan.free.fr/punbb/upload/index.php}{http://gconnan.free.fr/punbb/upload/index.php}}
 
-\date{14 juin 2008 - Version 3.00}
+\date{8 octobre 2008 - Version 4.00}
 
 
 
@@ -129,6 +111,37 @@ Forum d'aide ~:~\href{http://gconnan.free.fr/punbb/upload/index.php}{http://gcon
 Il  s'agit d'obtenir rapidement  un tableau  de signe  ou un  tableau de  variation en  entrant un
 minimum de commandes.
 
+\section{Nouveaut�s}
+
+\subsection{Changements depuis la version 3.00}
+
+La version 4.00 n'est  malheureusement plus compatible avec les versions
+ant�rieures car une option suppl�mentaire a �t� ajout�e pour traiter les
+fonctions trigonom�triques.
+
+Une  possibilit�  a de  plus  �t� ajout�e  pour  r�duire  la taille  des
+tableaux.
+
+
+\subsection{Professor.sty}
+
+
+\texttt{tablor.sty}  a   fait  des   petits...  Gr�ce  �   une  efficace
+collaboration  avec Denis \textsc{LE  FUR}, vous  disposez �  pr�sent de
+toute  une panoplie  d'outils similaires  pour tracer  des  courbes, des
+histogrammes, des arbres de probabilit�s, des graphes probabilistes, des
+lissages par moyennes  mobiles et j'en passe et  des meilleures... Allez
+d�couvrir                 ces                 tr�sors                sur
+\href{http://mathsp.tuxfamily.org/spip.php?rubrique46}{http://mathsp.tuxfamily.org/spip.php?rubrique46}.
+
+
+
+
+
+
+
+
+
 \section{Comment �a marche~?}
 
 \subsection{Principe g�n�ral}
@@ -200,7 +213,7 @@ fclose(sortie); // on ferme XCasmpfc.mp
 
 
 
-\begin{figure}
+\begin{figure}[!h]
               \begin{Idee}{Autres collaborations XCAS/\LaTeX{}}
 On peut  suivre ce m�me  principe pour cr�er d'autres  associations de
 vos outils pr�f�r�s. Voir par exemple~:
@@ -219,6 +232,17 @@ et
 
 \section{De quoi a-t-on besoin~?}
 
+\begin{figure}[!h]
+  \begin{Idee}{Conseils en lignes}
+    N'h�sitez pas � explorer la page suivante : 
+
+\href{http://mathsp.tuxfamily.org/spip.php?article186}{http://mathsp.tuxfamily.org/spip.php?article186}
+
+surtout si vous �tes sur XP :-)
+    \end{Idee}
+  \end{figure}
+
+
 \begin{itemize}
 
 \item Il faut avoir install� \texttt{XCAS}, logiciel multi-plateforme de calcul et de programmation~:
@@ -266,7 +290,7 @@ pour installer une nouvelle extension \LaTeX{}.
 
 \end{itemize}
 
-\begin{figure}
+\begin{figure}[!h]
 
               \begin{Idee}{shell-escape}
        Pour         les         utilisateurs         de        TeXnicCenter,         observez         cette
@@ -294,7 +318,7 @@ et l� il faut ajouter
                
       \end{figure}         
 
-\begin{figure}
+\begin{figure}[!h]
               \begin{DANGER}{Conflit d'extensions}
               L'extension  \verb+fancybox+   rentre  en  conflit   avec  \verb+fancyvrb+  qu'utilise
               \verb+tablor+ car elles d�finissent toutes deux diff�remment l'environnement \verb+VerbatimOut+.
@@ -314,14 +338,14 @@ et l� il faut ajouter
 
 
 
-% \begin{figure}
+% \begin{figure}[!h]
 %               %\begin{DANGER}
 % Le fichier \texttt{tablor.sty} est cod� en \texttt{latin-1}. Les utilisateurs de
 % \texttt{utf-8} devront donc utiliser \texttt{tablorutf8.sty} � la place. 
 %                %\end{DANGER}
 %                \end{figure}
 
-\pagebreak
+%\pagebreak
 
 \section{Comment l'utiliser~?}
 
@@ -343,7 +367,7 @@ Le pr�ambule sera toujours~:
 
 
 
-% \begin{figure}
+% \begin{figure}[!h]
 %               \begin{Idee}
 %               Les fontes utilis�es  dans les tableaux sont \verb+[upright]{fourier}+.  Il est tout �
 %               fait  possible  d'utiliser   d'autres  fontes.  Il  suffit  de   modifier  le  fichier
@@ -581,7 +605,55 @@ ou bien, selon les cas~:
 \end{lstlisting}
 
 
+\section{Facteur de r�duction}
 
+Si vous trouvez le tableau  trop grand, vous pouvez utilisez la commande
+\verb+\ech{nombre}+  o�  \texttt{nombre}  repr�sente le  coefficienr  de
+r�duction ou d'agrandissement du tableau.
+
+Par exemple, comparez~:
+
+ \begin{lstlisting}
+\begin{TV}
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
+\end{TV}
+  \end{lstlisting}
+
+  \begin{center}
+    
+  
+\begin{TV}
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
+\end{TV}
+
+\end{center}
+
+et 
+
+ \begin{lstlisting}
+\ech{0.7}
+\begin{TV}
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
+\end{TV}
+\ech{1}
+  \end{lstlisting}
+
+  \begin{center}
+    
+ \ech{0.7} 
+\begin{TV}
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
+\end{TV}
+\ech{1}
+
+\end{center}
+
+\begin{figure}[!h]
+              \begin{DANGER}{Remise � l'�chelle 1}
+              N'oubliez pas  de remettre �  l'�chelle 1 en entrant  � la
+              suite de l'environnement \verb+\ech{1}+
+               \end{DANGER}
+               \end{figure}
 
 
 \section{Tableaux des variations}
@@ -594,7 +666,7 @@ L'environnement s'appelle \texttt{TV}. On utilise une commande au format \texttt
 \xcas
 
 \begin{lstlisting}
-TV([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,t,\tv)
+TV([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,lignes,trigo,\tv)
 \end{lstlisting}
 
 \begin{itemize}
@@ -602,16 +674,18 @@ TV([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expr
 \item  \texttt{[borne inf,borne  sup]}  d�signe les  bornes  de l'ensemble  de  d�finition. On  note
   $+\infty$~:~\texttt{+infinity} et $-\infty$~:~\texttt{-infinity}. N'oubliez pas
   les crochets~!
-\item \texttt{[valeurs interdites]} d�signe la liste des valeurs interdites;
+\item \texttt{[valeurs interdites]} d�signe la liste des valeurs interdites~;
 \item  \texttt{"nom fonction"}  d�signe la  lettre repr�sentant  la fonction  telle que  vous voulez
   qu'elle apparaisse : $f$, $g$, $\varphi$, etc.
 \item \texttt{"nom variable"}~:~m�me  chose pour la variable, selon que vous  voulez la d�signer par
   $x$, $t$, etc. N'oubliez pas les guillemets~!
 \item \texttt{expression en fonction de x} d�signe l'expression de la fonction. Attention~! Utilisez
-  ici toujours $x$ pour d�signer la variable;
-\item le  param�tre \texttt{t} est � remplacer par 1 si vous voulez voir appara�tre une ligne
+  ici toujours $x$ pour d�signer la variable~;
+\item le  param�tre \texttt{lignes} est � remplacer par 1 si vous voulez voir appara�tre une ligne
   avec le signe de la d�riv�e, par 0 si vous ne voulez pas de cette ligne et par 2 si vous ne voulez
-  que le signe de la d�riv�e.
+  que le signe de la d�riv�e~;
+\item le param�tre  \texttt{trigo} est � remplacer par  \texttt{t} si la
+      fonction �tudi�e est trigonom�trique et par tout autre symbole sinon~;
 \item on termine par \verb+\tv+, une commande permettant de num�roter les tableaux en interne.
 
 \end{itemize}
@@ -627,7 +701,7 @@ Voyons � pr�sent quelques exemples.
 On obtient~:
 
 \begin{TV}
-TV([-5,7],[],"f","x",x^2,0,\tv);
+TV([-5,7],[],"f","x",x^2,0,n,\tv);
 \end{TV}
 
 
@@ -635,7 +709,7 @@ apr�s avoir entr�~:
 
 \begin{lstlisting}
 \begin{TV}
-TV([-5,7],[],"f","x",x^2,0,\tv)
+TV([-5,7],[],"f","x",x^2,0,n,\tv)
 \end{TV}
 \end{lstlisting}
 
@@ -645,12 +719,12 @@ TV([-5,7],[],"f","x",x^2,0,\tv)
 
   \begin{lstlisting}
 \begin{TV}
-TV([-infinity,+infinity],[],"f","x",x^2,1,\tv)
+TV([-infinity,+infinity],[],"f","x",x^2,1,n,\tv)
 \end{TV}
   \end{lstlisting}
 
 \begin{TV}
-TV([-infinity,+infinity],[],"f","x",x^2,1,\tv)
+TV([-infinity,+infinity],[],"f","x",x^2,1,n,\tv)
 \end{TV}
 
 \item Avec la m�me fonction sur \textbf{R} avec uniquement le signe de la d�riv�e~:
@@ -659,12 +733,12 @@ TV([-infinity,+infinity],[],"f","x",x^2,1,\tv)
 
   \begin{lstlisting}
 \begin{TV}
-TV([-infinity,+infinity],[],"f","x",x^2,2,\tv)
+TV([-infinity,+infinity],[],"f","x",x^2,2,n,\tv)
 \end{TV}
   \end{lstlisting}
 
 \begin{TV}
-TV([-infinity,+infinity],[],"f","x",x^2,2,\tv)
+TV([-infinity,+infinity],[],"f","x",x^2,2,n,\tv)
 \end{TV}
 
 
@@ -674,7 +748,7 @@ TV([-infinity,+infinity],[],"f","x",x^2,2,\tv)
 
   \begin{lstlisting}
 \begin{TV}
-TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,\tv)
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
 \end{TV}
   \end{lstlisting}
 
@@ -682,12 +756,30 @@ TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,\tv)
     
   
 \begin{TV}
-TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,\tv)
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
 \end{TV}
 
 \end{center}
 
 
+\item Pour la fonction $x\mapsto \sin(x)+\frac{1}{2}$ on n'oublie pas le
+      param�tre \texttt{t}~:
+
+ \begin{lstlisting}
+\begin{TV}
+TV([-pi,pi],[],"g","t",sin(x)+1/2,1,t,\tv)
+\end{TV}
+  \end{lstlisting}
+
+  \begin{center}
+\begin{TV}
+TV([-pi,pi],[],"g","t",sin(x)+1/2,1,t,\tv)
+\end{TV}
+\end{center}
+
+
+
+
 \item Il y aura  des probl�mes pour des �quations $f'(x)=0$ que  \texttt{XCAS} ne saurait pas r�soudre
   de  mani�re  formelle.   Il  faudrait  alors  utiliser  une   r�solution  num�rique  et  remplacer
   \texttt{resoudre} par \texttt{fsolve}.  Mais dans les �tudes demand�es au  Bac, l'�tude des signes
@@ -710,19 +802,19 @@ On utilise alors l'environnement \texttt{TVZ} (Z comme zone...).
 
 \begin{lstlisting}
 \begin{TVZ}
-  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,\tv)
+  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,\tv)
 \end{TVZ}
 \end{lstlisting}
 
 
 \begin{center}
   \begin{TVZ}
-  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,\tv)
+  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,\tv)
 \end{TVZ}
 \end{center}
 
 
-\begin{figure}
+\begin{figure}[!h]
               \begin{DANGER}{Listes des intervalles interdits}
               Le troisi�me argument est une liste  d'intervalles : la liste des �~zones interdites~�
               qui peut �ventuellemnt se r�duire � un seul intervalle comme dans l'exemple pr�c�dent.
@@ -735,7 +827,7 @@ Voici       un      exemple       comportant       plusieurs      zones       in
 
 \begin{lstlisting}
 \begin{TVZ}
-  TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,\tv)
+  TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,n,\tv)
 \end{TVZ}
 \end{lstlisting}
 
@@ -743,7 +835,7 @@ Voici       un      exemple       comportant       plusieurs      zones       in
 
 \begin{center}
   \begin{TVZ}
- TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,\tv)
+ TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,n,\tv)
 \end{TVZ}
 \end{center}
 
@@ -756,7 +848,7 @@ Si l'on  veut mettre en  �vidence les solutions  de l'�quation $f(x)=a$, on  uti
 La syntaxe est~:
 
 \begin{lstlisting}
-TVI([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,t,a,\tv)
+TVI([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,t,a,trigo,\tv)
 \end{lstlisting}
 
 Les param�tres sont les m�mes que pour \texttt{TV} mais on ajoute la valeur \texttt{a} bien s�r.
@@ -766,7 +858,7 @@ Par exemple, pour $f~:~x\mapsto \frac{x^2}{x^2-1}$ et l'�quation $f(x)=10$ on en
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,\tv)
+TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,n,\tv)
 \end{TVI}
 \end{lstlisting}
 
@@ -774,7 +866,7 @@ TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,\tv)
 et on obtient~:
 
 \begin{TVI}
-TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,\tv)
+TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,n,\tv)
 \end{TVI}
 
 Les solutions sont not�es $\alpha_1$, $\alpha_2$, etc.
@@ -784,7 +876,7 @@ Si l'�quation est plut�t $f(x)=-1$~:
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,\tv)
+TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,n,\tv)
 \end{TVI}
 \end{lstlisting}
 
@@ -792,7 +884,7 @@ TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,\tv)
 et on obtient~:
 
 \begin{TVI}
-TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,\tv)
+TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,n,\tv)
 \end{TVI}
 
 
@@ -823,7 +915,7 @@ On �tudie d'abord la fonction $x\mapsto g'(x)$~:
 
 
 % \begin{TVIapp}
-%  TVIapp([0,+infinity],[0],"g'","x",diff(ln(x)-x*exp(2-x),x),1,0,\tv)
+%  TVIapp([0,+infinity],[0],"g'","x",diff(ln(x)-x*exp(2-x),x),1,0,n,\tv)
 %  \end{TVIapp}
 
 \stepcounter{TVn}
@@ -860,18 +952,19 @@ La syntaxe est la suivante~:
 
 \begin{lstlisting}
  \begin{TVP}
-TVP(IE,VI,["x","y"],"t",[x(t),y(t)],a,trigo,\tv)
+TVP(IE,VI,["x","y"],"t",[x(t),y(t)],a,trigo,n,\tv)
  \end{TVP}
 \end{lstlisting}
 
 
 avec  \texttt{IE}  l'intervalle d'�tude,  \texttt{VI}  la liste  des  listes  de valeurs  interdites
 respectives pour les deux fonctions, \texttt{a} pour  avoir un tableau complet ou partiel comme dans
-les autres "TV", enfin \texttt{trigo} qui  vaut 1 si interviennent des fonctions trigonom�trqiues, 0
+les autres  "TV", enfin \texttt{trigo}  qui vaut \texttt{t} si  interviennent des
+fonctions trigonom�trqiues, autre chose
 sinon.
 
 
-\begin{figure}[h]
+\begin{figure}[!h]
               \begin{DANGER}{Version de XCAS}
               L'utilisation de TVP implique l'utilisation d'une version de XCAS d'une date post�rieure au 14 juin
               2008 !
@@ -892,13 +985,13 @@ sinon.
 \begin{lstlisting}
   
  \begin{TVP}
- TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv)
+ TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv)
  \end{TVP}
 
 \end{lstlisting}
  
  \begin{TVP}
- TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv)
+ TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv)
  \end{TVP}
 
 
@@ -919,14 +1012,14 @@ y(t)=\frac{t^2(t+2)}{t+1}
 
 \begin{lstlisting}
 \begin{TVP}
-TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,0,\tv)
+TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,\tv)
 \end{TVP}
 \end{lstlisting}
 
 
 
 \begin{TVP}
-TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,0,\tv)
+TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,\tv)
 \end{TVP}
 
 
@@ -957,7 +1050,7 @@ TSa(-2,3,-1,5,\tv);
 
 
 
-\begin{figure}[h]
+\begin{figure}[!h]
               \begin{DANGER}{Nouveaut� � partir de la version 2.08}
 Par souci de coh�rence  avec l'environnement TSq, on doit rajouter maintenant  en premier argument le
 nom de la fonction produit dans l'environnement TS.
@@ -977,7 +1070,7 @@ pr�cisant l'intervalle d'�tude~:
 
 \begin{lstlisting}
 \begin{TS}
- TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],\tv);
+ TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],n,\tv);
 \end{TS}
 \end{lstlisting}
 
@@ -985,7 +1078,7 @@ On obtient~:
 
 
 \begin{TS}
- TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],\tv);
+ TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],n,\tv);
 \end{TS}
 
 
@@ -994,13 +1087,13 @@ Ou bien, sur un intervalle born�~:
 
 \begin{lstlisting}
 \begin{TS}
-TS("f",[x-10,x+10],[-15,10],\tv)
+TS("f",[x-10,x+10],[-15,10],n,\tv)
 \end{TS}
 \end{lstlisting}
 
 
 \begin{TS}
-TS("f",[x-10,x+10],[-15,10],\tv)
+TS("f",[x-10,x+10],[-15,10],n,\tv)
 \end{TS}
 
 
@@ -1012,7 +1105,7 @@ On entre dans deux listes diff�rentes les facteurs du num�rateur et du d�nominat
 
 \begin{lstlisting}
 \begin{TSq}
-TSq("nom du quotient",[liste des facteurs du num�rateur],[liste des facteurs du d�nominateur],[inf,sup])
+TSq("nom du quotient",[liste des facteurs du num�rateur],[liste des facteurs du d�nominateur],[inf,sup],trigo,\tv)
 \end{TSq}
 \end{lstlisting}
 
@@ -1020,7 +1113,7 @@ Par exemple, pour �tudier le signe de $\frac{(-2x+3)(-4x+5)}{(x^2-16)(x-2)}$ sur
 
 \begin{lstlisting}
 \begin{TSq}
-TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],\tv)
+TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],n,\tv)
 \end{TSq}
 \end{lstlisting}
 
@@ -1028,21 +1121,21 @@ TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],\tv)
 
 
 \begin{TSq}
-TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],\tv)
+TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],n,\tv)
 \end{TSq}
 
-Sur un intervalle born�~:
+% Sur un intervalle born�~:
 
-\begin{lstlisting}
-\begin{TSq}
-TSq("Q",[x-10],[x+10],[-infinity,10],\tv)
-\end{TSq}
-\end{lstlisting}
+% \begin{lstlisting}
+% \begin{TSq}
+% TSq("Q",[x-10],[x+10],[-infinity,10],n,\tv)
+% \end{TSq}
+% \end{lstlisting}
 
 
-\begin{TSq}
-TSq("Q",[x-10],[x+10],[-infinity,10],\tv)
-\end{TSq}
+% \begin{TSq}
+% TSq("Q",[x-10],[x+10],[-infinity,10],n,\tv)
+% \end{TSq}
 
 
 
@@ -1055,14 +1148,14 @@ l'expression �tudi�e et l'intervalle consid�r�~:
 
 \begin{lstlisting}
 \begin{TSc}
-TSc((x-10)*(x+5),[-10,10],\tv)
+TSc((x-10)*(x+5),[-10,10],n,\tv)
 \end{TSc}
 \end{lstlisting}
 
 
 
 \begin{TSc}
-TSc((x-10)*(x+5),[-10,10],\tv)
+TSc((x-10)*(x+5),[-10,10],n,\tv)
 \end{TSc}
 
 
@@ -1087,7 +1180,7 @@ Si vous tapez~:
 
 \begin{lstlisting}
 \begin{TV*}{100}
-    TV([-1,+infinity],[],"f","x",x-ln(x+1),1,\tv)
+    TV([-1,+infinity],[],"f","x",x-ln(x+1),1,n,\tv)
 \end{TV*}
 \end{lstlisting}
 
@@ -1106,7 +1199,7 @@ Par exemple, je tape~:
 
 \begin{lstlisting}
 \begin{TS*}{100}
-    TS("F",[3*x+2,5*x^2-1],[-50,50],\tv)
+    TS("F",[3*x+2,5*x^2-1],[-50,50],n,\tv)
 \end{TS*}
 \end{lstlisting}
 
@@ -1125,7 +1218,7 @@ automatiquement pour m'afficher le tableau voulu~:
 
 \begin{center}
   \begin{TS*}{105}
-    TS("F",[3*x+2,5*x^2-1],[-50,50],\tv)
+    TS("F",[3*x+2,5*x^2-1],[-50,50],n,\tv)
   \end{TS*}
 \end{center}
 
@@ -1191,6 +1284,7 @@ dans un fichier \texttt{latex-tempo}:
                  "\""(p "nom de la variable :")"\","
                  ""(p "expression de la fonction (utiliser x) :")","
 ""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")","
+""(p "trigo ?(t:trigo, n:non trigo) :")","
                  "\\tv)" n>
                "\\end{TV}" n>
                "\\end{center}" > % ))
@@ -1203,6 +1297,7 @@ dans un fichier \texttt{latex-tempo}:
                   "\""(p "nom de la variable :")"\","
                   ""(p "expression de la fonction (utiliser x) :")","
 ""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")","
+""(p "trigo ?(t:trigo, n:non trigo) :")","
                   ""(p "f(x)=l pour la valeur l :")","
                   "\\tv)" n>
                   "\\end{TVI}" n>
@@ -1212,7 +1307,8 @@ dans un fichier \texttt{latex-tempo}:
                   "\\begin{TS}" n>
                   "TS(\""(p "nom du produit :")"\","
                  "["(p "liste des facteurs (,) :")"],"
-        "["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"],"        
+        "["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"],"
+""(p "trigo ?(t:trigo, n:non trigo) :")","        
                   "\\tv)" n>
                   "\\end{TS}" n>
                   "\\end{center}" > % ))
@@ -1223,6 +1319,7 @@ dans un fichier \texttt{latex-tempo}:
                   "["(p "liste des facteurs du numerateur (,) :")"],"
                   "["(p "liste des facteurs du denominateur (,) :")"],"
         "["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"],"
+""(p "trigo ?(t:trigo, n:non trigo) :")","
                   "\\tv)" n>    
                   "\\end{TSq}" n>
                   "\\end{center}" > % ))
@@ -1238,7 +1335,7 @@ dans un fichier \texttt{latex-tempo}:
                   "["(p "expression de la fonction x (utiliser t) :")","
                   ""(p "expression de la fonction y (utiliser t) :")"],"
 ""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")","
-                  ""(p "1 si fonctions trigo, 0 sinon :")","
+                  ""(p "t si fonctions trigo, n sinon :")","
                   "\\tv)" n>
                   "\\end{TVP}" n>
                   "\\end{center}" > % ))
@@ -1253,6 +1350,7 @@ dans un fichier \texttt{latex-tempo}:
                  "\""(p "nom de la variable :")"\","
                  ""(p "expression de la fonction (utiliser x) :")","
 ""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")","
+""(p "trigo ?(t:trigo, n:non trigo) :")","
                  "\\tv)" n>
                "\\end{TV}" n>
                "\\end{center}" > % ))
@@ -1267,133 +1365,127 @@ Voici quelques exemples de tableaux~:
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,\tv)
+TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,n,\tv)
 \end{TVI}
 \end{lstlisting}
 
 \begin{TVI}
-TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,\tv)
+TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,n,\tv)
 \end{TVI}
 
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([-1/2,+infinity],[],"f","x",x^2,1,2,\tv)
+TVI([-1/2,+infinity],[],"f","x",x^2,1,2,n,\tv)
 \end{TVI}
 \end{lstlisting}
 
 
 \begin{TVI}
-TVI([-1/2,+infinity],[],"f","x",x^2,1,2,\tv)
+TVI([-1/2,+infinity],[],"f","x",x^2,1,2,n,\tv)
 \end{TVI}
 
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([0,+infinity],[0],"f","x",ln(x),1,2,\tv)
+TVI([0,+infinity],[0],"f","x",ln(x),1,2,n,\tv)
 \end{TVI}
 \end{lstlisting}
 
 \begin{TVI}
-TVI([0,+infinity],[0],"f","x",ln(x),1,2,\tv)
+TVI([0,+infinity],[0],"f","x",ln(x),1,2,n,\tv)
 \end{TVI}
 
 \stepcounter{TVn}
 
 \begin{lstlisting}
 \begin{TV}
-TV([1,+infinity],[],"f","x",-ln(x),1,\tv)
+TV([1,+infinity],[],"f","x",-ln(x),1,n,\tv)
 \end{TV}
 \end{lstlisting}
 
 \begin{TV}
-TV([1,+infinity],[],"f","x",-ln(x),1,\tv)
+TV([1,+infinity],[],"f","x",-ln(x),1,n,\tv)
 \end{TV}
 
 
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([-pi,pi],[],"f","x",cos(x),1,1/2,\tv)
+TVI([-pi,pi],[],"f","x",cos(x),1,1/2,t,\tv)
 \end{TVI}
 \end{lstlisting}
 
 \begin{TVI}
-TVI([-pi,pi],[],"f","x",cos(x),1,1/2,\tv)
+TVI([-pi,pi],[],"f","x",cos(x),1,1/2,t,\tv)
 \end{TVI}
 
 \begin{lstlisting}
 \begin{TV}
-TV([0,2*pi],[],"f","x",cos(x),1,\tv)
+TV([0,2*pi],[],"f","x",cos(x),1,t,\tv)
 \end{TV}
 \end{lstlisting}
 
 \begin{TV}
-TV([0,2*Pi],[],"f","x",cos(x),1,\tv)
+TV([0,2*Pi],[],"f","x",cos(x),1,t,\tv)
 \end{TV}
 
 
-\begin{figure}
-              \begin{DANGER}{Fonctions p�riodiques}
-              Il y  aura des  probl�mes si vous  demandez un  tableau des variations  d'une fonction
-              p�riodique sur un intervalle
-              d'amplitude sup�rieure � la p�riode, mais est-ce vraiment utile ?...
-               \end{DANGER}
-               \end{figure}
+
 
 
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([0,pi],[pi/2],"h","t",tan(x),1,7,\tv)
+TVI([0,pi],[pi/2],"h","t",tan(x),1,7,t,\tv)
 \end{TVI}
 \end{lstlisting}
 
 \begin{TVI}
-TVI([0,pi],[pi/2],"h","t",tan(x),1,7,\tv)
+TVI([0,pi],[pi/2],"h","t",tan(x),1,7,t,\tv)
 \end{TVI}
 
 
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,\tv)
+TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,n,\tv)
 \end{TVI}
 \end{lstlisting}
 
 \begin{TVI}
-TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,\tv)
+TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,n,\tv)
 \end{TVI}
 
 \begin{lstlisting}
 \begin{TV}
-TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,\tv)
+TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,n,\tv)
 \end{TV}
 \end{lstlisting}
 
 \begin{TV}
-TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,\tv)
+TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,n,\tv)
 \end{TV}
 
 
 \begin{lstlisting}
 \begin{TS}
-TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],\tv);
+TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],n,\tv);
 \end{TS}
 \end{lstlisting}
 
 \begin{TS}
-TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],\tv);
+TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],n,\tv);
 \end{TS}
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,\tv)
+TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,n,\tv)
 \end{TVI}
 \end{lstlisting}
 
 \begin{TVI}
-TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,\tv)
+TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,n,\tv)
 \end{TVI}
 
 
@@ -1401,12 +1493,12 @@ TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,\tv)
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,\tv)
+TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,n,\tv)
 \end{TVI}
 \end{lstlisting}
 
 \begin{TVI}
-TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,\tv)
+TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,n,\tv)
 \end{TVI}
 
 \stepcounter{TVn}
@@ -1414,12 +1506,12 @@ TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,\tv)
 
 \begin{lstlisting}
 \begin{TV}
-TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,\tv)
+TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,n,\tv)
 \end{TV}
 \end{lstlisting}
 
 \begin{TV}
-TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,\tv)
+TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,n,\tv)
 \end{TV}
 
 
@@ -1428,91 +1520,91 @@ TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,\tv)
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([0,pi],[],"f","x",cos(x)-x,1,0,\tv)
+TVI([0,pi],[],"f","x",cos(x)-x,1,0,n,\tv)
 \end{TVI}
 \end{lstlisting}
 
 \begin{TVI}
-TVI([0,pi],[],"f","x",cos(x)-x,1,0,\tv)
+TVI([0,pi],[],"f","x",cos(x)-x,1,0,n,\tv)
 \end{TVI}
 
 \begin{lstlisting}
 \begin{TVI}
-TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,\tv)
+TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,n,\tv)
 \end{TVI}
 \end{lstlisting}
 
 
 
 \begin{TVI}
-TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,\tv)
+TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,n,\tv)
 \end{TVI}
 
 
 
 \begin{lstlisting}
 \begin{TSc}
-TSc((x-10)*(x+10),[-10,10],\tv)
+TSc((x-10)*(x+10),[-10,10],n,\tv)
 \end{TSc}
 \end{lstlisting}
 
 
 
 \begin{TSc}
-TSc((x-10)*(x+10),[-10,10],\tv)
+TSc((x-10)*(x+10),[-10,10],n,\tv)
 \end{TSc}
 
 
 \begin{lstlisting}
 \begin{TVZ}
-  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,\tv)
+  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,n,\tv)
 \end{TVZ}
 \end{lstlisting}
 
  \begin{TVZ}
-  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,\tv)
+  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,n,\tv)
   \end{TVZ}
    
   \begin{lstlisting}
 \begin{TVZ}
-  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,\tv)
+  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,n,\tv)
 \end{TVZ}
   \end{lstlisting}
 
  \begin{TVZ}
-  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,\tv)
+  TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,n,\tv)
   \end{TVZ}
 
 
 
   \begin{lstlisting}
 \begin{TVP}
-TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv)
+TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv)
 \end{TVP}
   \end{lstlisting}
 
 
 
 \begin{TVP}
-TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv)
+TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv)
 \end{TVP}
 
 
 \begin{lstlisting}
 \begin{TVP}
-TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,1,\tv)
+TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,t,\tv)
 \end{TVP}
 \end{lstlisting}
 
 
 \begin{TVP}
-TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,1,\tv)
+TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,t,\tv)
 \end{TVP}
 
 
 \begin{lstlisting}
 \begin{TVZ}
-  TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,\tv)
+  TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,n,\tv)
 \end{TVZ}
 \end{lstlisting}
 
@@ -1520,175 +1612,212 @@ TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,1,\tv)
 
 \begin{center}
   \begin{TVZ}
- TVZ([-infinity,+infinity],[],[[-1,1],[4,6]],"f","x",sqrt((x-5)^2-1)+sqrt(x^2-1),1,\tv)
+ TVZ([-infinity,+infinity],[],[[-1,1],[4,6]],"f","x",sqrt((x-5)^2-1)+sqrt(x^2-1),1,n,\tv)
 \end{TVZ}
 \end{center}
 
-\lat
+
 
 \begin{lstlisting}
-\begin{enumerate}
-\item 
+  \begin{TVP}
+    TVP([0,pi/2],[[],[]],["f","g"],"t",[(sin(3*t)),(sin(4*t))],1,t,\tv)
+    \end{TVP}
+\end{lstlisting}
+
+
+\begin{center}
+  \begin{TVP}
+    TVP([0,pi/2],[[],[]],["f","g"],"t",[(sin(3*t)),(sin(4*t))],1,t,\tv)
+    \end{TVP}
+  \end{center}
+
+\begin{lstlisting}
+\begin{TS}
+  TS(" f ",[cos(x)-1/2,sin(x)+1/2],[0,2*pi],t,\tv)
+\end{TS}
+\end{lstlisting}
+
 
- Selon le tableau de variation de la fonction $f$
-    ci-dessous, on peut affirmer que \ldots
+\begin{center}
+\begin{TS}
+  TS(" f ",[cos(x)-1/2,sin(x)+1/2],[0,2*pi],t,\tv)
+\end{TS}
+\end{center}
+
+
+
+
+
+
+
+
+
+
+% \lat
+
+% \begin{lstlisting}
+% \begin{enumerate}
+% \item 
+
+%  Selon le tableau de variation de la fonction $f$
+%     ci-dessous, on peut affirmer que \ldots
      
-\begin{TV}
-        TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,\tv)
-\end{TV}
+% \begin{TV}
+%         TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,n,\tv)
+% \end{TV}
 
-\VF
-\begin{itemize}
+% \VF
+% \begin{itemize}
 
-    \item[\ldots] 5 n'a pas d'ant�c�dent \Rep
-    \item[\ldots] 5 n'a pas d'image \Rep
-    \item[\ldots] 5 a deux ant�c�dents \Rep
-    \item[\ldots] 5 a une image sup�rieure � celle de $\sqrt{2}$\Rep
+%     \item[\ldots] 5 n'a pas d'ant�c�dent \Rep
+%     \item[\ldots] 5 n'a pas d'image \Rep
+%     \item[\ldots] 5 a deux ant�c�dents \Rep
+%     \item[\ldots] 5 a une image sup�rieure � celle de $\sqrt{2}$\Rep
   
-\end{itemize}
+% \end{itemize}
 
 
 
-\item Soit $f$ la fonction d�finie par $f~:~x\mapsto 3x^3-5x^2+2x-7$.  Les tableaux suivants peuvent
-  correspondre � $f$~:
+% \item Soit $f$ la fonction d�finie par $f~:~x\mapsto 3x^3-5x^2+2x-7$.  Les tableaux suivants peuvent
+%   correspondre � $f$~:
 
-\VF
+% \VF
 
-  \begin{enumerate}
+%   \begin{enumerate}
 
 
- \item Tableau 1 \Rep
+%  \item Tableau 1 \Rep
 
-\begin{TV}
-        TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,\tv)
-\end{TV}
+% \begin{TV}
+%         TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,n,\tv)
+% \end{TV}
 
-\item Tableau 2 \Rep
+% \item Tableau 2 \Rep
 
-\begin{TV}
-        TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,\tv)
-\end{TV}
+% \begin{TV}
+%         TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,n,\tv)
+% \end{TV}
 
-\item Tableau 3 \Rep
+% \item Tableau 3 \Rep
 
-\begin{TSc}
-        TSc(-3*x^3+5*x^2-2*x+7,[-20,20],\tv)
-\end{TSc}
+% \begin{TSc}
+%         TSc(-3*x^3+5*x^2-2*x+7,[-20,20],n,\tv)
+% \end{TSc}
 
 
-\item Tableau 4 \Rep
+% \item Tableau 4 \Rep
 
-\begin{TSc}
-        TSc(3*x^3-5*x^2+2*x-7,[-20,20],\tv)
-\end{TSc}
+% \begin{TSc}
+%         TSc(3*x^3-5*x^2+2*x-7,[-20,20],n,\tv)
+% \end{TSc}
 
 
-\end{enumerate}
+% \end{enumerate}
 
-\end{enumerate}
+% \end{enumerate}
 
-\end{lstlisting}
+% \end{lstlisting}
 
 
 
 
 
-\begin{enumerate}
-\item 
+% \begin{enumerate}
+% \item 
 
- Selon le tableau de variation de la fonction $f$
-    ci-dessous, on peut affirmer que \ldots
+%  Selon le tableau de variation de la fonction $f$
+%     ci-dessous, on peut affirmer que \ldots
      
-\begin{TV}
-        TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,\tv)
-\end{TV}
+% \begin{TV}
+%         TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,n,\tv)
+% \end{TV}
 
-\VF
-\begin{itemize}
+% \VF
+% \begin{itemize}
 
-    \item[\ldots] 5 n'a pas d'ant�c�dent \Rep
-    \item[\ldots] 5 n'a pas d'image \Rep
-    \item[\ldots] 5 a deux ant�c�dents \Rep
-    \item[\ldots] 5 a une image sup�rieure � celle de $\sqrt{2}$\Rep
+%     \item[\ldots] 5 n'a pas d'ant�c�dent \Rep
+%     \item[\ldots] 5 n'a pas d'image \Rep
+%     \item[\ldots] 5 a deux ant�c�dents \Rep
+%     \item[\ldots] 5 a une image sup�rieure � celle de $\sqrt{2}$\Rep
   
-\end{itemize}
+% \end{itemize}
 
 
 
-\item Soit $f$ la fonction d�finie par $f~:~x\mapsto 3x^3-5x^2+2x-7$.  Les tableaux suivants peuvent-ils
-  correspondre � la fonction $f$~:
+% \item Soit $f$ la fonction d�finie par $f~:~x\mapsto 3x^3-5x^2+2x-7$.  Les tableaux suivants peuvent-ils
+%   correspondre � la fonction $f$~:
 
-\VF
+% \VF
 
-  \begin{enumerate}
+%   \begin{enumerate}
 
 
- \item Tableau 1 \Rep
+%  \item Tableau 1 \Rep
 
 
-\begin{TV}
-        TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,\tv)
-\end{TV}
+% \begin{TV}
+%         TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,n,\tv)
+% \end{TV}
 
-\item Tableau 2 \Rep
+% \item Tableau 2 \Rep
 
-\begin{TV}
-        TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,\tv)
-\end{TV}
+% \begin{TV}
+%         TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,n,\tv)
+% \end{TV}
 
-\item Tableau 3 \Rep
+% \item Tableau 3 \Rep
 
-\begin{TSc}
-        TSc(-3*x^3+5*x^2-2*x+7,[-20,20],\tv)
-\end{TSc}
+% \begin{TSc}
+%         TSc(-3*x^3+5*x^2-2*x+7,[-20,20],n,\tv)
+% \end{TSc}
 
 
-\item Tableau 4 \Rep
+% \item Tableau 4 \Rep
 
-\begin{TSc}
-        TSc(3*x^3-5*x^2+2*x-7,[-20,20],\tv)
-\end{TSc}
+% \begin{TSc}
+%         TSc(3*x^3-5*x^2+2*x-7,[-20,20],n,\tv)
+% \end{TSc}
 
 
-\end{enumerate}
+% \end{enumerate}
 
-\end{enumerate}
+% \end{enumerate}
 
 
 
-\begin{lstlisting}
-On consid�re la fonction $f$ d�finie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$
+% \begin{lstlisting}
+% On consid�re la fonction $f$ d�finie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$
 
-�tudions sa d�riv�e~:
+% �tudions sa d�riv�e~:
 
 
-\begin{TVIapp}
- TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv)
- \end{TVIapp}
+% \begin{TVIapp}
+%  TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv)
+%  \end{TVIapp}
 
-On en d�duit le tableau de variation de $f$
+% On en d�duit le tableau de variation de $f$
 
 
-\begin{TVapp}
- TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv)
- \end{TVapp}
-\end{lstlisting}
+% \begin{TVapp}
+%  TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv)
+%  \end{TVapp}
+% \end{lstlisting}
 
-On consid�re la fonction $f$ d�finie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$
+% On consid�re la fonction $f$ d�finie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$
 
-�tudions sa d�riv�e~:
+% �tudions sa d�riv�e~:
 
 
-\begin{TVIapp}
- TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv)
- \end{TVIapp}
+% \begin{TVIapp}
+%  TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv)
+%  \end{TVIapp}
 
-On en d�duit le tableau de variation de $f$
+% On en d�duit le tableau de variation de $f$
 
 
-\begin{TVapp}
- TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv)
- \end{TVapp}
+% \begin{TVapp}
+%  TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv)
+%  \end{TVapp}
 
 
 
diff --git a/Master/texmf-dist/tex/latex/tablor/tablor.sty b/Master/texmf-dist/tex/latex/tablor/tablor.sty
index ebcb6445802..b759961e1a3 100644
--- a/Master/texmf-dist/tex/latex/tablor/tablor.sty
+++ b/Master/texmf-dist/tex/latex/tablor/tablor.sty
@@ -1,5 +1,5 @@
 \NeedsTeXFormat{LaTeX2e}[1995/12/01]
-\ProvidesPackage{tablor}[12/06/2008 v3.00 la machine a creer des tableaux de signes et variations]
+\ProvidesPackage{tablor}[08/10/2008 v4.00 la machine a creer des tableaux de signes et variations]
 
 % \copyleft Connan le Barbare (aka Guillaume Connan) \copyright
 % This work may be distributed and/or mofified under the conditions
@@ -18,29 +18,29 @@
 % %%%%%% Pour des tableaux de plus de 2 facteurs
 %
 % \begin{TS}
-% TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[a,b],\tv);
+% TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[a,b],n,\tv);
 % \end{TS}
 %
 % pour les tableaux de signes avec quotient
 %\begin{TSq}
-%TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],\tv)
+%TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],n,\tv)
 %%\end{TSq}
 % un tableau de variation :
 %
 % \begin{TV}
-% TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,\tv)
+% TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,n,\tv)
 % \end{TV}
 %
 % tableau de variation avec zones interdites
 %
 % \begin{TVZ}
-%   TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,\tv)
+%   TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,\tv)
 % \end{TVZ}
 %
 %
 % tableau avec valeurs intermediares
 %\begin{TVI}
-%TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,\tv)
+%TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,\tv)
 %\end{TVI}
 %%%
 % tableau de variations avec f' sans zero formel
@@ -62,12 +62,12 @@
 %
 % Courbes parametrees
 %  \begin{TVP}
-%  TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,0,\tv)
+%  TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,\tv)
 %  \end{TVP}
 %
 %
 % \begin{TVP}
-%  TVP([0,pi/2],[[],[]],["x","y"],"t",[2*cos(t),sin(2*t)],1,1,\tv)
+%  TVP([0,pi/2],[[],[]],["x","y"],"t",[2*cos(t),sin(2*t)],1,t,\tv)
 %  \end{TVP}
 % %
 
@@ -102,6 +102,7 @@
 \newboolean{windows}\setboolean{windows}{false}
 
 
+
 %% on configure  tablor  dans un fichier exterieur pour la plateforme
 %% et l'editeur
 
@@ -162,7 +163,7 @@
 %% Donne comme prefixe aux tableaux le prefixe courant
 %% Peut-��tre modifie par \initablor
 
-\newcommand{\Tableaux}{\jobname}
+\newcommand{\nomtravail}{\jobname}
 
 %% initialise les compteurs
 
@@ -179,17 +180,17 @@
 
 
 \newcommand{\initablor}[1][\jobname]{%
-\renewcommand{\Tableaux}{#1}%     Arret du nom des tableaux
+\renewcommand{\nomtravail}{#1}%     Arret du nom des tableaux
 \setcounter{TVn}{0}%     Initialisation du compteur de tableaux.
 \ifthenelse{\boolean{xcas}}%    Avec l'option XCas
-{\IfFileExists{\Tableaux.Tab.mp}%      Si Tableaux.mp est present...
-        {\immediate\write18{\rem \Tableaux.Tab.mp}}%  le detruire
+{\IfFileExists{\nomtravail.Tab.mp}%      Si Tableaux.mp est present...
+        {\immediate\write18{\rem \nomtravail.Tab.mp}}%  le detruire
         {}%   
- \immediate\write18{\cp  enteteMP.cfg \Tableaux.Tab.mp}% Reconstituer l'ent��te de Tableaux.mp
+ \immediate\write18{\cp  enteteMP.cfg \nomtravail.Tab.mp}% Reconstituer l'ent��te de Tableaux.mp
 } 
-{\IfFileExists{\Tableaux.Tab.mp}%      Sans l'option XCas, si
+{\IfFileExists{\nomtravail.Tab.mp}%      Sans l'option XCas, si
                                 %      Tableaux.mp existe
-{\immediate\write18{mpost -interaction=batchmode \Tableaux.Tab}}% l'executer pour reconstituer les figures
+{\immediate\write18{mpost -interaction=batchmode \nomtravail.Tab}}% l'executer pour reconstituer les figures
 {\PackageWarning{tablor}{Pas de source metapost pour creer les tableaux.}}% sinon message d'erreur
                                 % (mais pas d'arret car les tableaux
                                 % peuvent ��tre presents )
@@ -224,12 +225,52 @@
 
 
 \begin{VerbatimOut}{XcasTV.cxx}
-TV(L,F,nom,nomv,f,ftt,nmr):={
+TV(L,F,nom,nomv,f,ftt,trigo,nmr):={
 nl:=size(L);
 f:=unapply(f,x);
 fp:=fonction_derivee(f);
 Z:=concat(L,F);
+S:=[];
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k<ns;k++){
+m:=0;
+while(evalf(simplifier(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
 S:=resoudre(fp(x),x);
+}
+
+
+  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire
+                             qq:=member(simplifier(S[j]),Z)==0;
+                             kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
+                          if(kk==1){if(qq==1){Z:=append(Z,simplifier(S[j]))}};
+                          fpour
+  fsi;
+Z:=sort(Z);
+nz:=size(Z);
+
+
+ tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z);
+     ftantque;
+
+
+
+
+
+
+
   si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                              kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                           if(kk==1){Z:=append(Z,simplifier(S[j]))};
@@ -360,7 +401,7 @@ fclose(sortie);
 \begin{VerbatimOut}{XcasTVZ.cxx}
 
 
-TVZ(L,F,FF,nom,nomv,f,ftt,nmr):={
+TVZ(L,F,FF,nom,nomv,f,ftt,trigo,nmr):={
 nl:=size(L);
 nf:=size(FF);
  Ff:=NULL;IMIN:=NULL;IMAX:=NULL;
@@ -382,7 +423,32 @@ for(k:=0;k<nf;k++){
 Z:=concat(Z,FF[k]);
 }
 
+S:=[];
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k<ns;k++){
+m:=0;
+while(evalf(simplifier(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
 S:=resoudre(fp(x),x);
+}
+
+
+
+
+
+
   si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                          for(k:=0;k<nf;k++){  
                            kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
@@ -584,10 +650,22 @@ f:=unapply(f,x);
 fp:=fonction_derivee(f);
 z0:=concat(L,F);z:=sort(z0);
 nz:=size(z);
-if(L==[-infinity,+infinity]){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..100);}
-else{if(L[0]==-infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..L[1]);}
-else{if(L[1]==+infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=L[0]..100);}
-else{S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=z[0]..z[nz-1])}}};
+
+
+
+
+
+
+S:=NULL;
+if(L==[-infinity,+infinity]){j:=[seq(-100+k,k=0..200)]minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[0]==-infinity){j:=[seq(k,k=100..floor(L[1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[1]==+infinity){j:=[seq(k,k=floor(L[0])..100)] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for;}
+else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for;  }}};
+
+
+
+
+
 si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                              kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]);
                           if(kk==1){if(kok==1){z:=append(z,simplifier(S[j]))}};
@@ -746,12 +824,32 @@ fclose(sortie);
 \begin{VerbatimOut}{XcasTVI.cxx}
 
 
-TVI(L,F,nom,nomv,f,ftt,ao,nmr):={
+TVI(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={
 nl:=size(L);
 f:=unapply(f,x);
 fp:=fonction_derivee(f);
 Z:=concat(L,F);
+S:=[];
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k<ns;k++){
+m:=0;
+while(evalf(simplifier(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
 S:=resoudre(fp(x),x);
+}
+
   si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                             kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                           if(kk==1){Z:=append(Z,simplifier(S[j]))};
@@ -963,10 +1061,24 @@ f:=unapply(f,x);
 fp:=fonction_derivee(f);
 z0:=concat(L,F);z:=sort(z0);
 nz:=size(z);
-if(L==[-infinity,+infinity]){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..100);}
-else{if(L[0]==-infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..L[1]);}
-else{if(L[1]==+infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=L[0]..100);}
-else{S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=z[0]..z[nz-1])}}};
+
+
+
+
+
+S:=NULL;
+if(L==[-infinity,+infinity]){j:=[seq(-100+k,k=0..200)]minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[0]==-infinity){j:=[seq(k,k=100..floor(L[1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[1]==+infinity){j:=[seq(k,k=floor(L[0])..100)] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for;}
+else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for;  }}};
+
+
+
+
+
+
+
+
 si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                              kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]);
                           if(kk==1){if(kok==1){z:=append(z,simplifier(S[j]))}};
@@ -1186,8 +1298,6 @@ fclose(sortie);
 
 
 \begin{VerbatimOut}{XcasTVP.cxx}
-
-
 TVP(L,F,nom,nomv,ff,ftt,trigo,nmr):={
 //local Z,LLL,FFF,nl,fp,f,S,d,t,ns,k,m,x,j,kk,nz,u,l0;
 nl:=size(L);
@@ -1196,61 +1306,71 @@ S:=[];
 f:=ff;
 Z:=[];
 LLL:=[];
+
+
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+
 for(d:=0;d<=1;d++){
 f:=subst(f,f[d]=unapply(f[d],t));
 fp:=append(fp,fonction_derivee(f[d]));
 LLL:=concat(L,F[d]);
 Z:=LLL union Z;
+SS:=resoudre(factor(simplifier(fp[d](t))),t);
+ns:=size(SS);
 
-ns:=size(resoudre(factor(simplifier(fp[d](t))),t));
-reset_solve_counter(0);
 for(k:=0;k<ns;k++){
-if(trigo==1){
-all_trig_solutions:=1;
-reset_solve_counter(-1,-1);m:=0;
-while(simplifier(subst(resoudre(factor(simplifier(fp[d](t))),t)[k],n_1=m))<=evalf(L[nl-1])){
-reset_solve_counter(-1,-1);
-S:=concat(S,simplifier(subst(resoudre(factor(simplifier(fp[d](t))),t)[k],n_1=m)));m:=m+1;
-reset_solve_counter(-1,-1);
+if(trigo==t){
+m:=0;
+while(evalf(simplifier(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m+1;
+
 };m:=-1;
-while(evalf(subst(resoudre(factor(simplifier(fp[d](t))),t)[k],n_1=m))>=L[0]){
-reset_solve_counter(-1,-1);
-S:=concat(S,simplifier(subst(resoudre(factor(simplifier(fp[d](t))),t)[k],n_1=m)));m:=m-1;
-reset_solve_counter(-1,-1);
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m-1;
+
 }
 }else{
-S:=concat(S,resoudre(factor(simplifier(fp[d](x))),x));
+S:=concat(S,SS);
 }
 }
-  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
+
+
+  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire
                              qq:=member(simplifier(S[j]),Z)==0;
                              kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                           if(kk==1){if(qq==1){Z:=append(Z,simplifier(S[j]))}};
                           fpour
   fsi;
-
-Z:=sort(Z); 
+Z:=sort(Z);
 nz:=size(Z);
- 
 
 
- tantque simplifier(Z[0])==simplifier(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); 
+ tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z);
      ftantque;
 
+
+
+
 nz:=size(Z);
 u:=1;
  tantque (u<nz-2) and (nz>2) faire
-     tantque Z[u]==Z[u+1] faire 
+     tantque evalf(Z[u])==evalf(Z[u+1]) faire
          Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=size(Z);
      ftantque;
   u:=u+1;
  ftantque;
- };
 
 
-Z:=sort(Z); 
+ };
+
+Z:=sort(Z);
 nz:=size(Z);
 
+
+
  l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:="",""; lf:="","";lsp:="","";
 pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
 ";fpour;
@@ -1263,14 +1383,15 @@ for(d:=0;d<=1;d++){
 FFF[d]:=concat(F[d],[-infinity,+infinity]);
        k0:= evalf(limite(f[d](x),x=Z[0],1))> evalf(limite(f[d](x),x=Z[1],-1));
        kz:=evalf(limite(f[d](x),x=Z[nz-1],-1))> evalf(limite(f[d](x),x=Z[nz-2],1));
-                          
+//}
+//$
  lsi[d]:=lsic+nom[d]+"'("+nomv+")}$ etex);"+if(member(Z[0],FFF[d])==0){"valBarre(btex $"+latex(simplifier(fp[d](Z[0])))+"$ etex);"}else{if(Z[0]==-infinity){" "}else{"nonDefBarre;
 "}}+
      if(Z[0]==-infinity){if(sign(evalf(fp[d](if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F[d])==0){
                                                     if(sign(fp[d](Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{
                                                          if(sign(fp[d]((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}
- 
-if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp[d](Z[r]+0.01))>0;                     
+
+if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp[d](Z[r]+0.01))>0;
                                                lsp[d]:=lsp[d]+if(member(Z[r],F[d])==0){"valBarre(btex $"+latex(simplifier(fp[d](Z[r])))+"$ etex);"}else{"nonDefBarre;"}+
                                                 if(ksp==1){"plus;"}else{"moins;"}
                                                   }; }
@@ -1298,15 +1419,17 @@ lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex $"+latex(simplifier(fp[d](Z
 for(d:=0;d<=1;d++){
    K0[d]:= evalf(limite(f[d](x),x=Z[0],1))> evalf(limite(f[d](x),x=Z[1],-1));
   Kz[d]:=evalf(limite(f[d](x),x,Z[nz-1],-1))> evalf(limite(f[d](x),x,Z[nz-2],1));
+//{
+//$
 lm0[d]:=limite(f[d](x),x,Z[0],1)==-infinity;
      li[d]:=lvic+nom[d]+"}$ etex);"+
            if(member(Z[0],F[d])==0){"valPos(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[0],1)))}+"$ etex,"}
-             else{"nonDefBarre;limDroite(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[0],1)))}+"$ etex,"}+                               
+             else{"nonDefBarre;limDroite(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[0],1)))}+"$ etex,"}+
            if(K0[d]==1){"1"}else{"0"}+
                          ");";
-            
+
                      if(nz>2){ for(r:=1; r<=nz-2;r++){ krm[d]:=evalf(limite(f[d](x),x=Z[r-1],1))< evalf(limite(f[d](x),x=Z[r],-1));
-                                                 krp[d]:=evalf(limite(f[d](x),x=Z[r],1))> evalf(limite(f[d](x),x,Z[r+1],-1)) ;  
+                                                 krp[d]:=evalf(limite(f[d](x),x=Z[r],1))> evalf(limite(f[d](x),x,Z[r+1],-1)) ;
                          lmrm[d]:=limite(f[d](x),x,Z[r],-1)==-infinity;lmrp[d]:=limite(f[d](x),x,Z[r],1)==-infinity;
                                                   lp[d]:=lp[d]+if(member(Z[r],F[d])){
                                     "limGauche(btex
@@ -1318,9 +1441,9 @@ lm0[d]:=limite(f[d](x),x,Z[0],1)==-infinity;
                                                    }; }
 
 lnz[d]:=limite(f[d](x),x=Z[nz-1],-1)==-infinity;
-                           lf[d]:=if(member(Z[nz-1],F[d])==0){"valPos(btex $"+if(lnz[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[nz-1],-1)))}+"$ etex,"}+                               
+                           lf[d]:=if(member(Z[nz-1],F[d])==0){"valPos(btex $"+if(lnz[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[nz-1],-1)))}+"$ etex,"}+
            if(Kz[d]==1){"1);"}else{"0);
-"};    
+"};
 
 
 
@@ -1403,8 +1526,6 @@ fprint(sortie,Unquoted,MetaLfc);
 fclose(sortie);
 
 }:;
-
-
 \end{VerbatimOut}
 
 
@@ -1420,22 +1541,58 @@ fclose(sortie);
 \begin{VerbatimOut}{XcasTabSignL.cxx}
 
 
-TS(nomf,L,D,nmr):={
+TS(nomf,L,D,trigo,nmr):={
 L:=apply(f->unapply(f,x),L)
 n:=size(L);
 Z:=NULL;
-
+nl:=size(L);
+S:=[];
 mini:=D[0]; maxi:=D[1];
 
 pour k de 0 jusque n-1 faire 
-  S:=resoudre(L[k](x),x);
+
+
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(L[k](x))),x);
+ns:=size(SS);
+for(j:=0;j<ns;j++){
+m:=0;
+while(evalf(simplifier(subst(SS[j],n_1=m)))<=evalf(maxi)){
+S:=concat(S,simplifier(subst(SS[j],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){
+S:=concat(S,simplifier(subst(SS[j],n_1=m)));m:=m-1;
+}
+}
+
+}else{
+S:=resoudre(L[k](x),x);
+}
+
+
+
+
   si size(S)>0 alors  pour j de 0 jusque size(S)-1 faire 
                           if(S[j]>mini and S[j]<maxi){Z:=Z,simplifier(S[j]);}
                       fpour;
   fsi;
 fpour;
+
+
+
+
+
 Z:=sort(Z);
 nz:=size(Z);
+
+
+
+
+
 if(nz>2){pour u de 1 jusque nz-2 faire 
      si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1;
      fsi;
@@ -1537,7 +1694,7 @@ fclose(sortie);
 
 
 \begin{VerbatimOut}{XcasTabSignQ.cxx}
-TSq(nomf,L,Fo,D,nmr):={
+TSq(nomf,L,Fo,D,trigo,nmr):={
 L:=apply(f->unapply(f,x),L);
 Fo:=apply(f->unapply(f,x),Fo);
 L:=concat(L,Fo);
@@ -1546,10 +1703,36 @@ Z:=NULL;
 m:=size(Fo);
 F:=NULL;FF:=NULL;
 mini:=D[0]; maxi:=D[1];
-
+S:=[];
+SF:=[];
 
 pour k de 0 jusque n-1 faire 
-  S:=resoudre(L[k](x),x);
+
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(L[k](x))),x);
+ns:=size(SS);
+for(j:=0;j<ns;j++){
+mm:=0;
+while(evalf(simplifier(subst(SS[j],n_1=mm)))<=evalf(maxi)){
+S:=concat(S,simplifier(subst(SS[j],n_1=mm)));mm:=mm+1;
+};mm:=-1;
+while(evalf(subst(SS[j],n_1=mm))>=evalf(mini)){
+S:=concat(S,simplifier(subst(SS[j],n_1=mm)));mm:=mm-1;
+}
+}
+
+}else{
+S:=resoudre(L[k](x),x);
+}
+
+
+
+
+
   si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                           if(S[j]>mini and S[j]<maxi){Z:=Z,simplifier(S[j]);}
                       fpour;
@@ -1558,7 +1741,28 @@ fpour;
 
 
 pour k de 0 jusque m-1 faire 
-  SF:=resoudre(Fo[k](x),x);
+
+
+
+if(trigo==1){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SSF:=resoudre(factor(simplifier(Fo[k](x))),x);
+nsf:=size(SSF);
+for(j:=0;j<nsf;j++){
+mm:=0;
+while(evalf(simplifier(subst(SSF[j],n_1=mm)))<=evalf(maxi)){
+SF:=concat(SF,simplifier(subst(SSF[j],n_1=mm)));mm:=mm+1;
+};mm:=-1;
+while(evalf(subst(SSF[j],n_1=mm))>=evalf(mini)){
+SF:=concat(SF,simplifier(subst(SSF[j],n_1=mm)));mm:=mm-1;
+}
+}
+
+}else{
+SF:=resoudre(Fo[j](x),x);
+}
+
   si size(SF)>0 alors pour j de 0 jusque size(SF)-1 faire 
                           FF:=FF,simplifier(SF[j]);
                           if(SF[j]>mini and SF[j]<maxi){F:=F,simplifier(SF[j]);}
@@ -1756,7 +1960,7 @@ fclose(sortie);
 
 
 
-%%
+%%$
 %% Code giac/Xcas pour les Tableaux de Signes d'expression ne contenant 
 %% qu'un seul terme
 
@@ -1764,11 +1968,38 @@ fclose(sortie);
 
 
 \begin{VerbatimOut}{XcasTSc.cxx}
-TSc(g,D,nmr):={
+TSc(g,D,trigo,nmr):={
 f:=unapply(g,x);
 Z:=NULL;
 mini:=D[0]; maxi:=D[1];lm:=" ";
+
+S:=[];
+
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(f(x))),x);
+ns:=size(SS);
+for(j:=0;j<ns;j++){
+m:=0;
+while(evalf(simplifier(subst(SS[j],n_1=m)))<=evalf(maxi)){
+S:=concat(S,simplifier(subst(SS[j],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){
+S:=concat(S,simplifier(subst(SS[j],n_1=m)));m:=m-1;
+}
+}
+
+}else{
 S:=resoudre(f(x),x);
+}
+
+
+
+
+
 if(size(S)==0){
 l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
 li:=if(mini!=-infinity and f(mini)==0){"
@@ -1856,14 +2087,16 @@ fclose(sortie);
 
 
 
-%%
+%%$
 %%
 %% traitement des fichiers produits par giac/xcas
 %%
 %%
 
+% pour l'��chelle des tableaux taper \ech{facteur de r��duction}
 
-
+\newcommand\echelle{1}
+\newcommand\ech[1]{\renewcommand\echelle{#1}}
 
 
 \newcommand{\dresse}[1]{%
@@ -1872,24 +2105,25 @@ fclose(sortie);
                                    % exporter le source mp
                                    % puis lancer metapost pour creer
                                    % l'image du tableau
-         \immediate\write18{\cat XCasmpfc.mp >> \Tableaux.Tab.mp}
-         \immediate\write18{\cat enteteMP.cfg >> \Tableaux.Tab#1.mp}
-         \immediate\write18{\cat XCasmpfc.mp >> \Tableaux.Tab#1.mp}
-         \immediate\write18{\cat queue.mp >> \Tableaux.Tab#1.mp}
-         \immediate\write18{mpost   -jobname=\Tableaux.Tab \Tableaux.Tab#1.mp}
-          \immediate\write18{\rem \Tableaux.Tab#1.mp}  
+         \immediate\write18{\cat XCasmpfc.mp >> \nomtravail.Tab.mp}
+         \immediate\write18{\cat enteteMP.cfg >> \nomtravail.Tab#1.mp}
+         \immediate\write18{\cat XCasmpfc.mp >> \nomtravail.Tab#1.mp}
+         \immediate\write18{\cat queue.mp >> \nomtravail.Tab#1.mp}
+         \immediate\write18{mpost   -jobname=\nomtravail.Tab \nomtravail.Tab#1.mp}
+         \immediate\write18{\rem \nomtravail.Tab#1.mp}  
            }%
          {% sinon, si le tableau est absent, alerte.
-         \IfFileExists{\Tableaux.Tab.\theTVn}{}{% 
+         \IfFileExists{\nomtravail.Tab.\theTVn}{}{% 
          \PackageError{tablor}{Tableau absent non
          reconstituable.}{Pour compiler il faut, soit les fichiers de
-         tableaux, soit le fichier \Tableaux.Tab.mp, soit disposer de
+         tableaux, soit le fichier \nomtravail.Tab.mp, soit disposer de
          XCas.}}}
                 
 \begin{center}
-  \includegraphics{\Tableaux.Tab.\theTVn}
+  \includegraphics[scale=\echelle]{\nomtravail.Tab.\theTVn}
 \end{center}
-\stepcounter{TVn}}
+\stepcounter{TVn}
+}
 
 
 %%
@@ -1900,34 +2134,34 @@ fclose(sortie);
 
 
 \newcommand{\dressetoile}[1]{%
-\IfFileExists{\Tableaux.Tab.\theTVn}{% Test sur l'existence du tableau
+\IfFileExists{\nomtravail.Tab.\theTVn}{% Test sur l'existence du tableau
 % Si oui, inclusion du fichier source de sauvegarde mp dans Tableaux
-\immediate\write18{\cat TSav-\theTVn.mp >> \Tableaux.Tab.mp}}
+\immediate\write18{\cat TSav-\theTVn.mp >> \nomtravail.Tab.mp}}
 % Si  non,  lancement des operations de fabrication 
 {\executGiacmp{XCas#1.giac}%
 \immediate\write18{\editeur  XCasmpfc.mp }
 
   % Modification avec l'editeur choisi
-\immediate\write18{\cat  XCasmpfc.mp >> \Tableaux.Tab.mp} 
+\immediate\write18{\cat  XCasmpfc.mp >> \nomtravail.Tab.mp} 
 \immediate\write18{\cp  XCasmpfc.mp  TSav-\theTVn.mp}   % Sauvegarde du 
                                  % source mp sur le disque pour une
                                  % inclusion ulterieure dans Tableaux.mp. 
-\immediate\write18{\cat enteteMP.cfg >> \Tableaux.Tab#1.mp}
-\immediate\write18{\cat XCasmpfc.mp >> \Tableaux.Tab#1.mp}} % Inclusion du
+\immediate\write18{\cat enteteMP.cfg >> \nomtravail.Tab#1.mp}
+\immediate\write18{\cat XCasmpfc.mp >> \nomtravail.Tab#1.mp}} % Inclusion du
                                                      % source dans le
                                                      % fichier
                                                      % Tableaux 
-\immediate\write18{\cat queue.mp >> \Tableaux.Tab#1.mp}
-\immediate\write18{mpost  -jobname=\Tableaux.Tab \Tableaux.Tab#1.mp}% Reconstitution des tableaux
+\immediate\write18{\cat queue.mp >> \nomtravail.Tab#1.mp}
+\immediate\write18{mpost  -jobname=\nomtravail.Tab \nomtravail.Tab#1.mp}% Reconstitution des tableaux
                                 % et creation du dernier. L'option
                                 % pallie l'absence de end en fin de
                                 % fichier 
-\immediate\write18{\rem \Tableaux.Tab#1.mp}  
+\immediate\write18{\rem \nomtravail.Tab#1.mp}  
 
 \begin{center}
-  \includegraphics{\Tableaux.Tab.\theTVn}
+  \includegraphics[scale=\echelle]{\nomtravail.Tab.\theTVn}
 \end{center}
-
+\ech{1}
 \setcounter{TVn}{\theTVnbis}    % Restauration du compteur TVn
 }
 
@@ -2182,7 +2416,7 @@ read("XCasTVIapp.user");
 
 %% pour nettoyer les fichiers auxiliaires
 
-\AtEndDocument{\immediate\write18{\cat  queue.mp >> \Tableaux.Tab.mp}
+\AtEndDocument{\immediate\write18{\cat  queue.mp >> \nomtravail.Tab.mp}
                          }
author	Karl Berry <karl@freefriends.org>	2008-10-10 23:15:06 +0000
committer	Karl Berry <karl@freefriends.org>	2008-10-10 23:15:06 +0000
commit	41977cc6e6769af289a96d6846be398bdd94d133 (patch)
tree	e05fceb93f97d08ebc333e21ddc1f1f27c39200e /Master
parent	a4e7b650b36655b60114b5bcf614496a9dfcfc31 (diff)