tablor 4.0.2 (22oct08)

git-svn-id: svn://tug.org/texlive/trunk@11062 c570f23f-e606-0410-a88d-b1316a301751

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 %%EOF
diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.5 b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.5
index ae6786f19dc..b79363448db 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.5
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.5
@@ -2,7 +2,7 @@
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diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.6 b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.6
index ca1b0bed322..574a0faa410 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.6
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.6
@@ -2,7 +2,7 @@
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diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.7 b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.7
index 817f128737b..7fd27a0f1db 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.7
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.7
@@ -2,7 +2,7 @@
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index 6c6bfe5a2cf..f6200e0ad7f 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.8
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.8
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index 6c89a54adba..66aaeecbe5d 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.9
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.9
@@ -2,7 +2,7 @@
 %%BoundingBox: -1 -87 511 1 
 %%HiResBoundingBox: -0.25 -86.98239 510.43356 0.25 
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-%%CreationDate: 2008.10.08:2116
+%%CreationDate: 2008.10.19:0903
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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 fa53635eeb2..301f93997ec 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
@@ -21,7 +21,6 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);va
                                             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);
@@ -37,7 +36,6 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);va
                                             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);
@@ -81,7 +79,6 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);va
                                             etex,1);limGauche(btex
                                     $-\infty$
                                     etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0);
-
 endTableau;
 
 beginTableau(6) newLigneVariables(btex $t$ etex);val(btex $-\pi $ etex);
@@ -94,7 +91,6 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);va
                                             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);
@@ -188,7 +184,6 @@ limGauche(btex
                                             etex,1);limGauche(btex
                                     $-\infty$
                                     etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0);
-
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex); moins;valBarre(btex $\frac{-64}{9}$ etex);moins;nonDefBarre;moins;valBarre(btex $0$ etex);plus;valBarre(btex $\frac{44}{9}$ etex);plus; 
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle y}$ etex);valPos(btex $+\infty $ etex,1);valPos(btex          $\frac{32}{3}$
                                             etex,0.5);limGauche(btex
@@ -320,8 +315,33 @@ 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);
-                              plus;valBarre(btex 0 etex); moins;valBarre(btex 0 etex);
+                               plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);
+endTableau;
+
+
+
+beginTableau(20)
+newLigneVariables(btex $\displaystyle  {x}$ etex);
+   val(btex $-10$ etex);val(btex $2$ etex);
+val(btex $5$ etex);
+
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \frac{(x+10)}{(x-5) (x-2)}}$ etex);
+                                valBarre(btex 0 etex); plus;nonDefBarre;moins;nonDefBarre;
+endTableau;
+
+
+
+beginTableau(21)
+newLigneVariables(btex $\displaystyle  {x}$ etex);
+   val(btex $0$ etex);val(btex $\frac{\pi }{2}$ etex);
+val(btex $\pi $ etex);
+val(btex $\frac{3 \pi }{2}$ etex);
+val(btex $2 \pi $ etex);
+
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \tan\left(x\right)}$ etex);
+                                valBarre(btex 0 etex); plus;nonDefBarre;moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;valBarre(btex 0 etex);
 endTableau;
 
   beginTableau(105)
@@ -345,7 +365,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle F(x)}$ etex);
                               
 endTableau;
 
- 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);
+ beginTableau(22) 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          $-1$
@@ -353,7 +373,7 @@ nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPo
                                             $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(21) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(23) 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          $0$
@@ -361,21 +381,20 @@ valPos(btex $\frac{1}{4}$ etex,1);  valPos(btex          $0$
                                             $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(22) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(24) 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(24) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
+beginTableau(26) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
 val(btex $+\infty $ etex);
 
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);valPos(btex $0$ etex,1);valPos(btex $-\infty$ etex,0);
-
 endTableau;
 
-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);
+beginTableau(27) 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          $1$
@@ -383,7 +402,7 @@ 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(26) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(28) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
 val(btex $\pi $ etex);
 val(btex $2 \pi $ etex);
 
@@ -393,14 +412,14 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);va
 valPos(btex $1$ etex,1);
 endTableau;
 
-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);
+beginTableau(29) 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(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);
+beginTableau(30) 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          $\frac{3 \sqrt{3}}{4}$
@@ -408,17 +427,16 @@ valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex          $\frac
                                             $ 1 $ etex,0.5);valPos(btex $0$ etex,0);
 endTableau;
 
-beginTableau(29) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
+beginTableau(31) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
 val(btex $0$ etex);
 val(btex $+\infty $ etex);
 
 newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus; valBarre(btex 0 etex);moins;
 newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);nonDefBarre;limDroite(btex $-\infty$ etex,0); valPos(btex          $0$
                                             etex,1);valPos(btex $-\infty$ etex,0);
-
 endTableau;
 
-  beginTableau(30)
+  beginTableau(32)
 newLigneVariables(btex $ {x}$ etex);
    val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex);
 val(btex $-1$ etex);
@@ -460,7 +478,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex);
                               
 endTableau;
 
- beginTableau(31) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+ beginTableau(33) 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          $-\left(e^{-4}\right)-1$
@@ -468,7 +486,7 @@ valPos(btex $-1$ etex,1);  valPos(btex          $-\left(e^{-4}\right)-1$
                                             $ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1);
 endTableau;
 
-beginTableau(32) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(34) 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          $2$
@@ -476,23 +494,22 @@ valPos(btex $1$ etex,0);  valPos(btex          $2$
                                             $ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0);
 endTableau;
 
-beginTableau(34) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(36) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
 val(btex $1$ 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 $0$ etex,0); valPos(btex          $\ln\left(\frac{(e^{1}+1)}{e^{1}}\right)$
                                             etex,1);valPos(btex $0$ etex,0);
-
 endTableau;
 
-beginTableau(35) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex);
+beginTableau(37) 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(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);
+beginTableau(38) 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          $\frac{1}{4}$
@@ -502,15 +519,15 @@ endTableau;
 
 
 
-beginTableau(37)
+beginTableau(39)
 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);
-                                valBarre(btex 0 etex);plus; 
+                                valBarre(btex 0 etex);moins; 
                                 valBarre(btex 0 etex);
 endTableau;
 
-beginTableau(38) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(40) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
 val(btex $-\left(\sqrt{2}\right)$ etex);
 val(btex $-1$ etex);
 val(btex $1$ etex);
@@ -521,7 +538,7 @@ 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(39) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(41) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
 val(btex $-1$ etex);
 val(btex $1$ etex);
 val(btex $+\infty $ etex);
@@ -530,7 +547,7 @@ 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 $+\infty $ etex,1);
 endTableau;
 
-beginTableau(40) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+beginTableau(42) 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);
@@ -550,7 +567,7 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle y}$ etex);va
 valPos(btex $0$ etex,1);
 endTableau;
 
-beginTableau(41) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+beginTableau(43) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
 val(btex $\frac{\pi }{3}$ etex);
 val(btex $\pi $ etex);
 val(btex $\frac{5 \pi }{3}$ etex);
@@ -562,7 +579,6 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle x}$ etex);va
 valPos(btex          $\pi $
                                             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          $0$
                                             etex,0.5);valPos(btex          $-3$
@@ -571,7 +587,7 @@ valPos(btex          $0$
                                             etex,0.5);valPos(btex $1$ etex,1);
 endTableau;
 
-beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(44) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
 val(btex $-1$ etex);
 val(btex $1$ etex);
 val(btex $\frac{5}{2}$ etex);
@@ -583,7 +599,7 @@ 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 $\sqrt{35}$ 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(43) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+beginTableau(45) 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);
@@ -594,7 +610,6 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle f}$ etex);va
                                             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);
-
 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          $\frac{\sqrt{3}}{2}$
@@ -603,7 +618,7 @@ newLigneVariations(btex $\hbox{  Variations de }\atop{\displaystyle g}$ etex);va
 valPos(btex $0$ etex,1);
 endTableau;
 
-  beginTableau(44)
+  beginTableau(46)
 newLigneVariables(btex $ {x}$ etex);
    val(btex $0$ etex);val(btex $\frac{\pi }{3}$ etex);
 val(btex $\frac{\pi }{3}$ etex);
diff --git a/Master/texmf-dist/doc/latex/tablor/README b/Master/texmf-dist/doc/latex/tablor/README
index fdca3aea0e7..d6475d58bf8 100644
--- a/Master/texmf-dist/doc/latex/tablor/README
+++ b/Master/texmf-dist/doc/latex/tablor/README
@@ -9,7 +9,7 @@ The tablor package requires that shell escape be enabled.
 
 For instance :
 
-\begin{TV} TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,\tv) \end{TV} 
+\begin{TV} TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) \end{TV} 
 
 draws table of  variations  of  x->x^2/(x^2-1). 
 
@@ -24,4 +24,4 @@ The     non-french     users    need     to     comment    out     every
 
 " \usepackage[upright]{fourier} "
 
-Just put tablor.sty and tablor.cfg into /texmf/tex/latex/tablor/
\ No newline at end of file
+Just put tablor.sty and tablor.cfg into /texmf/tex/latex/tablor/
diff --git a/Master/texmf-dist/doc/latex/tablor/README-fr.txt b/Master/texmf-dist/doc/latex/tablor/README-fr.txt
index 5efc255fa76..df707265453 100644
--- a/Master/texmf-dist/doc/latex/tablor/README-fr.txt
+++ b/Master/texmf-dist/doc/latex/tablor/README-fr.txt
@@ -4,7 +4,7 @@ pour les tableaux.
 
 On rentre par exemple:
 
-\begin{TV} TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,\tv) \end{TV} 
+\begin{TV} TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) \end{TV} 
 
 et on obtient le tableau de variation de x->x^2/(x^2-1). 
 
diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.html b/Master/texmf-dist/doc/latex/tablor/tablor.html
index e4f32c8810f..7854e0762b3 100644
--- a/Master/texmf-dist/doc/latex/tablor/tablor.html
+++ b/Master/texmf-dist/doc/latex/tablor/tablor.html
@@ -7,7 +7,7 @@
     <!--
       body {
         color: #f5deb3;
-        background-color: #000000;
+        background-color: #262626;
         font-weight: bold;
       }
       .comment {
@@ -22,7 +22,7 @@
       }
       .constant {
         /* font-lock-constant-face */
-        color: #9932cc;
+        color: #68228b;
         font-weight: bold;
       }
       .flyspell-duplicate {
@@ -31,9 +31,15 @@
         font-weight: bold;
         text-decoration: underline;
       }
+      .flyspell-incorrect {
+        /* flyspell-incorrect-face */
+        color: #ff4500;
+        font-weight: bold;
+        text-decoration: underline;
+      }
       .font-latex-math {
         /* font-latex-math-face */
-        color: #ffa500;
+        color: #436eee;
       }
       .font-latex-sedate {
         /* font-latex-sedate-face */
@@ -54,11 +60,11 @@
       }
       .function-name {
         /* font-lock-function-name-face */
-        color: #87ceeb;
+        color: #6ca6cd;
       }
       .keyword {
         /* font-lock-keyword-face */
-        color: #6495ed;
+        color: #32cd32;
         font-weight: bold;
       }
       .variable-name {
@@ -81,15 +87,15 @@
   <body>
     <pre>
 <span class="font-latex-sedate">\NeedsTeXFormat</span>{LaTeX2e}[1995/12/01]
-<span class="font-latex-sedate">\ProvidesPackage</span>{tablor}[12/06/2008 v3.00 la machine a creer des tableaux de signes et variations]
+<span class="font-latex-sedate">\ProvidesPackage</span>{<span class="flyspell-duplicate">tablor</span>}[21/10/2008 v4.02 la machine a creer des tableaux de signes et variations]
 
 <span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\copyleft</span></span><span class="comment"> Connan le Barbare (aka Guillaume Connan) </span><span class="font-latex-sedate"><span class="comment">\copyright</span></span><span class="comment">
 </span><span class="comment-delimiter">% </span><span class="comment">This work may be distributed and/or mofified under the conditions
 </span><span class="comment-delimiter">% </span><span class="comment">or the LaTeX Project Public Licence, either v1.3 or (at your option)
-</span><span class="comment-delimiter">% </span><span class="comment">any later version. The latest version is in
+</span><span class="comment-delimiter">% </span><span class="comment">any later version. </span><span class="comment"><span class="flyspell-incorrect">The</span></span><span class="comment"> latest version is in
 </span><span class="comment-delimiter">%   </span><span class="comment">http://www.latex-project.org/lppl/
-</span><span class="comment-delimiter">% </span><span class="comment">This work consists of the files tablor.sty, tablor.cfg, tablor.tex,
-</span><span class="comment-delimiter">% </span><span class="comment">tablor.pdf and tablor.html
+</span><span class="comment-delimiter">% </span><span class="comment">This work consists of the files tablor.</span><span class="comment"><span class="flyspell-incorrect">sty</span></span><span class="comment">, </span><span class="comment"><span class="flyspell-incorrect">tablor-xetex</span></span><span class="comment">.</span><span class="comment"><span class="flyspell-duplicate">sty</span></span><span class="comment">,  tablor.cfg, tablor.tex,
+</span><span class="comment-delimiter">% </span><span class="comment">tablor.pdf and tablor.</span><span class="comment"><span class="flyspell-incorrect">html</span></span><span class="comment">
 </span>
 
 <span class="comment-delimiter">%% </span><span class="comment">Cree 16 environnements :
@@ -100,29 +106,35 @@
 </span><span class="comment-delimiter">% </span><span class="comment">%%%%%% Pour des tableaux de plus de 2 facteurs
 </span><span class="comment-delimiter">%</span><span class="comment">
 </span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TS}
-</span><span class="comment-delimiter">% </span><span class="comment">TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[a,b],</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">);
+</span><span class="comment-delimiter">% </span><span class="comment">TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[a,b],n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">);
 </span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TS}
 </span><span class="comment-delimiter">%</span><span class="comment">
 </span><span class="comment-delimiter">% </span><span class="comment">pour les tableaux de signes avec quotient
 </span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TSq}
-</span><span class="comment-delimiter">%</span><span class="comment">TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
+</span><span class="comment-delimiter">%</span><span class="comment">TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
 </span><span class="comment-delimiter">%%</span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TSq}
 </span><span class="comment-delimiter">% </span><span class="comment">un tableau de variation :
 </span><span class="comment-delimiter">%</span><span class="comment">
+</span><span class="comment-delimiter">% </span><span class="comment">pour les tableaux de signes &#224; une seule ligne
+</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TSc}
+</span><span class="comment-delimiter">% </span><span class="comment"><span class="flyspell-duplicate">TSc</span></span><span class="comment">((x+10)/((x-5)*(x-2)),[-10,5],[2,5],n,0)
+</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TSc}
+</span><span class="comment-delimiter">%</span><span class="comment">
+</span><span class="comment-delimiter">%</span><span class="comment">
 </span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TV}
-</span><span class="comment-delimiter">% </span><span class="comment">TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
+</span><span class="comment-delimiter">% </span><span class="comment">TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
 </span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TV}
 </span><span class="comment-delimiter">%</span><span class="comment">
 </span><span class="comment-delimiter">% </span><span class="comment">tableau de variation avec zones interdites
 </span><span class="comment-delimiter">%</span><span class="comment">
 </span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVZ}
-</span><span class="comment-delimiter">%   </span><span class="comment">TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
+</span><span class="comment-delimiter">%   </span><span class="comment">TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
 </span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVZ}
 </span><span class="comment-delimiter">%</span><span class="comment">
 </span><span class="comment-delimiter">%</span><span class="comment">
 </span><span class="comment-delimiter">% </span><span class="comment">tableau avec valeurs intermediares
 </span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVI}
-</span><span class="comment-delimiter">%</span><span class="comment">TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
+</span><span class="comment-delimiter">%</span><span class="comment">TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
 </span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVI}
 </span><span class="comment-delimiter">%%%</span><span class="comment">
 </span><span class="comment-delimiter">% </span><span class="comment">tableau de variations avec f' sans zero formel
@@ -142,17 +154,26 @@
 </span><span class="comment-delimiter">% </span><span class="comment">fichier metapost pour le modifier
 </span><span class="comment-delimiter">%</span><span class="comment">
 </span><span class="comment-delimiter">%</span><span class="comment">
-</span><span class="comment-delimiter">% </span><span class="comment">Courbes parametrees
+</span><span class="comment-delimiter">% </span><span class="comment">Courbes </span><span class="comment"><span class="flyspell-duplicate">parametrees</span></span><span class="comment">
 </span><span class="comment-delimiter">%  </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVP}
-</span><span class="comment-delimiter">%  </span><span class="comment">TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,0,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
+</span><span class="comment-delimiter">%  </span><span class="comment">TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
 </span><span class="comment-delimiter">%  </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVP}
 </span><span class="comment-delimiter">%</span><span class="comment">
 </span><span class="comment-delimiter">%</span><span class="comment">
 </span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVP}
-</span><span class="comment-delimiter">%  </span><span class="comment">TVP([0,pi/2],[[],[]],["x","y"],"t",[2*cos(t),sin(2*t)],1,1,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
+</span><span class="comment-delimiter">%  </span><span class="comment">TVP([0,pi/2],[[],[]],["x","y"],"t",[2*cos(t),sin(2*t)],1,t,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
 </span><span class="comment-delimiter">%  </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVP}
 </span><span class="comment-delimiter">% </span><span class="comment">%
 </span>
+<span class="comment-delimiter">% </span><span class="comment">Fonctions </span><span class="comment"><span class="flyspell-incorrect">prolongeables</span></span><span class="comment"> par continuit&#233;
+</span><span class="comment-delimiter">% </span><span class="comment"><span class="flyspell-duplicate">TVPC</span></span><span class="comment">([intervalles d'&#233;tude],[valeurs </span><span class="comment"><span class="flyspell-duplicate">prolongeables</span></span><span class="comment">],[valeurs interdites pour f'],"g","t",e^(-1/x^2),1,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">); 
+</span>
+
+<span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVPC}
+</span><span class="comment-delimiter">% </span><span class="comment">TVPC([-infinity,+infinity],[0],[0],"g","t",e^(-1/x^2),1,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">); 
+</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVPC}
+</span>
+
 
 
 
@@ -162,17 +183,17 @@
 </span>
 
 <span class="font-latex-sedate">\RequirePackage</span>{filecontents}
-<span class="font-latex-sedate">\RequirePackage</span>{ifthen}
-<span class="font-latex-sedate">\RequirePackage</span>{fancyvrb}
-<span class="font-latex-sedate">\RequirePackage</span>{ifpdf}
+<span class="font-latex-sedate">\RequirePackage</span>{<span class="flyspell-incorrect">ifthen</span>}
+<span class="font-latex-sedate">\RequirePackage</span>{<span class="flyspell-incorrect">fancyvrb</span>}
+<span class="font-latex-sedate">\RequirePackage</span>{<span class="flyspell-duplicate">ifpdf</span>}
 
-<span class="font-latex-sedate">\fvset</span>{gobble=0}
+<span class="font-latex-sedate">\fvset</span>{<span class="flyspell-incorrect">gobble</span>=0}
 
-<span class="comment-delimiter">% </span><span class="comment">option xcas present 
+<span class="comment-delimiter">% </span><span class="comment">option xcas </span><span class="comment"><span class="flyspell-duplicate">present</span></span><span class="comment"> 
 </span>
 
-<span class="font-latex-sedate">\newboolean</span>{xcas}<span class="font-latex-sedate">\setboolean</span>{xcas}{false}
-<span class="font-latex-sedate">\DeclareOption</span>{xcas}{<span class="font-latex-sedate">\setboolean</span>{xcas}{true}}
+<span class="font-latex-sedate">\newboolean</span>{xcas}<span class="font-latex-sedate">\setboolean</span>{xcas}{<span class="flyspell-duplicate">false</span>}
+<span class="font-latex-sedate">\DeclareOption</span>{xcas}{<span class="font-latex-sedate">\setboolean</span>{xcas}{<span class="flyspell-incorrect">true</span>}}
 
 
 <span class="font-latex-sedate">\ProcessOptions</span><span class="font-latex-sedate">\relax</span>
@@ -180,22 +201,23 @@
 
 
 
-<span class="comment-delimiter">%% </span><span class="comment">Initialisation du choix d'OS
-</span><span class="font-latex-sedate">\newboolean</span>{windows}<span class="font-latex-sedate">\setboolean</span>{windows}{false}
+<span class="comment-delimiter">%% </span><span class="comment">Initialisation du choix </span><span class="comment"><span class="flyspell-incorrect">d'OS</span></span><span class="comment">
+</span><span class="font-latex-sedate">\newboolean</span>{windows}<span class="font-latex-sedate">\setboolean</span>{windows}{<span class="flyspell-duplicate">false</span>}
+
 
 
 <span class="comment-delimiter">%% </span><span class="comment">on configure  tablor  dans un fichier exterieur pour la plateforme
-</span><span class="comment-delimiter">%% </span><span class="comment">et l'editeur
+</span><span class="comment-delimiter">%% </span><span class="comment">et </span><span class="comment"><span class="flyspell-duplicate">l'editeur</span></span><span class="comment">
 </span>
-<span class="font-latex-sedate">\IfFileExists</span>{tablor.cfg}{<span class="font-latex-sedate"><span class="keyword">\input</span></span><span class="constant">{tablor.cfg}</span>}<span class="comment">%</span><span class="font-latex-sedate"><span class="comment">\typeout</span></span><span class="comment">{pas de fichier tablor.cfg}}
+<span class="font-latex-sedate">\IfFileExists</span>{tablor.cfg}{<span class="font-latex-sedate"><span class="keyword">\input</span></span><span class="constant">{tablor.cfg}</span>}<span class="comment">%</span><span class="font-latex-sedate"><span class="comment">\typeout</span></span><span class="comment">{pas de fichier tablor.</span><span class="comment"><span class="flyspell-duplicate">cfg</span></span><span class="comment">}}
 </span>
 
 <span class="comment-delimiter">%% </span><span class="comment">Definit des commandes disque selon l'OS utilise
-</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{windows}}<span class="comment">%
+</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{<span class="flyspell-duplicate">windows</span>}}<span class="comment">%
 </span>    {<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\rem</span></span><span class="function-name">}</span>{DEL } <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cat</span></span><span class="function-name">}</span>{TYPE }
-      <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{COPY }}<span class="comment">%
-</span>    {<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\rem</span></span><span class="function-name">}</span>{rm }<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cat</span></span><span class="function-name">}</span>{cat }
-      <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{cp }}
+      <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{<span class="flyspell-incorrect">COPY</span> }}<span class="comment">%
+</span>    {<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\rem</span></span><span class="function-name">}</span>{rm }<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cat</span></span><span class="function-name">}</span>{<span class="flyspell-duplicate">cat</span> }
+      <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{<span class="flyspell-duplicate">cp</span> }}
 
 
 
@@ -203,26 +225,26 @@
 
 
 
-<span class="comment-delimiter">%% </span><span class="comment">pour ceux compilant via pdflatex
+<span class="comment-delimiter">%% </span><span class="comment">pour ceux compilant via </span><span class="comment"><span class="flyspell-incorrect">pdflatex</span></span><span class="comment">
 </span>
 <span class="font-latex-sedate">\ifpdf</span>
-<span class="font-latex-sedate">\DeclareGraphicsRule</span>{*}{mps}{*}{}
+<span class="font-latex-sedate">\DeclareGraphicsRule</span>{*}{<span class="flyspell-incorrect">mps</span>}{*}{}
 <span class="font-latex-sedate">\fi</span>
 
 <span class="comment-delimiter">%% </span><span class="comment">pour nettoyer les fichiers auxiliaires
 </span>
-<span class="font-latex-sedate">\AtEndDocument</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> *.user XCas* Xcas* *.mpx}
+<span class="font-latex-sedate">\AtEndDocument</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> *.user XCas* Xcas* *.<span class="flyspell-incorrect">mpx</span>}
                          }
 
 
 
 
-<span class="comment-delimiter">%% </span><span class="comment">Pour clore les fichiers metapost 
+<span class="comment-delimiter">%% </span><span class="comment">Pour clore les fichiers </span><span class="comment"><span class="flyspell-duplicate">metapost</span></span><span class="comment"> 
 </span>
 
-  <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{queue.mp}
+  <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{queue.<span class="flyspell-duplicate">mp</span>}
   
-  end
+  <span class="flyspell-duplicate">end</span>
 
   <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
 
@@ -235,7 +257,7 @@
 
 
 <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\nettoyer</span></span><span class="function-name">}</span>[1][<span class="font-latex-sedate">\jobname</span>]<span class="comment">%
-</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> #1.Tab.log  queue.mp enteteMP.cfg session.tex config.cxx}
+</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> #1.Tab.log  queue.mp enteteMP.cfg session.tex config.<span class="flyspell-duplicate">cxx</span>}
 }
 
 
@@ -244,48 +266,48 @@
 <span class="comment-delimiter">%% </span><span class="comment">Donne comme prefixe aux tableaux le prefixe courant
 </span><span class="comment-delimiter">%% </span><span class="comment">Peut-&#234;tre modifie par </span><span class="font-latex-sedate"><span class="comment">\initablor</span></span><span class="comment">
 </span>
-<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\Tableaux</span></span><span class="function-name">}</span>{<span class="font-latex-sedate">\jobname</span>}
+<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\nomtravail</span></span><span class="function-name">}</span>{<span class="font-latex-sedate">\jobname</span>}
 
 <span class="comment-delimiter">%% </span><span class="comment">initialise les compteurs
 </span>
-<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{TVn}</span>
+<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVn</span></span><span class="function-name">}</span>
 <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\tv</span></span><span class="function-name">}</span>{<span class="font-latex-sedate">\theTVn</span>}
 
-<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{TVnbis}</span>
+<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVnbis</span></span><span class="function-name">}</span>
 <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\tvbis</span></span><span class="function-name">}</span>{<span class="font-latex-sedate">\theTVnbis</span>}
 
 
 
 <span class="comment-delimiter">%% </span><span class="comment">permet de donner un prefixe aux tableaux produits (</span><span class="font-latex-sedate"><span class="comment">\jobname</span></span><span class="comment"> par defaut)
-</span><span class="comment-delimiter">%% </span><span class="comment">effectue quelques verifications :
+</span><span class="comment-delimiter">%% </span><span class="comment">effectue quelques </span><span class="comment"><span class="flyspell-incorrect">verifications</span></span><span class="comment"> :
 </span>
 
 <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\initablor</span></span><span class="function-name">}</span>[1][<span class="font-latex-sedate">\jobname</span>]{<span class="comment">%
-</span><span class="font-latex-sedate"><span class="keyword">\renewcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\Tableaux</span></span><span class="function-name">}</span>{#1}<span class="comment">%     Arret du nom des tableaux
+</span><span class="font-latex-sedate"><span class="keyword">\renewcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\nomtravail</span></span><span class="function-name">}</span>{#1}<span class="comment">%     Arret du nom des tableaux
 </span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{0}</span><span class="comment">%     Initialisation du compteur de tableaux.
-</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{xcas}}<span class="comment">%    Avec l'option XCas
-</span>{<span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\Tableaux</span>.Tab.mp}<span class="comment">%      Si Tableaux.mp est present...
-</span>        {<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> <span class="font-latex-sedate">\Tableaux</span>.Tab.mp}}<span class="comment">%  le detruire
+</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{xcas}}<span class="comment">%    Avec l'option </span><span class="comment"><span class="flyspell-duplicate">XCas</span></span><span class="comment">
+</span>{<span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\nomtravail</span>.Tab.mp}<span class="comment">%      Si Tableaux.mp est </span><span class="comment"><span class="flyspell-duplicate">present</span></span><span class="comment">...
+</span>        {<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> <span class="font-latex-sedate">\nomtravail</span>.Tab.mp}}<span class="comment">%  le </span><span class="comment"><span class="flyspell-incorrect">detruire</span></span><span class="comment">
 </span>        {}<span class="comment">%   
-</span> <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cp</span>  enteteMP.cfg <span class="font-latex-sedate">\Tableaux</span>.Tab.mp}<span class="comment">% Reconstituer l'ent&#234;te de Tableaux.mp
+</span> <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cp</span>  enteteMP.cfg <span class="font-latex-sedate">\nomtravail</span>.Tab.mp}<span class="comment">% Reconstituer l'ent&#234;te de Tableaux.</span><span class="comment"><span class="flyspell-duplicate">mp</span></span><span class="comment">
 </span>} 
-{<span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\Tableaux</span>.Tab.mp}<span class="comment">%      Sans l'option XCas, si
+{<span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\nomtravail</span>.Tab.mp}<span class="comment">%      Sans l'option XCas, si
 </span>                                <span class="comment">%      Tableaux.mp existe
-</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost -interaction=batchmode <span class="font-latex-sedate">\Tableaux</span>.Tab}}<span class="comment">% l'executer pour reconstituer les figures
+</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost -interaction=batchmode <span class="font-latex-sedate">\nomtravail</span>.Tab}}<span class="comment">% l'executer pour reconstituer les figures
 </span>{<span class="font-latex-sedate">\PackageWarning</span>{tablor}{Pas de source metapost pour creer les tableaux.}}<span class="comment">% sinon message d'erreur
 </span>                                <span class="comment">% (mais pas d'arret car les tableaux
-</span>                                <span class="comment">% peuvent &#234;tre presents )
+</span>                                <span class="comment">% peuvent &#234;tre </span><span class="comment"><span class="flyspell-incorrect">presents</span></span><span class="comment"> )
 </span>}}<span class="comment">%
 </span>
 
 
-<span class="comment-delimiter">%% </span><span class="comment">commande pour lancer giac selon l'OS
+<span class="comment-delimiter">%% </span><span class="comment">commande pour lancer giac selon </span><span class="comment"><span class="flyspell-duplicate">l'OS</span></span><span class="comment">
 </span>
 <span class="font-latex-sedate">\makeatletter</span>
 <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\executGiacmp</span></span><span class="function-name">}</span>[1]{<span class="comment">%
-</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{windows}}<span class="comment">%
-</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{giac #1 }}<span class="comment">%
-</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{giac  &lt;#1 }}}
+</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{<span class="flyspell-duplicate">windows</span>}}<span class="comment">%
+</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="flyspell-duplicate">giac</span> #1 }}<span class="comment">%
+</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="flyspell-duplicate">giac</span>  &lt;#1 }}}
 <span class="font-latex-sedate">\makeatother</span>
 
 
@@ -293,7 +315,7 @@
 
 <span class="comment-delimiter">%%%</span><span class="comment">
 </span><span class="comment-delimiter">%</span><span class="comment">
-</span><span class="comment-delimiter">%%% </span><span class="comment">LES SCRIPTS GIAC/XCAS
+</span><span class="comment-delimiter">%%% </span><span class="comment">LES SCRIPTS GIAC/</span><span class="comment"><span class="flyspell-incorrect">XCAS</span></span><span class="comment">
 </span><span class="comment-delimiter">%</span><span class="comment">
 </span><span class="comment-delimiter">%%%</span><span class="comment">
 </span>
@@ -306,83 +328,326 @@
 </span>
 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTV.cxx}
-TV(L,F,nom,nomv,f,ftt,nmr):={
-nl:=size(L);
+<span class="flyspell-duplicate">TV</span>(L,F,nom,nomv,f,ftt,trigo,nmr):={
+<span class="flyspell-duplicate">nl</span>:=size(L);
 f:=unapply(f,x);
-fp:=fonction_derivee(f);
+<span class="flyspell-duplicate">fp</span>:=function_diff(f);
 Z:=concat(L,F);
-S:=resoudre(fp(x),x);
-  si size(S)&gt;0 alors   pour j de 0 jusque size(S)-1 faire 
-                             kk:=(evalf(S[j])&gt;=evalf(L[0])) and (evalf(S[j])&lt;=evalf(L[nl-1]));
-                          if(kk==1){Z:=append(Z,simplifier(S[j]))};
-                          fpour
+S:=[];
+
+
+if(trigo==t){
+<span class="flyspell-duplicate">all</span>_trig_solutions:=1;
+<span class="flyspell-duplicate">reset</span>_solve_counter(-1,-1);
+<span class="flyspell-duplicate">SS</span>:=solve(factor(simplify(fp(x))),x);
+<span class="flyspell-duplicate">ns</span>:=size(SS);
+for(k:=0;k&lt;ns;k++){
+m:=0;
+<span class="flyspell-duplicate">while</span>(evalf(simplify(subst(SS[k],n_1=m)))&lt;=evalf(L[nl-1])){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+<span class="flyspell-duplicate">while</span>(evalf(subst(SS[k],n_1=m))&gt;=L[0]){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
+S:=solve(fp(x),x);
+}
+
+
+  si size(S)&gt;0 alors   pour j de 0 jusque size(S)-1 faire
+                             qq:=member(simplify(S[j]),Z)==0;
+                             kk:=(evalf(S[j])&gt;=evalf(L[0])) and (evalf(S[j])&lt;=evalf(L[<span class="flyspell-duplicate">nl</span>-1]));
+                          if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}};
+                          <span class="flyspell-duplicate">fpour</span>
   fsi;
+Z:=sort(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+
+
+ tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z);
+     <span class="flyspell-duplicate">ftantque</span>;
+
+
+
+
+
+
+
+  si size(S)&gt;0 alors   pour j de 0 jusque size(S)-1 faire 
+                             kk:=(evalf(S[j])&gt;=evalf(L[0])) and (evalf(S[j])&lt;=evalf(L[<span class="flyspell-duplicate">nl</span>-1]));
+                          if(kk==1){Z:=append(Z,simplify(S[j]))};
+                          <span class="flyspell-duplicate">fpour</span>
+  <span class="flyspell-duplicate">fsi</span>;
 
 Z:=sort(Z); 
-nz:=size(Z);
- si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1; 
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+ si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1; 
      fsi;
 pour u de 1 jusque nz-2 faire 
-     si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1; 
+     si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1; 
      fsi;
-fpour;
-nz:=size(Z);
+<span class="flyspell-duplicate">fpour</span>;
+<span class="flyspell-duplicate">nz</span>:=size(Z);
 l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" ";
-pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);
-";fpour; 
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> <span class="flyspell-duplicate">etex</span>);
+";<span class="flyspell-duplicate">fpour</span>; 
 
-       k0:= evalf(limite(f(x),x=Z[0],1))&gt; evalf(limite(f(x),x=Z[1],-1));
-       kz:=evalf(limite(f(x),x=Z[nz-1],-1))&gt; evalf(limite(f(x),x=Z[nz-2],1));
+       k0:= evalf(limit(f(x),x=Z[0],1))&gt; evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))&gt; evalf(limit(f(x),x=Z[<span class="flyspell-duplicate">nz</span>-2],1));
                           
-lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
+<span class="flyspell-duplicate">lsi</span>:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
      if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
                                                     if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
                                                     if(sign(fp(Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
                                                          if(sign(fp((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5))))==1){"plus;"}else{"moins;"} }}
  
-if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.01))&gt;0;                     
+if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.1))&gt;0;                     
                                                lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                                 if(ksp==1){"plus;"}else{"moins;"}
                                                   }; }
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;
+</span><span class="font-latex-math"><span class="flyspell-duplicate">lsf</span></span><span class="font-latex-math">:=if(member(Z[nz-1],F)==0){""}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">;
 "}
-lm0:=limite(f(x),x=Z[0],1)==-infinity;
+</span><span class="font-latex-math"><span class="flyspell-duplicate">lm</span></span><span class="font-latex-math">0:=limit(f(x),x=Z[0],1)==-</span><span class="font-latex-math"><span class="flyspell-duplicate">infinity</span></span><span class="font-latex-math">;
      li:=lvic+nom+"}$</span> etex);"+
-           if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}
-             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}+                               
+           if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}
+             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+                               
            if(k0==1){"1"}else{"0"}+
                          ");";
             
-                     if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){ krm:=evalf(limite(f(x),x=Z[r-1],1))&lt; evalf(limite(f(x),x=Z[r],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[r],1))&gt; evalf(limite(f(x),x=Z[r+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+                     if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){ krm:=evalf(limit(f(x),x=Z[r-1],1))&lt; evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))&gt; evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                   lp:=lp+if(member(Z[r],F)){
                                     "limGauche(btex
-                                    <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$</span>
-                                    etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span>
+                                    <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span>
+                                    etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span>
                                             etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
 "}}}
                                                    }; }
 
-lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
-                           lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+                               
-           if(kz==1){"1);"}else{"0);
-"};    
+<span class="flyspell-duplicate">lnz</span>:=limit(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>;
+                          
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+
+             if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}
+    else{"limGauche(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);<span class="flyspell-duplicate">nonDefBarre</span>;"}};    
     
 
-MetaLfc:=if(ftt==2){if(nz&gt;2){"
 
-beginTableau("+nmr+")"+
+
+
+<span class="flyspell-duplicate">MetaLfc</span>:=if(ftt==2){if(<span class="flyspell-duplicate">nz</span>&gt;2){"
+
+<span class="flyspell-duplicate">beginTableau</span>("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+lsi+lsp+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{
-intro+"beginTableau("+nmr+")"+
+<span class="flyspell-duplicate">intro</span>+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+        l0+
+<span class="flyspell-duplicate">lsi</span>+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";
+}
+}else{ if(ftt==0){if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+        l0+
+li+
+<span class="flyspell-duplicate">lp</span>+
+<span class="flyspell-duplicate">lf</span>
++"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+        l0+
+li+
+<span class="flyspell-duplicate">lf</span>
++"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}}else{
+if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+        l0+
+<span class="flyspell-duplicate">lsi</span>+lsp+lsf+
+li+
+<span class="flyspell-duplicate">lp</span>+
+<span class="flyspell-duplicate">lf</span>
++"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+        l0+
+<span class="flyspell-duplicate">lsi</span>+lsf+
+li+
+<span class="flyspell-duplicate">lf</span>
++"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}
+}}
+
+
+sortie:=fopen("XCasmpfc.mp");
+<span class="flyspell-duplicate">fprint</span>(sortie,Unquoted,<span class="flyspell-duplicate">MetaLfc</span>);
+<span class="flyspell-duplicate">fclose</span>(sortie);
+
+
+ }:;
+
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+
+
+
+
+
+
+<span class="comment-delimiter">%%%%</span><span class="comment">
+</span>
+
+<span class="comment-delimiter">%</span><span class="comment">
+</span><span class="comment-delimiter">%</span><span class="comment">
+</span><span class="comment-delimiter">%  </span><span class="comment"><span class="flyspell-duplicate">TVPC</span></span><span class="comment"> : pour les fonctions </span><span class="comment"><span class="flyspell-duplicate">prolongeables</span></span><span class="comment"> par continuit&#233;.
+</span><span class="comment-delimiter">%%</span><span class="comment">
+</span><span class="comment-delimiter">%%</span><span class="comment">
+</span>
+
+
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{<span class="flyspell-incorrect">XcasTVPC</span>.cxx}
+<span class="flyspell-duplicate">TVPC</span>(L,F,<span class="flyspell-incorrect">FP</span>,nom,nomv,f,ftt,trigo,nmr):={
+nl:=size(L);
+f:=unapply(f,x);
+fp:=function_diff(f);
+Z:=concat(L,F);
+Z:=<span class="flyspell-duplicate">concat</span>(Z,<span class="flyspell-duplicate">FP</span>);
+S:=[];
+
+
+if(trigo==t){
+<span class="flyspell-duplicate">all</span>_trig_solutions:=1;
+<span class="flyspell-duplicate">reset</span>_solve_counter(-1,-1);
+<span class="flyspell-duplicate">SS</span>:=solve(factor(simplify(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k&lt;ns;k++){
+m:=0;
+<span class="flyspell-duplicate">while</span>(evalf(simplify(subst(SS[k],n_1=m)))&lt;=evalf(L[nl-1])){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))&gt;=L[0]){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
+S:=solve(fp(x),x);
+}
+
+
+  si size(S)&gt;0 alors   pour j de 0 jusque size(S)-1 faire
+                             qq:=member(simplify(S[j]),Z)==0;
+                             kk:=(evalf(S[j])&gt;=evalf(L[0])) and (evalf(S[j])&lt;=evalf(L[nl-1]));
+                          if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}};
+                          <span class="flyspell-duplicate">fpour</span>
+  fsi;
+Z:=sort(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+
+
+ tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z);
+     <span class="flyspell-duplicate">ftantque</span>;
+
+
+
+
+
+
+
+  si size(S)&gt;0 alors   pour j de 0 jusque size(S)-1 faire 
+                             kk:=(evalf(S[j])&gt;=evalf(L[0])) and (evalf(S[j])&lt;=evalf(L[<span class="flyspell-duplicate">nl</span>-1]));
+                          if(kk==1){Z:=append(Z,simplify(S[j]))};
+                          <span class="flyspell-duplicate">fpour</span>
+  <span class="flyspell-duplicate">fsi</span>;
+
+Z:=sort(Z); 
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+ si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1; 
+     fsi;
+pour u de 1 jusque nz-2 faire 
+     si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1; 
+     fsi;
+<span class="flyspell-duplicate">fpour</span>;
+nz:=size(Z);
+l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" ";
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> <span class="flyspell-duplicate">etex</span>);
+";<span class="flyspell-duplicate">fpour</span>; 
+
+       k0:= evalf(limit(f(x),x=Z[0],1))&gt; evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))&gt; evalf(limit(f(x),x=Z[<span class="flyspell-duplicate">nz</span>-2],1));
+                          
+<span class="flyspell-duplicate">lsi</span>:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
+     if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],FP)==0){
+                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+                                                    if(sign(fp(Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
+                                                         if(sign(fp((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5))))==1){"plus;"}else{"moins;"} }}
+ 
+if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.1))&gt;0;                     
+                                               lsp:=lsp+if(member(Z[r],FP)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                                if(ksp==1){"plus;"}else{"moins;"}
+                                                  }; }
+
+lsf:=if(member(Z[nz-1],</span><span class="font-latex-math"><span class="flyspell-duplicate">FP</span></span><span class="font-latex-math">)==0){""}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">;
+"}
+</span><span class="font-latex-math"><span class="flyspell-duplicate">lm</span></span><span class="font-latex-math">0:=limit(f(x),x=Z[0],1)==-</span><span class="font-latex-math"><span class="flyspell-duplicate">infinity</span></span><span class="font-latex-math">;
+     li:=lvic+nom+"}$</span> etex);"+
+           if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(</span><span class="font-latex-math"><span class="flyspell-duplicate">lm</span></span><span class="font-latex-math">0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}
+             else{"limDroite(btex <span class="font-latex-math">$"+if(</span><span class="font-latex-math"><span class="flyspell-duplicate">lm</span></span><span class="font-latex-math">0==1){"-\\infty"}</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+                               
+           if(k0==1){"1"}else{"0"}+
+                         ");";
+            
+                     if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){ krm:=evalf(limit(f(x),x=Z[r-1],1))&lt; evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))&gt; evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
+                                                  lp:=lp+if(member(Z[r],F)){ 
+                                    "valPos(btex
+                                    <span class="font-latex-math">$"+if(</span><span class="font-latex-math"><span class="flyspell-duplicate">lmrm</span></span><span class="font-latex-math">==1){"-\\infty"}</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{latex(</span><span class="font-latex-math"><span class="flyspell-duplicate">simplify</span></span><span class="font-latex-math">(limit(f(x),x=Z[r],-1)))}+"$</span>
+                                    etex,"+if(krm==1){"1);"}else{"0);"} }
+                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span>
+                                            etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+"}}}
+                                                   }; }
+
+lnz:=limit(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>;
+                          
+
+
+<span class="flyspell-duplicate">lf</span>:=if(member(Z[nz-1],F)==0){"valPos(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+
+             if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}
+    else{"limGauche(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ 
+           if(<span class="flyspell-duplicate">kz</span>==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}};    
+    
+
+
+
+
+MetaLfc:=if(ftt==2){if(<span class="flyspell-duplicate">nz</span>&gt;2){"
+
+<span class="flyspell-duplicate">beginTableau</span>("+nmr+")"+
+        l0+lsi+lsp+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}else{
+<span class="flyspell-duplicate">intro</span>+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
 lsi+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";
 }
@@ -390,41 +655,41 @@ endTableau;
         l0+
 li+
 lp+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{"beginTableau("+nmr+")"+
         l0+
 li+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}}else{
-if(nz&gt;2){"beginTableau("+nmr+")"+
+if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
-lsi+lsp+lsf+
+<span class="flyspell-duplicate">lsi</span>+lsp+lsf+
 li+
-lp+
+<span class="flyspell-duplicate">lp</span>+
 lf
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
-";}else{"beginTableau("+nmr+")"+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
 lsi+lsf+
 li+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}
 }}
 
 
 sortie:=fopen("XCasmpfc.mp");
-fprint(sortie,Unquoted,MetaLfc);
+<span class="flyspell-duplicate">fprint</span>(sortie,Unquoted,MetaLfc);
 fclose(sortie);
 
 
@@ -433,6 +698,16 @@ fclose(sortie);
 <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
 
 
+
+
+
+
+
+
+
+
+
+
 <span class="comment-delimiter">%%</span><span class="comment">
 </span><span class="comment-delimiter">%%</span><span class="comment">
 </span><span class="comment-delimiter">%% </span><span class="comment">TV avec une zone interdite : on rajoute comme argument la liste des intervalles interdits
@@ -442,9 +717,9 @@ fclose(sortie);
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVZ.cxx}
 
 
-TVZ(L,F,FF,nom,nomv,f,ftt,nmr):={
-nl:=size(L);
-nf:=size(FF);
+<span class="flyspell-duplicate">TVZ</span>(L,F,FF,nom,nomv,f,ftt,trigo,nmr):={
+<span class="flyspell-duplicate">nl</span>:=size(L);
+nf:=size(<span class="flyspell-duplicate">FF</span>);
  Ff:=NULL;IMIN:=NULL;IMAX:=NULL;
 for(k:=0;k&lt;nf;k++){
 if(FF[k][0]&gt;L[0]){Imin[k]:=FF[k][0];LL:=L}else{Imin[k]:=L[0];LL:=[L[1]]};
@@ -453,57 +728,82 @@ if(FF[k][1]&lt;L[1]){Imax[k]:=FF[k][1];LL:=L}else{Imax[k]:=L[1];LL:=[L[0]]};
  IMIN:=IMIN,Imin[k];
  IMAX:=IMAX,Imax[k];
  }
- FF:=[Ff];
- IMIN:=[IMIN];
+ FF:=[<span class="flyspell-duplicate">Ff</span>];
+ IMIN:=[<span class="flyspell-duplicate">IMIN</span>];
  IMAX:=[IMAX];
  f:=unapply(f,x);
-fp:=fonction_derivee(f);
+<span class="flyspell-duplicate">fp</span>:=function_diff(f);
 Z:=concat(LL,F);
 
 for(k:=0;k&lt;nf;k++){
 Z:=concat(Z,FF[k]);
 }
 
-S:=resoudre(fp(x),x);
+S:=[];
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+<span class="flyspell-duplicate">reset</span>_solve_counter(-1,-1);
+SS:=solve(factor(simplify(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k&lt;ns;k++){
+m:=0;
+while(<span class="flyspell-duplicate">evalf</span>(simplify(subst(SS[k],n_1=m)))&lt;=<span class="flyspell-duplicate">evalf</span>(L[nl-1])){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(<span class="flyspell-duplicate">evalf</span>(subst(SS[k],n_1=m))&gt;=L[0]){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
+S:=solve(fp(x),x);
+}
+
+
+
+
+
+
   si size(S)&gt;0 alors   pour j de 0 jusque size(S)-1 faire 
                          for(k:=0;k&lt;nf;k++){  
-                           kk:=(evalf(S[j])&gt;=evalf(L[0])) and (evalf(S[j])&lt;=evalf(L[nl-1]));
-                             kK:=(evalf(S[j])&lt;evalf(Imin[k])) or (evalf(S[j])&gt;evalf(Imax[k]));
+                           kk:=(<span class="flyspell-duplicate">evalf</span>(S[j])&gt;=<span class="flyspell-duplicate">evalf</span>(L[0])) and (<span class="flyspell-duplicate">evalf</span>(S[j])&lt;=<span class="flyspell-duplicate">evalf</span>(L[<span class="flyspell-duplicate">nl</span>-1]));
+                             kK:=(<span class="flyspell-duplicate">evalf</span>(S[j])&lt;<span class="flyspell-duplicate">evalf</span>(Imin[k])) or (<span class="flyspell-duplicate">evalf</span>(S[j])&gt;<span class="flyspell-duplicate">evalf</span>(Imax[k]));
                              Kk:=(kk) and kK;
-                          if(Kk==1){Z:=append(Z,simplifier(S[j]))};
+                          if(Kk==1){Z:=append(Z,simplify(S[j]))};
                           }
                         fpour
-  fsi;
+  <span class="flyspell-duplicate">fsi</span>;
 
 Z:=sort(Z); 
 nz:=size(Z);
 
 
 
- si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1; 
+ si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1; 
      fsi;
 pour u de 1 jusque nz-2 faire 
-     si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1; 
+     si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1; 
      fsi;
-fpour;
-nz:=size(Z);
+<span class="flyspell-duplicate">fpour</span>;
+<span class="flyspell-duplicate">nz</span>:=size(Z);
 
 for(j:=0;j&lt;nf;j++){
  for(k:=1;k&lt;nz;k++){
-   if ((Z[k]&gt;Imin[j])and(Z[k]&lt;Imax[j])){Z:=augment(Z[0..k-1],Z[k+1..nz-1]);nz:=nz-1;
+   if ((Z[k]&gt;Imin[j])and(Z[k]&lt;Imax[j])){Z:=augment(Z[0..k-1],Z[k+1..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1;
    }
   }
 }
 nz:=size(Z);
 
-l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" ";
-pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);
+l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; <span class="flyspell-duplicate">lf</span>:=" ";lsp:=" ";
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> <span class="flyspell-duplicate">etex</span>);
 ";fpour; 
 
-       k0:= evalf(limite(f(x),x=Z[0],1))&gt; evalf(limite(f(x),x=Z[1],-1));
-       kz:=evalf(limite(f(x),x=Z[nz-1],-1))&gt; evalf(limite(f(x),x=Z[nz-2],1));
+       k0:= <span class="flyspell-duplicate">evalf</span>(limit(f(x),x=Z[0],1))&gt; <span class="flyspell-duplicate">evalf</span>(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))&gt; evalf(limit(f(x),x=Z[<span class="flyspell-duplicate">nz</span>-2],1));
                           
-lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
+<span class="flyspell-duplicate">lsi</span>:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
 if(member(Z[0],IMIN)!=0){"debutNonDef;"}else{if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
                                                     if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
                                                     if(sign(fp(Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
@@ -512,121 +812,130 @@ if(member(Z[0],IMIN)!=0){"debutNonDef;"}else{if(Z[0]==-infinity){if(sign(evalf(f
 
 
 if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))&gt;0; 
-                                               lsp:=lsp+if(member(Z[r],IMIN)!=0){"debutNonDef;"}else{
-                                                       if(member(Z[r],IMAX)!=0){"finNonDef;"+
-                                                if(ksp==1){"plus;"}else{"moins;"}}else{
+                                               lsp:=lsp+if(member(Z[r],IMIN)!=0){"debutNonDef;"}</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{
+                                                       if(member(Z[r],IMAX)!=0){"</span><span class="font-latex-math"><span class="flyspell-duplicate">finNonDef</span></span><span class="font-latex-math">;"+
+                                                if(ksp==1){"plus;"}else{"moins;"}}</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{
                                                  if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                                 if(ksp==1){"plus;"}else{"moins;"}
                                                   }}}}; 
 
 
 
-lsf:=if(member(Z[0],IMAX)!=0){"finNonDef;"}else{if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;
+</span><span class="font-latex-math"><span class="flyspell-duplicate">lsf</span></span><span class="font-latex-math">:=if(member(Z[0],IMAX)!=0){"finNonDef;"}else{if(member(Z[nz-1],F)==0){""}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">;
 "}}
 
 
-lm0:=limite(f(x),x=Z[0],1)==-infinity;
+</span><span class="font-latex-math"><span class="flyspell-duplicate">lm</span></span><span class="font-latex-math">0:=limit(f(x),x=Z[0],1)==-</span><span class="font-latex-math"><span class="flyspell-duplicate">infinity</span></span><span class="font-latex-math">;
      li:=lvic  +nom+"}$</span> etex);"+
-           if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}
-             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}+                               
+           if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}
+             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+                               
            if(k0==1){"1"}else{"0"}+
                          ");";
             
 if(nz&gt;2){ 
    for(r:=1; r&lt;=nz-2;r++){ 
-     krm:=evalf(limite(f(x),x=Z[r-1],1))&lt; evalf(limite(f(x),x=Z[r],-1));
-     krp:=evalf(limite(f(x),x=Z[r],1))&gt; evalf(limite(f(x),x=Z[r+1],-1)) ;  
-     lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+     krm:=evalf(limit(f(x),x=Z[r-1],1))&lt; evalf(limit(f(x),x=Z[r],-1));
+     krp:=evalf(limit(f(x),x=Z[r],1))&gt; evalf(limit(f(x),x=Z[r+1],-1)) ;  
+     lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
 
      lp:=lp+if(member(Z[r],IMIN)!=0){"limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){
              "-\\infty"}else{
-                latex(simplifier(limite(f(x),x=Z[r],-1)))}
-         +"$</span> etex,"+if(krm==1){
-             "1);"}else{"0);"}
-         +"debutNonDef;"
-       }//fsi Zr=Imin
+                latex(simplify(limit(f(x),x=Z[r],-1)))}
+         +"$</span> etex,"+if(<span class="flyspell-duplicate">krm</span>==1){
+             "1);"}<span class="flyspell-duplicate">else</span>{"0);"}
+         +"<span class="flyspell-duplicate">debutNonDef</span>;"
+       }//fsi Zr=<span class="flyspell-duplicate">Imin</span>
       else{
         if (member(Z[r],IMAX)!=0) {"finNonDef;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){
-             "-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}
-         +"$</span> etex,"+if(krp==1){
-             "1);"}else{"0);"}          
+             "-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}
+         +"$</span> etex,"+if(<span class="flyspell-duplicate">krp</span>==1){
+             "1);"}<span class="flyspell-duplicate">else</span>{"0);"}          
        }
         else {
           if(member(Z[r],F)){
          "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){
              "-\\infty"}else{
-                latex(simplifier(limite(f(x),x=Z[r],-1)))}
-         +"$</span> etex,"+if(krm==1){
+                latex(simplify(limit(f(x),x=Z[r],-1)))}
+         +"$</span> etex,"+if(<span class="flyspell-duplicate">krm</span>==1){
              "1);"}else{"0);"}
          +"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){
-             "-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}
-         +"$</span> etex,"+if(krp==1){
-             "1);"}else{"0);"}
+             "-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}
+         +"$</span> etex,"+if(<span class="flyspell-duplicate">krp</span>==1){
+             "1);"}<span class="flyspell-duplicate">else</span>{"0);"}
          }//fsi (member Zr F)
-          else{"valPos(btex<span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span>etex,"+
+          else{"valPos(btex<span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span>etex,"+
              if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){
-               "0.5);"}else{
-                    if(krp==1){
-                       "1);"}else{"0);"}//felse(krp)
+               "0.5);"}<span class="flyspell-duplicate">else</span>{
+                    if(<span class="flyspell-duplicate">krp</span>==1){
+                       "1);"}else{"0);"}//felse(<span class="flyspell-duplicate">krp</span>)
                     }//felse(valpos)
                }//felse(member Zr F)
                } //felse(Zr=Imax)
-              }//felse(Zr=Imin)
-           };//ffor 
-         }//fsi nz
-
-lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
-                           lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+                               
-           if(kz==1){"1);"}else{"0);
-"};    
+              }//felse(Zr=<span class="flyspell-duplicate">Imin</span>)
+           };//<span class="flyspell-incorrect">ffor</span> 
+         }//fsi <span class="flyspell-duplicate">nz</span>
+
+lnz:=limit(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>;
+
+
+
+<span class="flyspell-duplicate">lf</span>:=if(member(Z[nz-1],F)==0){"valPos(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);<span class="flyspell-duplicate">nonDefBarre</span>;"}};    
     
 
-MetaLfc:=if(ftt==2){if(nz&gt;2){"
 
-beginTableau("+nmr+")"+
+    
+
+<span class="flyspell-duplicate">MetaLfc</span>:=if(ftt==2){if(nz&gt;2){"
+
+<span class="flyspell-duplicate">beginTableau</span>("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+lsi+lsp+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{
-intro+"beginTableau("+nmr+")"+
+intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
-lsi+lsf+"
-endTableau;
+<span class="flyspell-duplicate">lsi</span>+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";
 }
-}else{ if(ftt==0){if(nz&gt;2){"beginTableau("+nmr+")"+
+}else{ if(ftt==0){if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
 li+
 lp+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
-";}else{"beginTableau("+nmr+")"+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
 li+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}}else{
 if(nz&gt;2){"beginTableau("+nmr+")"+
         l0+
-lsi+lsp+lsf+
+<span class="flyspell-duplicate">lsi</span>+lsp+lsf+
 li+
 lp+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{"beginTableau("+nmr+")"+
         l0+
 lsi+lsf+
 li+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}
 }}
@@ -634,7 +943,7 @@ endTableau;
 
 sortie:=fopen("XCasmpfc.mp");
 fprint(sortie,Unquoted,MetaLfc);
-fclose(sortie);
+<span class="flyspell-duplicate">fclose</span>(sortie);
 
  }
 :;
@@ -650,7 +959,7 @@ fclose(sortie);
 </span>
 
 
-<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVapp.cxx}
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVapp.<span class="flyspell-duplicate">cxx</span>}
 
 
 
@@ -661,20 +970,32 @@ fclose(sortie);
 TVapp(L,F,nom,nomv,f,ftt,nmr):={
 
 
-nl:=size(L);
+<span class="flyspell-duplicate">nl</span>:=size(L);
 f:=unapply(f,x);
-fp:=fonction_derivee(f);
+fp:=function_diff(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}
+<span class="flyspell-duplicate">else</span>{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)&gt;0 alors   pour j de 0 jusque size(S)-1 faire 
                              kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])&gt;=L[0]) and (evalf(S[j])&lt;=L[1]);
-                          if(kk==1){if(kok==1){z:=append(z,simplifier(S[j]))}};
+                          if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}};
                           fpour;
-fsi;
+<span class="flyspell-duplicate">fsi</span>;
 
 
 S:=NULL;
@@ -686,7 +1007,7 @@ for(j:=1;j&lt;size(z);j++){
 z:=[S];
 
 Z:=sort(z);
-nz:=size(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
 
 S:=NULL;
 S:=S,Z[0];
@@ -697,13 +1018,13 @@ for(j:=1;j&lt;nz;j++){
 Z:=[S]; 
 
 
-nz:=size(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
 l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" ";
 pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);
-";fpour; 
+";<span class="flyspell-duplicate">fpour</span>; 
 
-       k0:= evalf(limite(f(x),x=Z[0],1))&gt; evalf(limite(f(x),x=Z[1],-1));
-       kz:=evalf(limite(f(x),x=Z[nz-1],-1))&gt; evalf(limite(f(x),x=Z[nz-2],1));
+       k0:= evalf(limit(f(x),x=Z[0],1))&gt; evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))&gt; evalf(limit(f(x),x=Z[<span class="flyspell-duplicate">nz</span>-2],1));
                           
 lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
      if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
@@ -716,72 +1037,75 @@ if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.01))&gt;0;
                                                 if(ksp==1){"plus;"}else{"moins;"}
                                                   }; }
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;
+</span><span class="font-latex-math"><span class="flyspell-duplicate">lsf</span></span><span class="font-latex-math">:=if(member(Z[nz-1],F)==0){""}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">;
 "}
-lm0:=limite(f(x),x=Z[0],1)==-infinity;
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
      li:=lvic+nom+"}$</span> etex);"+
-           if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}
-             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}+                               
+           if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}
+             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+                               
            if(k0==1){"1"}else{"0"}+
                          ");";
             
-                     if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){  krm:=evalf(limite(f(x),x=Z[r-1],1))&lt; evalf(limite(f(x),x=Z[r],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[r],1))&gt; evalf(limite(f(x),x=Z[r+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+                     if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){  krm:=evalf(limit(f(x),x=Z[r-1],1))&lt; evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))&gt; evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                   lp:=lp+if(member(Z[r],F)){
-                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span>
+                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span>
                                             etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
 "}}}
                                                    }; }
 
-lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
-                           lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+                               
-           if(kz==1){"1);"}else{"0);
-"};    
-    
-
+lnz:=limit(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>;
+ 
 
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+
+             if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}
+    else{"limGauche(btex <span class="font-latex-math">$"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);<span class="flyspell-duplicate">nonDefBarre</span>;"}};    
+    
 
 
-MetaLfc:=if(ftt==2){if(nz&gt;2){"
+<span class="flyspell-duplicate">MetaLfc</span>:=if(ftt==2){if(nz&gt;2){"
 
-beginTableau("+nmr+")"+
+beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+lsi+lsp+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{
 intro+"beginTableau("+nmr+")"+
         l0+
-lsi+lsf+"
-endTableau;
+<span class="flyspell-duplicate">lsi</span>+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";
 }
-}else{ if(ftt==0){if(nz&gt;2){"beginTableau("+nmr+")"+
+}else{ if(ftt==0){if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
 li+
 lp+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{"beginTableau("+nmr+")"+
         l0+
 li+
 lf
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}}else{
 if(nz&gt;2){"beginTableau("+nmr+")"+
         l0+
 lsi+lsp+lsf+
 li+
-lp+
-lf
+<span class="flyspell-duplicate">lp</span>+
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{"beginTableau("+nmr+")"+
         l0+
@@ -789,7 +1113,7 @@ lsi+lsf+
 li+
 lf
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}
 }}
@@ -818,7 +1142,7 @@ fclose(sortie);
 
 <span class="comment-delimiter">%%</span><span class="comment">
 </span><span class="comment-delimiter">%% </span><span class="comment">Code giac/Xcas pour les Tableaux de Variations avec 
-</span><span class="comment-delimiter">%% </span><span class="comment">Valeurs intermediaires
+</span><span class="comment-delimiter">%% </span><span class="comment">Valeurs </span><span class="comment"><span class="flyspell-incorrect">intermediaires</span></span><span class="comment">
 </span><span class="comment-delimiter">%%</span><span class="comment">
 </span>
 
@@ -828,58 +1152,78 @@ fclose(sortie);
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVI.cxx}
 
 
-TVI(L,F,nom,nomv,f,ftt,ao,nmr):={
+<span class="flyspell-duplicate">TVI</span>(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={
 nl:=size(L);
 f:=unapply(f,x);
-fp:=fonction_derivee(f);
+<span class="flyspell-duplicate">fp</span>:=function_diff(f);
 Z:=concat(L,F);
-S:=resoudre(fp(x),x);
+S:=[];
+
+
+if(trigo==t){
+<span class="flyspell-duplicate">all</span>_trig_solutions:=1;
+<span class="flyspell-duplicate">reset</span>_solve_counter(-1,-1);
+SS:=solve(factor(simplify(fp(x))),x);
+<span class="flyspell-duplicate">ns</span>:=size(SS);
+for(k:=0;k&lt;ns;k++){
+m:=0;
+<span class="flyspell-duplicate">while</span>(evalf(simplify(subst(SS[k],n_1=m)))&lt;=evalf(L[nl-1])){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+<span class="flyspell-duplicate">while</span>(evalf(subst(SS[k],n_1=m))&gt;=L[0]){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
+S:=solve(fp(x),x);
+}
+
   si size(S)&gt;0 alors   pour j de 0 jusque size(S)-1 faire 
                             kk:=(evalf(S[j])&gt;=evalf(L[0])) and (evalf(S[j])&lt;=evalf(L[nl-1]));
-                          if(kk==1){Z:=append(Z,simplifier(S[j]))};
-                          fpour
+                          if(kk==1){Z:=append(Z,simplify(S[j]))};
+                          <span class="flyspell-duplicate">fpour</span>
   fsi;
 
 Z:=sort(Z); 
-nz:=size(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
  si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1; 
      fsi;
 pour u de 1 jusque nz-2 faire 
      si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1; 
      fsi;
-fpour;
+<span class="flyspell-duplicate">fpour</span>;
 nz:=size(Z);
-l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" ";
+l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";<span class="flyspell-duplicate">lsp</span>:=" ";
 
 
 
-LI:=limite(f(x),x,Z[0],1);
-LF:=limite(f(x),x,Z[nz-1],-1);
+LI:=limit(f(x),x,Z[0],1);
+LF:=limit(f(x),x,Z[nz-1],-1);
 LP:=NULL;
-if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){LP:=LP,if(member(Z[r],F)){limite(f(x),x,Z[r],-1),limite(f(x),x,Z[r],1)}else{f(Z[r])}}};
-if(nz&gt;2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
+if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}}};
+if(nz&gt;2){ LL:=[LI,LP,LF]}else{LL:=[LI,<span class="flyspell-duplicate">LF</span>]};
       
-NL:=size(LL);
+<span class="flyspell-duplicate">NL</span>:=size(LL);
 A:=NULL;aa:=1;kk:=0;
 
 if(NL==nz){for(k:=0;k&lt;nz-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
 if(TestS==0){A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"}}
-l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);"};
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> <span class="flyspell-duplicate">etex</span>);"};
 
 if(NL&gt;nz){for(k:=0;k&lt;NL-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
 TestL:=(abs(LL[k])==abs(LL[k+1]));
 if(TestS==0){ if( TestL==1 ){l0:=l0}else{
 A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;kk:=kk+1}}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=kk+1}}
-l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> <span class="flyspell-duplicate">etex</span>);
 "};
 
 
 
-TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
-       k0:= evalf(limite(f(x),x=Z[0],1))&gt; evalf(limite(f(x),x=Z[1],-1));
-       kz:=evalf(limite(f(x),x=Z[nz-1],-1))&gt; evalf(limite(f(x),x=Z[nz-2],1));
+TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-<span class="flyspell-duplicate">ao</span>))==0.0);
+       k0:= evalf(limit(f(x),x=Z[0],1))&gt; evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))&gt; evalf(limit(f(x),x=Z[nz-2],1));
                           
-lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
+<span class="flyspell-duplicate">lsi</span>:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
      if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
                                                     if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
                                                     if(sign(fp((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-10))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
@@ -889,60 +1233,60 @@ lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
 
 
  
-if(nz&gt;2){rr:=1; if(nz==NL){for(r:=1; r&lt;=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
+if(nz&gt;2){rr:=1; if(nz==NL){for(r:=1; r&lt;=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-</span><span class="font-latex-math"><span class="flyspell-duplicate">ao</span></span><span class="font-latex-math">))==0.0); 
                                                  ksp:=evalf(fp(Z[r]+0.01))&gt;0;  
                                                  TestL:=(abs(LL[r])==abs(LL[r+1]));
                                  lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
-                                  if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $</span>  <span class="font-latex-math">$ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "};
+                                  if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $</span>  <span class="font-latex-math">$ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{" "};
                                              }}
-else{for(r:=1; r&lt;=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))&gt;0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{for(r:=1; r&lt;=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))&gt;0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-</span><span class="font-latex-math"><span class="flyspell-duplicate">ao</span></span><span class="font-latex-math">))==0.0);
                                           TestL:=(abs(LL[r])==abs(LL[r+1]));
                       if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
-                                  if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $</span>  <span class="font-latex-math">$ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
+                                  if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $</span>  <span class="font-latex-math">$ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=</span><span class="font-latex-math"><span class="flyspell-duplicate">rr</span></span><span class="font-latex-math">+1;}
                                    } else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
-                                  if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}        
+                                  if(kspp==1){"plus;"}else{"moins;"};rr:=</span><span class="font-latex-math"><span class="flyspell-duplicate">rr</span></span><span class="font-latex-math">+1;}        
 }}     
   }; 
 
 
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;"}
-lm0:=limite(f(x),x=Z[0],1)==-infinity;
+</span><span class="font-latex-math"><span class="flyspell-duplicate">lsf</span></span><span class="font-latex-math">:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;"}
+</span><span class="font-latex-math"><span class="flyspell-duplicate">lm</span></span><span class="font-latex-math">0:=limit(f(x),x=Z[0],1)==-</span><span class="font-latex-math"><span class="flyspell-duplicate">infinity</span></span><span class="font-latex-math">;
 
 TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
 
      li:=lvic+nom+"}$</span> etex);
-"+  if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}
-             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}+                               
+"+  if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}
+             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+                               
            if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}else{" "}; 
                          
             
                      if(nz&gt;2){if(nz==NL){for(r:=1; r&lt;=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
-                                                 krm:=evalf(limite(f(x),x=Z[r-1],1))&lt; evalf(limite(f(x),x=Z[r],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[r],1))&gt; evalf(limite(f(x),x=Z[r+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+                                                 krm:=evalf(limit(f(x),x=Z[r-1],1))&lt; evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))&gt; evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                   lp:=lp+if(member(Z[r],F)) {
-                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span>
+                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span>
                                             etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
                                             <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"
                                                            }else{" "}; 
 };//for
 }else{rr:=1;for(r:=1; r&lt;=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
-                                                 krm:=evalf(limite(f(x),x=Z[rr-1],1))&lt; evalf(limite(f(x),x=Z[rr],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[rr],1))&gt; evalf(limite(f(x),x=Z[rr+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[rr],-1)==-infinity;lmrp:=limite(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
+                                                 krm:=evalf(limit(f(x),x=Z[rr-1],1))&lt; evalf(limit(f(x),x=Z[rr],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[rr],1))&gt; evalf(limit(f(x),x=Z[rr+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
 if(TestS==0){if( TestL==1 ){lp:=lp}else{  lp:=lp+if(member(Z[rr],F)) {
-                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplifier(f(Z[rr])))+"$</span>
+                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span>
                                             etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
                                             <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);
                                                                  ";rr:=rr+1;
 }// else testL==1
 }//testS==0
 else{lp:=lp+if(member(Z[rr],F)){
-                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplifier(f(Z[rr])))+"$</span>
+                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplify(f(Z[</span><span class="font-latex-math"><span class="flyspell-duplicate">rr</span></span><span class="font-latex-math">])))+"$</span>
                                             etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
                                                             "}}};rr:=rr+1;
 }//else testS==0
@@ -952,57 +1296,63 @@ else{lp:=lp+if(member(Z[rr],F)){
 };//if nz&gt;2
 
 
-lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
-                           lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+                               
-           if(kz==1){"1);"}else{"0);"};    
+lnz:=limit(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>;
+
+
+<span class="flyspell-duplicate">lf</span>:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex <span class="font-latex-math">$"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);<span class="flyspell-duplicate">nonDefBarre</span>;"}};    
     
 
 
 
-MetaLfc:= if(ftt==2){if(nz&gt;2){"beginTableau("+nmr+")"+
+MetaLfc:= if(ftt==2){if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+lsi+lsp+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{
 "beginTableau("+nmr+")"+
         l0+
-lsi+lsf+"
-endTableau;
+<span class="flyspell-duplicate">lsi</span>+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";
 }
 }else{
-if(ftt==0){if(nz&gt;2){"beginTableau("+nmr+")"+
+if(ftt==0){if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
 li+
 lp+
 lf
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
-";}else{"beginTableau("+nmr+")"+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
 li+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 ";}}else{
 if(nz&gt;2){"beginTableau("+nmr+")"+
         l0+
 lsi+lsp+lsf+
 li+
-lp+
-lf
+<span class="flyspell-duplicate">lp</span>+
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
-";}else{"beginTableau("+nmr+")"+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
-lsi+lsf+
+<span class="flyspell-duplicate">lsi</span>+lsf+
 li+
 lf
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}
 }};
@@ -1010,7 +1360,7 @@ endTableau;
 
 
 sortie:=fopen("XCasmpfc.mp");
-fprint(sortie,Unquoted,MetaLfc);
+<span class="flyspell-duplicate">fprint</span>(sortie,Unquoted,MetaLfc);
 fclose(sortie);
 
 
@@ -1037,23 +1387,37 @@ fclose(sortie);
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVIapp.cxx}
 
 
-TVIapp(L,F,nom,nomv,f,ftt,ao,nmr):={
+<span class="flyspell-duplicate">TVIapp</span>(L,F,nom,nomv,f,ftt,ao,<span class="flyspell-duplicate">nmr</span>):={
 
 
-nl:=size(L);
+<span class="flyspell-duplicate">nl</span>:=size(L);
 f:=unapply(f,x);
-fp:=fonction_derivee(f);
+fp:=function_diff(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])}}};
+<span class="flyspell-duplicate">nz</span>:=size(z);
+
+
+
+
+
+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}
+<span class="flyspell-duplicate">else</span>{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)&gt;0 alors   pour j de 0 jusque size(S)-1 faire 
                              kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])&gt;=L[0]) and (evalf(S[j])&lt;=L[1]);
-                          if(kk==1){if(kok==1){z:=append(z,simplifier(S[j]))}};
+                          if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}};
                           fpour;
-fsi;
+<span class="flyspell-duplicate">fsi</span>;
 
 
 S:=NULL;
@@ -1067,7 +1431,7 @@ z:=[S];
 
 
 Z:=sort(z);
-nz:=size(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
 
 S:=NULL;
 S:=S,Z[0];
@@ -1078,38 +1442,38 @@ for(j:=1;j&lt;nz;j++){
 Z:=[S]; 
 
 
-nz:=size(Z);
-l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" ";
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";<span class="flyspell-duplicate">lsp</span>:=" ";
 
 
 
-LI:=limite(f(x),x,Z[0],1);
-LF:=limite(f(x),x,Z[nz-1],-1);
-LP:=NULL;
-if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){LP:=LP,if(member(Z[r],F)){limite(f(x),x,Z[r],-1),limite(f(x),x,Z[r],1)}else{f(Z[r])}}};
+LI:=limit(f(x),x,Z[0],1);
+<span class="flyspell-duplicate">LF</span>:=limit(f(x),x,Z[nz-1],-1);
+<span class="flyspell-duplicate">LP</span>:=NULL;
+if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}}};
 if(nz&gt;2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
       
-NL:=size(LL);
-A:=NULL;aa:=1;kk:=0;
+<span class="flyspell-duplicate">NL</span>:=size(LL);
+A:=NULL;aa:=1;<span class="flyspell-duplicate">kk</span>:=0;
 
 if(NL==nz){for(k:=0;k&lt;nz-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
 if(TestS==0){A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"}}
-l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);"};
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> <span class="flyspell-duplicate">etex</span>);"};
 
 if(NL&gt;nz){for(k:=0;k&lt;NL-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
-TestL:=(abs(LL[k])==abs(LL[k+1]));
+<span class="flyspell-duplicate">TestL</span>:=(abs(LL[k])==abs(LL[k+1]));
 if(TestS==0){ if( TestL==1 ){l0:=l0}else{
 A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;kk:=kk+1}}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=kk+1}}
-l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> <span class="flyspell-duplicate">etex</span>);
 "};
 
 
 
-TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
-       k0:= evalf(limite(f(x),x=Z[0],1))&gt; evalf(limite(f(x),x=Z[1],-1));
-       kz:=evalf(limite(f(x),x=Z[nz-1],-1))&gt; evalf(limite(f(x),x=Z[nz-2],1));
+TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-<span class="flyspell-duplicate">ao</span>))==0.0);
+       k0:= evalf(limit(f(x),x=Z[0],1))&gt; evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))&gt; evalf(limit(f(x),x=Z[<span class="flyspell-duplicate">nz</span>-2],1));
                           
-lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
+<span class="flyspell-duplicate">lsi</span>:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
      if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
                                                     if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
                                                     if(sign(fp((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-10))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
@@ -1119,60 +1483,60 @@ lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+
 
 
  
-if(nz&gt;2){rr:=1; if(nz==NL){for(r:=1; r&lt;=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
+if(nz&gt;2){rr:=1; if(nz==NL){for(r:=1; r&lt;=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-</span><span class="font-latex-math"><span class="flyspell-duplicate">ao</span></span><span class="font-latex-math">))==0.0); 
                                                  ksp:=evalf(fp(Z[r]+0.01))&gt;0;  
                                                  TestL:=(abs(LL[r])==abs(LL[r+1]));
-                                 lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                 lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">;"}+
                                   if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $</span>  <span class="font-latex-math">$ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "};
                                              }}
-else{for(r:=1; r&lt;=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))&gt;0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{for(r:=1; r&lt;=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))&gt;0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
                                           TestL:=(abs(LL[r])==abs(LL[r+1]));
-                      if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
-                                  if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $</span>  <span class="font-latex-math">$ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
-                                   } else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
-                                  if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}        
+                      if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">;"}+
+                                  if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $</span>  <span class="font-latex-math">$ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=</span><span class="font-latex-math"><span class="flyspell-duplicate">rr</span></span><span class="font-latex-math">+1;}
+                                   } else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">;"}+
+                                  if(kspp==1){"plus;"}else{"moins;"};rr:=</span><span class="font-latex-math"><span class="flyspell-duplicate">rr</span></span><span class="font-latex-math">+1;}        
 }}     
   }; 
 
 
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;"}
-lm0:=limite(f(x),x=Z[0],1)==-infinity;
+</span><span class="font-latex-math"><span class="flyspell-duplicate">lsf</span></span><span class="font-latex-math">:=if(member(Z[nz-1],F)==0){""}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">;"}
+</span><span class="font-latex-math"><span class="flyspell-duplicate">lm</span></span><span class="font-latex-math">0:=limit(f(x),x=Z[0],1)==-infinity;
 
-TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
+TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-</span><span class="font-latex-math"><span class="flyspell-duplicate">ao</span></span><span class="font-latex-math">))==0.0);
 
      li:=lvic+nom+"}$</span> etex);
-"+  if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}
-             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}+                               
+"+  if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}
+             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+                               
            if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}else{" "}; 
                          
             
                      if(nz&gt;2){if(nz==NL){for(r:=1; r&lt;=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
-                                                 krm:=evalf(limite(f(x),x=Z[r-1],1))&lt; evalf(limite(f(x),x=Z[r],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[r],1))&gt; evalf(limite(f(x),x=Z[r+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+                                                 krm:=evalf(limit(f(x),x=Z[r-1],1))&lt; evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))&gt; evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                   lp:=lp+if(member(Z[r],F)) {
-                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span>
+                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span>
                                             etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
                                             <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"
                                                            }else{" "}; 
 };//for
 }else{rr:=1;for(r:=1; r&lt;=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
-                                                 krm:=evalf(limite(f(x),x=Z[rr-1],1))&lt; evalf(limite(f(x),x=Z[rr],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[rr],1))&gt; evalf(limite(f(x),x=Z[rr+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[rr],-1)==-infinity;lmrp:=limite(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
+                                                 krm:=evalf(limit(f(x),x=Z[rr-1],1))&lt; evalf(limit(f(x),x=Z[rr],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[rr],1))&gt; evalf(limit(f(x),x=Z[rr+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
 if(TestS==0){if( TestL==1 ){lp:=lp}else{  lp:=lp+if(member(Z[rr],F)) {
-                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplifier(f(Z[rr])))+"$</span>
+                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span>
                                             etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
                                             <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);
                                                                  ";rr:=rr+1;
 }// else testL==1
 }//testS==0
 else{lp:=lp+if(member(Z[rr],F)){
-                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplifier(f(Z[rr])))+"$</span>
+                                    "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplify(f(Z[</span><span class="font-latex-math"><span class="flyspell-duplicate">rr</span></span><span class="font-latex-math">])))+"$</span>
                                             etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
                                                             "}}};rr:=rr+1;
 }//else testS==0
@@ -1182,57 +1546,67 @@ else{lp:=lp+if(member(Z[rr],F)){
 };//if nz&gt;2
 
 
-lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
-                           lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+                               
-           if(kz==1){"1);"}else{"0);"};    
+lnz:=limit(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>;
+
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex <span class="font-latex-math">$"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);<span class="flyspell-duplicate">nonDefBarre</span>;"}};    
     
 
 
 
-MetaLfc:= if(ftt==2){if(nz&gt;2){"beginTableau("+nmr+")"+
+
+
+
+<span class="flyspell-duplicate">MetaLfc</span>:= if(ftt==2){if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+lsi+lsp+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{
-"beginTableau("+nmr+")"+
+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
-lsi+lsf+"
-endTableau;
+<span class="flyspell-duplicate">lsi</span>+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";
 }
 }else{
-if(ftt==0){if(nz&gt;2){"beginTableau("+nmr+")"+
+if(ftt==0){if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
 li+
-lp+
-lf
+<span class="flyspell-duplicate">lp</span>+
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
-";}else{"beginTableau("+nmr+")"+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
 li+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
 endTableau;
 ";}}else{
 if(nz&gt;2){"beginTableau("+nmr+")"+
         l0+
-lsi+lsp+lsf+
+<span class="flyspell-duplicate">lsi</span>+lsp+lsf+
 li+
 lp+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{"beginTableau("+nmr+")"+
         l0+
 lsi+lsf+
 li+
-lf
+<span class="flyspell-duplicate">lf</span>
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}
 }};
@@ -1241,7 +1615,7 @@ endTableau;
 
 sortie:=fopen("XCasmpfc.mp");
 fprint(sortie,Unquoted,MetaLfc);
-fclose(sortie);
+<span class="flyspell-duplicate">fclose</span>(sortie);
 
 
  }:;
@@ -1268,96 +1642,105 @@ fclose(sortie);
 
 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{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);
-fp:=[];
+<span class="flyspell-duplicate">nl</span>:=size(L);
+<span class="flyspell-duplicate">fp</span>:=[];
 S:=[];
-f:=ff;
+f:=<span class="flyspell-duplicate">ff</span>;
 Z:=[];
-LLL:=[];
+<span class="flyspell-duplicate">LLL</span>:=[];
+
+
+all_trig_solutions:=1;
+<span class="flyspell-duplicate">reset</span>_solve_counter(-1,-1);
+
 for(d:=0;d&lt;=1;d++){
 f:=subst(f,f[d]=unapply(f[d],t));
-fp:=append(fp,fonction_derivee(f[d]));
+<span class="flyspell-duplicate">fp</span>:=append(fp,function_<span class="flyspell-duplicate">diff</span>(f[d]));
 LLL:=concat(L,F[d]);
 Z:=LLL union Z;
+SS:=solve(factor(simplify(fp[d](t))),t);
+ns:=size(<span class="flyspell-duplicate">SS</span>);
 
-ns:=size(resoudre(factor(simplifier(fp[d](t))),t));
-reset_solve_counter(0);
 for(k:=0;k&lt;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))&lt;=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(simplify(subst(SS[k],n_1=m)))&lt;=evalf(L[nl-1])){
+
+S:=concat(S,simplify(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))&gt;=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);
+<span class="flyspell-duplicate">while</span>(evalf(subst(SS[k],n_1=m))&gt;=L[0]){
+
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
+
 }
 }else{
-S:=concat(S,resoudre(factor(simplifier(fp[d](x))),x));
+S:=concat(S,<span class="flyspell-duplicate">SS</span>);
 }
 }
-  si size(S)&gt;0 alors   pour j de 0 jusque size(S)-1 faire 
-                             qq:=member(simplifier(S[j]),Z)==0;
-                             kk:=(evalf(S[j])&gt;=evalf(L[0])) and (evalf(S[j])&lt;=evalf(L[nl-1]));
-                          if(kk==1){if(qq==1){Z:=append(Z,simplifier(S[j]))}};
-                          fpour
+
+
+  si size(S)&gt;0 alors   pour j de 0 jusque size(S)-1 faire
+                             qq:=member(simplify(S[j]),Z)==0;
+                             kk:=(evalf(S[j])&gt;=evalf(L[0])) and (evalf(S[j])&lt;=evalf(L[<span class="flyspell-duplicate">nl</span>-1]));
+                          if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}};
+                          <span class="flyspell-duplicate">fpour</span>
   fsi;
+Z:=sort(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+
+
+ tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z);
+     <span class="flyspell-duplicate">ftantque</span>;
 
-Z:=sort(Z); 
-nz:=size(Z);
- 
 
 
- tantque simplifier(Z[0])==simplifier(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); 
-     ftantque;
 
 nz:=size(Z);
 u:=1;
  tantque (u&lt;nz-2) and (nz&gt;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;
+     <span class="flyspell-duplicate">ftantque</span>;
   u:=u+1;
- ftantque;
+ <span class="flyspell-duplicate">ftantque</span>;
+
+
  };
 
+Z:=sort(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+
 
-Z:=sort(Z); 
-nz:=size(Z);
 
  l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:="",""; lf:="","";lsp:="","";
 pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);
-";fpour;
+";<span class="flyspell-duplicate">fpour</span>;
 
  lsi:="","";
 
-FFF:=[[],[]];
+<span class="flyspell-duplicate">FFF</span>:=[[],[]];
 
 for(d:=0;d&lt;=1;d++){
-FFF[d]:=concat(F[d],[-infinity,+infinity]);
-       k0:= evalf(limite(f[d](x),x=Z[0],1))&gt; evalf(limite(f[d](x),x=Z[1],-1));
-       kz:=evalf(limite(f[d](x),x=Z[nz-1],-1))&gt; evalf(limite(f[d](x),x=Z[nz-2],1));
-                          
- lsi[d]:=lsic+nom[d]+"'("+nomv+")}<span class="font-latex-math">$ etex);"+if(member(Z[0],FFF[d])==0){"valBarre(btex $</span>"+latex(simplifier(fp[d](Z[0])))+"<span class="font-latex-math">$ etex);"}else{if(Z[0]==-infinity){" "}else{"nonDefBarre;
+<span class="flyspell-duplicate">FFF</span>[d]:=concat(F[d],[-infinity,+<span class="flyspell-duplicate">infinity</span>]);
+       k0:= evalf(limit(f[d](x),x=Z[0],1))&gt; evalf(limit(f[d](x),x=Z[1],-1));
+       kz:=evalf(limit(f[d](x),x=Z[nz-1],-1))&gt; evalf(limit(f[d](x),x=Z[<span class="flyspell-duplicate">nz</span>-2],1));
+//}
+//<span class="font-latex-math">$
+ lsi[d]:=lsic+nom[d]+"'("+nomv+")}$</span> etex);"+if(member(Z[0],FFF[d])==0){"valBarre(btex <span class="font-latex-math">$"+latex(simplify(fp[d](Z[0])))+"$</span> etex);"}else{if(Z[0]==-infinity){" "}else{"<span class="flyspell-duplicate">nonDefBarre</span>;
 "}}+
-     if(Z[0]==-infinity){if(sign(evalf(fp[d](if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F[d])==0){
-                                                    if(sign(fp[d](Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)))==1){"plus;"}else{"moins;"}}else{
-                                                         if(sign(fp[d]((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5))))==1){"plus;"}else{"moins;"} }}
- 
-if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){      ksp:=evalf(fp[d](Z[r]+0.01))&gt;0;                     
-                                               lsp[d]:=lsp[d]+if(member(Z[r],F[d])==0){"valBarre(btex $</span>"+latex(simplifier(fp[d](Z[r])))+"<span class="font-latex-math">$ etex);"}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&gt;2){ for(r:=1; r&lt;=nz-2;r++){      ksp:=evalf(fp[d](Z[r]+0.01))&gt;0;
+                                               lsp[d]:=lsp[d]+if(member(Z[r],F[d])==0){"valBarre(btex <span class="font-latex-math">$"+latex(simplify(fp[d](Z[r])))+"$</span> etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+
                                                 if(ksp==1){"plus;"}else{"moins;"}
                                                   }; }
 
-lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex $</span>"+latex(simplifier(fp[d](Z[nz-1])))+"<span class="font-latex-math">$ etex);"}else{if(Z[nz-1]==+infinity){" "}else{"nonDefBarre;"}}
+lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex <span class="font-latex-math">$"+latex(simplify(fp[d](Z[nz-1])))+"$</span> etex);"}else{if(Z[nz-1]==+infinity){" "}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}}
 
 
 
@@ -1378,31 +1761,39 @@ lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex $</span>"+latex(simplifier(
 
 
 for(d:=0;d&lt;=1;d++){
-   K0[d]:= evalf(limite(f[d](x),x=Z[0],1))&gt; evalf(limite(f[d](x),x=Z[1],-1));
-  Kz[d]:=evalf(limite(f[d](x),x,Z[nz-1],-1))&gt; 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]+"}$</span> etex);"+
-           if(member(Z[0],F[d])==0){"valPos(btex <span class="font-latex-math">$"+if(lm0[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[0],1)))}+"$</span> etex,"}
-             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[0],1)))}+"$</span> etex,"}+                               
+   K0[d]:= evalf(limit(f[d](x),x=Z[0],1))&gt; evalf(limit(f[d](x),x=Z[1],-1));
+  Kz[d]:=evalf(limit(f[d](x),x,Z[nz-1],-1))&gt; evalf(limit(f[d](x),x,Z[nz-2],1));
+//{
+//<span class="font-latex-math">$
+lm0[d]:=limit(f[d](x),x,Z[0],1)==-infinity;
+     li[d]:=lvic+nom[d]+"}$</span> <span class="flyspell-duplicate">etex</span>);"+
+           if(member(Z[0],F[d])==0){"valPos(btex <span class="font-latex-math">$"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$</span> etex,"}
+             else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$</span> etex,"}+
            if(K0[d]==1){"1"}else{"0"}+
                          ");";
-            
-                     if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){ krm[d]:=evalf(limite(f[d](x),x=Z[r-1],1))&lt; evalf(limite(f[d](x),x=Z[r],-1));
-                                                 krp[d]:=evalf(limite(f[d](x),x=Z[r],1))&gt; evalf(limite(f[d](x),x,Z[r+1],-1)) ;  
-                         lmrm[d]:=limite(f[d](x),x,Z[r],-1)==-infinity;lmrp[d]:=limite(f[d](x),x,Z[r],1)==-infinity;
+
+                     if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){ krm[d]:=evalf(limit(f[d](x),x=Z[r-1],1))&lt; evalf(limit(f[d](x),x=Z[r],-1));
+                                                 krp[d]:=evalf(limit(f[d](x),x=Z[r],1))&gt; evalf(limit(f[d](x),x,Z[r+1],-1)) ;
+                         lmrm[d]:=limit(f[d](x),x,Z[r],-1)==-infinity;lmrp[d]:=limit(f[d](x),x,Z[r],1)==-infinity;
                                                   lp[d]:=lp[d]+if(member(Z[r],F[d])){
                                     "limGauche(btex
-                                    <span class="font-latex-math">$"+if(lmrm[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[r],-1)))}+"$</span>
-                                    etex,"+if(krm[d]==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[r],1)))}+"$</span> etex,"+if(krp[d]==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplifier(f[d](Z[r])))+"$</span>
-                                            etex,"+if(sign(evalf(fp[d](Z[r]-0.001)))==sign(evalf((fp[d](Z[r]+0.001))) )){"0.5);"}else{if(krp[d]==1){"1);"}else{"0);
+                                    <span class="font-latex-math">$"+if(lmrm[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],-1)))}+"$</span>
+                                    etex,"+if(krm[d]==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],1)))}+"$</span> etex,"+if(krp[d]==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          <span class="font-latex-math">$"+latex(simplify(f[d](Z[r])))+"$</span>
+                                            etex,"+if(sign(evalf(fp[d](Z[r]-0.001)))==sign(evalf((fp[d](Z[r]+0.001))) )){"0.5);"}else{if(krp[d]==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);
 "}}}
                                                    }; }
 
-lnz[d]:=limite(f[d](x),x=Z[nz-1],-1)==-infinity;
-                           lf[d]:=if(member(Z[nz-1],F[d])==0){"valPos(btex <span class="font-latex-math">$"+if(lnz[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[nz-1],-1)))}+"$</span> etex,"}+                               
-           if(Kz[d]==1){"1);"}else{"0);
-"};    
+<span class="flyspell-duplicate">lnz</span>[d]:=limit(f[d](x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>;
+
+
+<span class="flyspell-duplicate">lf</span>[d]:=if(member(Z[nz-1],F[d])==0){"valPos(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$"+
+           if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"+
+             if(<span class="flyspell-duplicate">Kz</span>[d]==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}
+    else{"limGauche(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$"+
+         if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"+ 
+           if(<span class="flyspell-duplicate">Kz</span>[d]==1){"1);nonDefBarre;"}else{"0);<span class="flyspell-duplicate">nonDefBarre</span>;"}};    
+    
 
 
 
@@ -1417,17 +1808,17 @@ lnz[d]:=limite(f[d](x),x=Z[nz-1],-1)==-infinity;
 
 
 
-MetaLfc:=if(ftt==2){if(nz&gt;2){"
+<span class="flyspell-duplicate">MetaLfc</span>:=if(ftt==2){if(nz&gt;2){"
 
 beginTableau("+nmr+")"+
         l0+lsi[0]+lsp[0]+lsf[0]+lsi[1]+lsp[1]+lsf[1]+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{
 intro+"beginTableau("+nmr+")"+
         l0+
 lsi[0]+lsf[0]+lsi[1]+lsf[1]+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";
 }
@@ -1435,24 +1826,24 @@ endTableau;
         l0+
 li[0]+
 lp[0]+
-lf[0]+
+<span class="flyspell-duplicate">lf</span>[0]+
 li[1]+
 lp[1]+
 lf[1]
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{"beginTableau("+nmr+")"+
         l0+
 li[0]+
 lf[0]+
 li[1]+
-lf[1]
+<span class="flyspell-duplicate">lf</span>[1]
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}}else{
-if(nz&gt;2){"beginTableau("+nmr+")"+
+if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
         l0+
 lsi[0]+lsp[0]+lsf[0]+
 li[0]+
@@ -1463,18 +1854,18 @@ li[1]+
 lp[1]+
 lf[1]
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}else{"beginTableau("+nmr+")"+
         l0+
 lsi[0]+lsf[0]+
 li[0]+
 lf[0]+
-lsi[1]+lsf[1]+
+<span class="flyspell-duplicate">lsi</span>[1]+lsf[1]+
 li[1]+
 lf[1]
 +"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
 
 ";}
 }
@@ -1485,8 +1876,6 @@ fprint(sortie,Unquoted,MetaLfc);
 fclose(sortie);
 
 }:;
-
-
 <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
 
 
@@ -1502,26 +1891,62 @@ fclose(sortie);
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignL.cxx}
 
 
-TS(nomf,L,D,nmr):={
+TS(nomf,L,D,trigo,nmr):={
 L:=apply(f-&gt;unapply(f,x),L)
 n:=size(L);
 Z:=NULL;
-
+<span class="flyspell-duplicate">nl</span>:=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);
+<span class="flyspell-duplicate">SS</span>:=solve(factor(simplify(L[k](x))),x);
+ns:=size(SS);
+for(j:=0;j&lt;ns;j++){
+m:=0;
+while(evalf(simplify(subst(SS[j],n_1=m)))&lt;=evalf(maxi)){
+S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[j],n_1=m))&gt;=evalf(mini)){
+S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1;
+}
+}
+
+}else{
+S:=solve(L[k](x),x);
+}
+
+
+
+
   si size(S)&gt;0 alors  pour j de 0 jusque size(S)-1 faire 
-                          if(S[j]&gt;mini and S[j]&lt;maxi){Z:=Z,simplifier(S[j]);}
+                          if(S[j]&gt;mini and S[j]&lt;maxi){Z:=Z,simplify(S[j]);}
                       fpour;
   fsi;
-fpour;
+<span class="flyspell-duplicate">fpour</span>;
+
+
+
+
+
 Z:=sort(Z);
-nz:=size(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+
+
+
+
+
 if(nz&gt;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;
-fpour;};
+<span class="flyspell-duplicate">fpour</span>;};
 nz:=size(Z);
 
 if(nz==0){li:="";l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);";
@@ -1537,8 +1962,8 @@ if(L[p]((mini+maxi)*0.5&gt;0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p
            lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)&gt;0){"plus;"}else{"moins;"};
 
 
-MetaLfc:="    beginTableau("+nmr+")
-newLigneVariables(btex $</span> {x}<span class="font-latex-math">$ etex);
+</span><span class="font-latex-math"><span class="flyspell-duplicate">MetaLfc</span></span><span class="font-latex-math">:="    beginTableau("+nmr+")
+newLigneVariables(btex $</span> {x}<span class="font-latex-math">$ </span><span class="font-latex-math"><span class="flyspell-duplicate">etex</span></span><span class="font-latex-math">);
    "+l0+li+ lsic+nomf+"(x)}$</span> etex);"+
                if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){"
                                 valBarre(btex 0 etex);"}else{"
@@ -1553,9 +1978,9 @@ endTableau;
 }else{
 
 l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);";li:=" ";lr:=" "; 
-pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> <span class="flyspell-duplicate">etex</span>);
 ";fpour; 
-l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);";
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> <span class="flyspell-duplicate">etex</span>);";
 
 
 for(p:=0;p&lt;=n-1;p++){lp:="";                                     
@@ -1566,25 +1991,25 @@ for(p:=0;p&lt;=n-1;p++){lp:="";
            if(L[p](Z[0]-0.01)&gt;0){"plus;"}else{"moins;"};
                                
                            for(r:=0; r&lt;=nz-2;r++){  
-                             lp:=lp+if(simplifier(L[p](Z[r]))==0){"
+                             lp:=lp+if(simplify(L[p](Z[r]))==0){"
                                 valBarre(btex 0 etex);"}else{"barre;
                               "}+ 
                              if(L[p]((Z[r]+Z[r+1])*.5)&gt;0){"plus;"}else{"moins;"}};
  
-                li:=li+lp+ if(simplifier(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
+                li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
                           if(L[p](Z[nz-1]+1.0)&gt;0){"plus;"}else{"moins;
     "}+if(maxi!=+infinity and L[p](maxi)==0){"
-                                valBarre(btex 0 etex);"}else{"
+                                valBarre(btex 0 etex);"}</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{"
                               "}
     };  
 
 
 pour t de 0 jusque nz-2 faire 
-                           lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"                    
+                           lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+"valBarre(btex 0 </span><span class="font-latex-math"><span class="flyspell-duplicate">etex</span></span><span class="font-latex-math">);"                    
                          fpour
 
 MetaLfc:="  beginTableau("+nmr+")
-newLigneVariables(btex $</span> {x}<span class="font-latex-math">$ etex);
+</span><span class="font-latex-math"><span class="flyspell-duplicate">newLigneVariables</span></span><span class="font-latex-math">(btex $</span> {x}<span class="font-latex-math">$ etex);
    "+l0+
                      li
                      + lsic+nomf+"(x)}$</span> etex);"+
@@ -1619,51 +2044,98 @@ fclose(sortie);
 
 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignQ.cxx}
-TSq(nomf,L,Fo,D,nmr):={
+TSq(nomf,L,Fo,D,trigo,nmr):={
 L:=apply(f-&gt;unapply(f,x),L);
-Fo:=apply(f-&gt;unapply(f,x),Fo);
+<span class="flyspell-duplicate">Fo</span>:=apply(f-&gt;unapply(f,x),Fo);
 L:=concat(L,Fo);
 n:=size(L);
 Z:=NULL;
 m:=size(Fo);
-F:=NULL;FF:=NULL;
+F:=NULL;FF:=<span class="flyspell-duplicate">NULL</span>;
 mini:=D[0]; maxi:=D[1];
-
+S:=[];
+<span class="flyspell-duplicate">SF</span>:=[];
 
 pour k de 0 jusque n-1 faire 
-  S:=resoudre(L[k](x),x);
+
+
+
+if(trigo==t){
+<span class="flyspell-duplicate">all</span>_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+<span class="flyspell-duplicate">SS</span>:=solve(factor(simplify(L[k](x))),x);
+ns:=size(SS);
+for(j:=0;j&lt;ns;j++){
+mm:=0;
+while(evalf(simplify(subst(SS[j],n_1=mm)))&lt;=evalf(maxi)){
+S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm+1;
+};mm:=-1;
+while(evalf(subst(SS[j],n_1=mm))&gt;=evalf(mini)){
+S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm-1;
+}
+}
+
+}else{
+S:=solve(L[k](x),x);
+}
+
+
+
+
+
   si size(S)&gt;0 alors   pour j de 0 jusque size(S)-1 faire 
-                          if(S[j]&gt;mini and S[j]&lt;maxi){Z:=Z,simplifier(S[j]);}
+                          if(S[j]&gt;mini and S[j]&lt;maxi){Z:=Z,simplify(S[j]);}
                       fpour;
   fsi;
-fpour;
+<span class="flyspell-duplicate">fpour</span>;
 
 
 pour k de 0 jusque m-1 faire 
-  SF:=resoudre(Fo[k](x),x);
+
+
+
+if(trigo==1){
+<span class="flyspell-duplicate">all</span>_trig_solutions:=1;
+<span class="flyspell-duplicate">reset</span>_solve_counter(-1,-1);
+SSF:=solve(factor(simplify(Fo[k](x))),x);
+nsf:=size(SSF);
+for(j:=0;j&lt;nsf;j++){
+mm:=0;
+<span class="flyspell-duplicate">while</span>(evalf(simplify(subst(SSF[j],n_1=mm)))&lt;=evalf(maxi)){
+<span class="flyspell-duplicate">SF</span>:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm+1;
+};mm:=-1;
+while(evalf(subst(SSF[j],n_1=mm))&gt;=evalf(mini)){
+<span class="flyspell-duplicate">SF</span>:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm-1;
+}
+}
+
+}else{
+SF:=solve(Fo[j](x),x);
+}
+
   si size(SF)&gt;0 alors pour j de 0 jusque size(SF)-1 faire 
-                          FF:=FF,simplifier(SF[j]);
-                          if(SF[j]&gt;mini and SF[j]&lt;maxi){F:=F,simplifier(SF[j]);}
-                      fpour;
+                          FF:=FF,simplify(SF[j]);
+                          if(SF[j]&gt;mini and SF[j]&lt;maxi){F:=F,simplify(SF[j]);}
+                      <span class="flyspell-duplicate">fpour</span>;
   fsi;
-fpour;
+<span class="flyspell-duplicate">fpour</span>;
 
 
 
 Z:=sort(Z); // on classe les zeros dans l'ordre croissant 
-nz:=size(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
 if(nz&gt;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; // pour les zeros en double
      fsi;
-fpour;}
+<span class="flyspell-duplicate">fpour</span>;}
 
 
 Z:=sort(Z);
 nz:=size(Z);
 if(nz&gt;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;
+     si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=<span class="flyspell-duplicate">nz</span>-1;
      fsi;
-fpour;};
+<span class="flyspell-duplicate">fpour</span>;};
 nz:=size(Z);
 
 if(nz==0){li:="";l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);";
@@ -1681,9 +2153,9 @@ if(L[p]((mini+maxi)*0.5&gt;0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p
 
 
 
-MetaLfc:=" 
+</span><span class="font-latex-math"><span class="flyspell-duplicate">MetaLfc</span></span><span class="font-latex-math">:=" 
 beginTableau("+nmr+")
-newLigneVariables(btex $</span> {x}<span class="font-latex-math">$ etex);
+newLigneVariables(btex $</span> {x}<span class="font-latex-math">$ </span><span class="font-latex-math"><span class="flyspell-duplicate">etex</span></span><span class="font-latex-math">);
    "+l0+li+
    lsic+nomf+"(x)}$</span> etex);"+
               if(member(mini,FF)==0){if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){"
@@ -1700,13 +2172,13 @@ endTableau;
 
 
 
-}else{
+}<span class="flyspell-duplicate">else</span>{
 
 
 l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);";li:=" ";lr:=" "; 
-pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> <span class="flyspell-duplicate">etex</span>);
 ";fpour; 
-l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);";
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> <span class="flyspell-duplicate">etex</span>);";
 
 
 for(p:=0;p&lt;=n-1;p++){lp:="";                                     
@@ -1717,15 +2189,15 @@ for(p:=0;p&lt;=n-1;p++){lp:="";
            if(L[p](Z[0]-0.01)&gt;0){"plus;"}else{"moins;"};
                                
                            for(r:=0; r&lt;=nz-2;r++){  
-                             lp:=lp+if(simplifier(L[p](Z[r]))==0){"
+                             lp:=lp+if(simplify(L[p](Z[r]))==0){"
                                 valBarre(btex 0 etex);"}else{"barre;
                               "}+ 
                              if(L[p]((Z[r]+Z[r+1])*.5)&gt;0){"plus;"}else{"moins;"}};
  
-                li:=li+lp+ if(simplifier(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
+                li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
                           if(L[p](Z[nz-1]+1.0)&gt;0){"plus;"}else{"moins;
     "}+if(maxi!=+infinity and L[p](maxi)==0){"
-                                valBarre(btex 0 etex);"}else{" "}
+                                valBarre(btex 0 etex);"}</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{" "}
                               
     };  
 
@@ -1733,14 +2205,14 @@ for(p:=0;p&lt;=n-1;p++){lp:="";
 pour t de 0 jusque nz-2 faire 
                            lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+
                                       if(member(Z[t+1],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"}                   
-                         fpour
+                         </span><span class="font-latex-math"><span class="flyspell-duplicate">fpour</span></span><span class="font-latex-math">
 
 
 
 
-MetaLfc:="
+</span><span class="font-latex-math"><span class="flyspell-duplicate">MetaLfc</span></span><span class="font-latex-math">:="
 beginTableau("+nmr+")
-newLigneVariables(btex $</span> {x}<span class="font-latex-math">$ etex);
+newLigneVariables(btex $</span> {x}<span class="font-latex-math">$ </span><span class="font-latex-math"><span class="flyspell-duplicate">etex</span></span><span class="font-latex-math">);
    "+l0+
                      li
                      +
@@ -1765,7 +2237,7 @@ endTableau;
 
 
 sortie:=fopen("XCasmpfc.mp");
-fprint(sortie,Unquoted,MetaLfc);
+<span class="flyspell-duplicate">fprint</span>(sortie,Unquoted,MetaLfc);
 fclose(sortie);
 
 
@@ -1788,16 +2260,16 @@ fclose(sortie);
 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSigna.cxx}
 TSa(a,b,c,d,nmr):={
-zA:=resoudre(a*x+b=0,x)[0];
-zB:=resoudre(c*x+d=0,x)[0];
+zA:=solve(a*x+b=0,x)[0];
+<span class="flyspell-duplicate">zB</span>:=solve(c*x+d=0,x)[0];
 zmin:=min(zA,zB);
-zmax:=max(zA,zB);
+<span class="flyspell-duplicate">zmax</span>:=max(zA,<span class="flyspell-duplicate">zB</span>);
   Meta:= " 
           beginTableau("+nmr+")
-   newLigneVariables(btex <span class="font-latex-math">$ {x}$</span> etex);
+   newLigneVariables(btex <span class="font-latex-math">$ {x}$</span> <span class="flyspell-duplicate">etex</span>);
    val(btex <span class="font-latex-math">$-\\infty$</span> etex);val(btex <span class="font-latex-math">$"+latex(zmin)+"$</span> etex);
 val(btex <span class="font-latex-math">$"+latex(zmax)+"$</span>etex);
-val(btex <span class="font-latex-math">$+\\infty$</span> etex); 
+val(btex <span class="font-latex-math">$+\\infty$</span> <span class="flyspell-duplicate">etex</span>); 
   "+lsic+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+"}<span class="font-latex-math">$ etex);"
         +   if(a&gt;0){"moins;"}else{"plus;"}+
                                  if(zmin==zA){"valBarre(btex 0 etex);"}else{"barre;"}+
@@ -1808,8 +2280,8 @@ val(btex <span class="font-latex-math">$+\\infty$</span> etex);
      +lsic+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+"}$</span> etex);"
         +     if(c&gt;0){"moins"}else{"plus"}+";"+
                                  if(zmin==zB){"valBarre(btex 0 etex);"}else{"barre;"}+
-                                 if(zmin==zB){si c&gt;0 alors "plus;"; sinon "moins;";fsi}
-                                             else{si c&gt;0 alors "moins;"; sinon "plus;"; fsi}+
+                                 if(zmin==zB){si c&gt;0 alors "plus;"; sinon "moins;";<span class="flyspell-duplicate">fsi</span>}
+                                             else{si c&gt;0 alors "moins;"; sinon "plus;"; <span class="flyspell-duplicate">fsi</span>}+
                                  if(zmin==zB){"barre;"}else{"valBarre(btex 0 etex);"}+
                                  if(c&gt;0){"plus;"}else{"moins;"}  
      
@@ -1826,7 +2298,7 @@ endTableau;
 
 
 sortie:=fopen("XCasmpfc.mp");
-fprint(sortie,Unquoted,Meta);
+</span><span class="font-latex-math"><span class="flyspell-duplicate">fprint</span></span><span class="font-latex-math">(sortie,Unquoted,Meta);
 fclose(sortie);
 
 
@@ -1838,71 +2310,101 @@ fclose(sortie);
 
 
 
-%%
-%% Code giac/Xcas pour les Tableaux de Signes d'expression ne contenant 
-%% qu'un seul terme
-
+%%$</span>
+<span class="comment-delimiter">%% </span><span class="comment">Code giac/Xcas pour les Tableaux de Signes d'expression ne contenant 
+</span><span class="comment-delimiter">%% </span><span class="comment">qu'un seul terme
+</span>
 
 
 
-</span><span class="font-latex-sedate"><span class="keyword"><span class="font-latex-math">\begin</span></span></span><span class="function-name"><span class="font-latex-math">{VerbatimOut}</span></span><span class="font-latex-math">{XcasTSc.cxx}
-TSc(g,D,nmr):={
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{<span class="flyspell-duplicate">XcasTSc</span>.<span class="flyspell-duplicate">cxx</span>}
+<span class="flyspell-duplicate">TSc</span>(g,D,F,trigo,nmr):={
 f:=unapply(g,x);
-Z:=NULL;
 mini:=D[0]; maxi:=D[1];lm:=" ";
-S:=resoudre(f(x),x);
+Z:=mini,maxi;
+S:=[];
+
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+<span class="flyspell-duplicate">reset</span>_solve_counter(-1,-1);
+<span class="flyspell-duplicate">SS</span>:=solve(factor(simplify(f(x))),x);
+<span class="flyspell-duplicate">ns</span>:=size(SS);
+for(j:=0;j&lt;ns;j++){
+m:=0;
+while(evalf(simplify(subst(SS[j],n_1=m)))&lt;=evalf(maxi)){
+S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1;
+};m:=-1;
+<span class="flyspell-duplicate">while</span>(evalf(subst(SS[j],n_1=m))&gt;=evalf(mini)){
+S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1;
+}
+}
+
+}else{
+S:=<span class="flyspell-duplicate">solve</span>(f(x),x);
+}
+
+
+
+
+
 if(size(S)==0){
-l0:="val(btex $</span>"+latex(D[0])+"<span class="font-latex-math">$ etex);val(btex $</span>"+latex(D[1])+"<span class="font-latex-math">$ etex);";
-li:=if(mini!=-infinity and f(mini)==0){"
-                                valBarre(btex 0 etex);"}else{"
-                              "}+ 
+l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);";
+li:=if(member(mini,F)!=0){"nonDefBarre;"}else{if(mini!=-infinity and f(mini)==0){"
+                                valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
+                              "}}+ 
 if(mini!=-infinity or maxi!=+infinity){if(f((mini+maxi)*0.5&gt;0)){"plus;"}else{"moins;"}}else{if(f(0)&gt;0){"plus;"}else{"moins;"}};
-lf:=if(maxi!=+infinity and f(maxi)==0){"
-                                valBarre(btex 0 etex);"}else{"
-                              "};
+<span class="flyspell-duplicate">lf</span>:=if(member(maxi,F)!=0){"nonDefBarre;"}else{if(maxi!=+infinity and f(maxi)==0){"
+                                valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
+                              "}};
 }
-else{pour j de 0 jusque size(S)-1 faire 
-                           if(S[j]&gt;mini and S[j]&lt;maxi){Z:=Z,simplifier(S[j])};
+<span class="flyspell-duplicate">else</span>{pour j de 0 jusque size(S)-1 faire 
+                           if(S[j]&gt;mini and S[j]&lt;maxi){Z:=Z,<span class="flyspell-duplicate">simplify</span>(S[j])};
                       fpour;
 
-
+Z:=concat([Z],F);
 Z:=sort(Z);
-nz:=size(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
 if(nz&gt;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;
+     si Z[u]==Z[u+1] alors Z:=concat(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1;
      fsi;
-fpour;}
+<span class="flyspell-duplicate">fpour</span>;}
 
+if(Z[0]==Z[1]){Z:=Z[1..nz-1];nz:=nz-1;}
+if(Z[nz-2]==Z[nz-1]){Z:=Z[0..nz-2];nz:=<span class="flyspell-duplicate">nz</span>-1;}
 
 nz:=size(Z);
 l0:=" ";li:=" ";lr:=" "; 
-if(nz==0){l0:="val(btex $</span>"+latex(D[0])+"<span class="font-latex-math">$ etex);val(btex $</span>"+latex(D[1])+"<span class="font-latex-math">$ etex);";
+if(nz==2){l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);";
 li:=if(mini!=-infinity and f(mini)==0){"
-                                valBarre(btex 0 etex);"}else{"
-                              "}+ 
-if(f((mini+maxi)*0.5&gt;0)){"plus;"}else{"moins;"};
-lf:=if(maxi!=+infinity and f(maxi)==0){"
-                                valBarre(btex 0 etex);"}else{"
-                              "};
-
-}else{
-l0:="val(btex $</span>"+latex(D[0])+"<span class="font-latex-math">$ etex);";li:=" ";
-pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $</span>"+latex(Z[m])+"<span class="font-latex-math">$ etex);
+                                valBarre(btex 0 etex);"}else{if(member(mini,F)==0){"
+                              "}else{"nonDefBarre;"}}+ 
+if(f((mini+maxi)*0.5)&gt;0){"plus;"}else{"moins;"};
+lf:=if(maxi!=+infinity and f(<span class="flyspell-duplicate">maxi</span>)==0){"
+                                valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){"
+                              "}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}
+                              };
+
+}<span class="flyspell-duplicate">else</span>{
+l0:="val(btex <span class="font-latex-math">$"+latex(Z[0])+"$</span> etex);";li:=" ";
+pour m de 1 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> <span class="flyspell-duplicate">etex</span>);
 ";
-fpour; 
-l0:=l0+"val(btex $</span>"+latex(D[1])+"<span class="font-latex-math">$ etex);";
+<span class="flyspell-duplicate">fpour</span>; 
+
                                      
 li:= if(mini!=-infinity and f(mini)==0){"
-                                valBarre(btex 0 etex);"}else{"
-                              "}+ 
-if(f(Z[0]-0.01)&gt;0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);";                               
+                                valBarre(btex 0 etex);"}else{if(member(mini,F)==0){"
+                              "}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}
+                              }                         
 
-lm:=if(nz&gt;=2){for(r:=0; r&lt;=nz-2;r++){lm:=lm+if(f((Z[r]+Z[r+1])*.5)&gt;0){"plus;"}else{"moins;"}+
-                                      "valBarre(btex 0 etex);" 
-                           }}else{" "}; 
+lm:=if(nz&gt;2){for(r:=0; r&lt;nz-2;r++){lm:=lm+if(f((Z[r]+Z[r+1])*.5)&gt;0){"plus;"}else{"moins;"}+
+            if(member(Z[r+1],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"} 
+                           }}<span class="flyspell-duplicate">else</span>{" "}; 
 
-lf:=if(f(Z[nz-1]+1.0)&gt;0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}else{"
-                              "};
+<span class="flyspell-duplicate">lf</span>:=if(f(Z[<span class="flyspell-duplicate">nz</span>-2]+0.1)&gt;0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){"
+                              "}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}
+                              };
 }};  
 
 
@@ -1911,8 +2413,8 @@ lf:=if(f(Z[nz-1]+1.0)&gt;0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi
 MetaLfc:="
 
 beginTableau("+nmr+")
-newLigneVariables(btex $</span><span class="font-latex-warning">\\</span>displaystyle  {x}<span class="font-latex-math">$ etex);
-   "+l0+lsic+latex(f(x))+"}$</span> etex);"+
+<span class="flyspell-duplicate">newLigneVariables</span>(btex <span class="font-latex-math">$\\displaystyle  {x}$</span> <span class="flyspell-duplicate">etex</span>);
+   "+l0+lsic+latex(f(x))+"}<span class="font-latex-math">$ etex);"+
                      li+lm+lf
                      +"
 endTableau;
@@ -1923,14 +2425,12 @@ endTableau;
 
 
 
-sortie:=fopen("XCasmpfc.mp");
-fprint(sortie,Unquoted,MetaLfc);
+sortie:=fopen("XCasmpfc.</span><span class="font-latex-math"><span class="flyspell-duplicate">mp</span></span><span class="font-latex-math">");
+</span><span class="font-latex-math"><span class="flyspell-duplicate">fprint</span></span><span class="font-latex-math">(sortie,Unquoted,MetaLfc);
 fclose(sortie);
 
-
-
  }:;
-<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+</span><span class="font-latex-sedate"><span class="keyword"><span class="font-latex-math">\end</span></span></span><span class="function-name"><span class="font-latex-math">{VerbatimOut}</span></span><span class="font-latex-math">
 
 
 
@@ -1938,14 +2438,16 @@ fclose(sortie);
 
 
 
+%%$</span>
 <span class="comment-delimiter">%%</span><span class="comment">
-</span><span class="comment-delimiter">%%</span><span class="comment">
 </span><span class="comment-delimiter">%% </span><span class="comment">traitement des fichiers produits par giac/xcas
 </span><span class="comment-delimiter">%%</span><span class="comment">
 </span><span class="comment-delimiter">%%</span><span class="comment">
 </span>
-
-
+<span class="comment-delimiter">% </span><span class="comment">pour l'&#233;chelle des tableaux taper </span><span class="font-latex-sedate"><span class="comment">\ech</span></span><span class="comment">{facteur de r&#233;duction}
+</span>
+<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="font-latex-sedate">\echelle</span>{1}
+<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="font-latex-sedate">\ech</span>[1]{<span class="font-latex-sedate"><span class="keyword">\renewcommand</span></span><span class="font-latex-sedate">\echelle</span>{#1}}
 
 
 <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\dresse</span></span><span class="function-name">}</span>[1]{<span class="comment">%
@@ -1954,63 +2456,64 @@ fclose(sortie);
 </span>                                   <span class="comment">% exporter le source mp
 </span>                                   <span class="comment">% puis lancer metapost pour creer
 </span>                                   <span class="comment">% l'image du tableau
-</span>         <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab.mp}
-         <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> enteteMP.cfg &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab#1.mp}
-         <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab#1.mp}
-         <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> queue.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab#1.mp}
-         <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost   -jobname=<span class="font-latex-sedate">\Tableaux</span>.Tab <span class="font-latex-sedate">\Tableaux</span>.Tab#1.mp}
-          <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> <span class="font-latex-sedate">\Tableaux</span>.Tab#1.mp}  
+</span>         <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp &gt;&gt; <span class="font-latex-sedate">\nomtravail</span>.Tab.mp}
+         <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> enteteMP.cfg &gt;&gt; <span class="font-latex-sedate">\nomtravail</span>.Tab#1.mp}
+         <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp &gt;&gt; <span class="font-latex-sedate">\nomtravail</span>.Tab#1.mp}
+         <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> queue.mp &gt;&gt; <span class="font-latex-sedate">\nomtravail</span>.Tab#1.mp}
+         <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost   -jobname=<span class="font-latex-sedate">\nomtravail</span>.Tab <span class="font-latex-sedate">\nomtravail</span>.Tab#1.mp}
+         <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> <span class="font-latex-sedate">\nomtravail</span>.Tab#1.mp}  
            }<span class="comment">%
 </span>         {<span class="comment">% sinon, si le tableau est absent, alerte.
-</span>         <span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\Tableaux</span>.Tab.<span class="font-latex-sedate">\theTVn</span>}{}{<span class="comment">% 
+</span>         <span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\nomtravail</span>.Tab.<span class="font-latex-sedate">\theTVn</span>}{}{<span class="comment">% 
 </span>         <span class="font-latex-sedate">\PackageError</span>{tablor}{Tableau absent non
          reconstituable.}{Pour compiler il faut, soit les fichiers de
-         tableaux, soit le fichier <span class="font-latex-sedate">\Tableaux</span>.Tab.mp, soit disposer de
+         tableaux, soit le fichier <span class="font-latex-sedate">\nomtravail</span>.Tab.mp, soit disposer de
          XCas.}}}
                 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span>
-  <span class="font-latex-sedate"><span class="keyword">\includegraphics</span></span><span class="constant">{</span><span class="font-latex-sedate"><span class="constant">\Tableaux</span></span><span class="constant">.Tab.</span><span class="font-latex-sedate"><span class="constant">\theTVn</span></span><span class="constant">}</span>
+  <span class="font-latex-sedate">\includegraphics</span>[scale=<span class="font-latex-sedate">\echelle</span>]{<span class="font-latex-sedate">\nomtravail</span>.Tab.<span class="font-latex-sedate">\theTVn</span>}
 <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span>
-<span class="font-latex-sedate">\stepcounter</span>{TVn}}
+<span class="font-latex-sedate">\stepcounter</span>{<span class="flyspell-duplicate">TVn</span>}
+}
 
 
 <span class="comment-delimiter">%%</span><span class="comment">
 </span><span class="comment-delimiter">%% </span><span class="comment">traitement des fichiers produits par giac/xcas avec possibilite
-</span><span class="comment-delimiter">%% </span><span class="comment">de modifier le fichier metapost (environnement etoile))
+</span><span class="comment-delimiter">%% </span><span class="comment">de modifier le fichier metapost (environnement </span><span class="comment"><span class="flyspell-incorrect">etoile</span></span><span class="comment">))
 </span><span class="comment-delimiter">%%</span><span class="comment">
 </span>
 
 
 <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\dressetoile</span></span><span class="function-name">}</span>[1]{<span class="comment">%
-</span><span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\Tableaux</span>.Tab.<span class="font-latex-sedate">\theTVn</span>}{<span class="comment">% Test sur l'existence du tableau
+</span><span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\nomtravail</span>.Tab.<span class="font-latex-sedate">\theTVn</span>}{<span class="comment">% Test sur l'existence du tableau
 </span><span class="comment-delimiter">% </span><span class="comment">Si oui, inclusion du fichier source de sauvegarde mp dans Tableaux
-</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> TSav-<span class="font-latex-sedate">\theTVn</span>.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab.mp}}
+</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> TSav-<span class="font-latex-sedate">\theTVn</span>.mp &gt;&gt; <span class="font-latex-sedate">\nomtravail</span>.Tab.mp}}
 <span class="comment-delimiter">% </span><span class="comment">Si  non,  lancement des operations de fabrication 
 </span>{<span class="font-latex-sedate">\executGiacmp</span>{XCas#1.giac}<span class="comment">%
 </span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\editeur</span>  XCasmpfc.mp }
 
   <span class="comment">% Modification avec l'editeur choisi
-</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span>  XCasmpfc.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab.mp} 
+</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span>  XCasmpfc.mp &gt;&gt; <span class="font-latex-sedate">\nomtravail</span>.Tab.mp} 
 <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cp</span>  XCasmpfc.mp  TSav-<span class="font-latex-sedate">\theTVn</span>.mp}   <span class="comment">% Sauvegarde du 
 </span>                                 <span class="comment">% source mp sur le disque pour une
 </span>                                 <span class="comment">% inclusion ulterieure dans Tableaux.mp. 
-</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> enteteMP.cfg &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab#1.mp}
-<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab#1.mp}} <span class="comment">% Inclusion du
+</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> enteteMP.cfg &gt;&gt; <span class="font-latex-sedate">\nomtravail</span>.Tab#1.mp}
+<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp &gt;&gt; <span class="font-latex-sedate">\nomtravail</span>.Tab#1.mp}} <span class="comment">% Inclusion du
 </span>                                                     <span class="comment">% source dans le
 </span>                                                     <span class="comment">% fichier
 </span>                                                     <span class="comment">% Tableaux 
-</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> queue.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab#1.mp}
-<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost  -jobname=<span class="font-latex-sedate">\Tableaux</span>.Tab <span class="font-latex-sedate">\Tableaux</span>.Tab#1.mp}<span class="comment">% Reconstitution des tableaux
+</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> queue.mp &gt;&gt; <span class="font-latex-sedate">\nomtravail</span>.Tab#1.mp}
+<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost  -jobname=<span class="font-latex-sedate">\nomtravail</span>.Tab <span class="font-latex-sedate">\nomtravail</span>.Tab#1.mp}<span class="comment">% Reconstitution des tableaux
 </span>                                <span class="comment">% et creation du dernier. L'option
 </span>                                <span class="comment">% pallie l'absence de end en fin de
 </span>                                <span class="comment">% fichier 
-</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> <span class="font-latex-sedate">\Tableaux</span>.Tab#1.mp}  
+</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> <span class="font-latex-sedate">\nomtravail</span>.Tab#1.mp}  
 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span>
-  <span class="font-latex-sedate"><span class="keyword">\includegraphics</span></span><span class="constant">{</span><span class="font-latex-sedate"><span class="constant">\Tableaux</span></span><span class="constant">.Tab.</span><span class="font-latex-sedate"><span class="constant">\theTVn</span></span><span class="constant">}</span>
+  <span class="font-latex-sedate">\includegraphics</span>[scale=<span class="font-latex-sedate">\echelle</span>]{<span class="font-latex-sedate">\nomtravail</span>.Tab.<span class="font-latex-sedate">\theTVn</span>}
 <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span>
-
-<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVnbis</span></span><span class="variable-name">}</span>    <span class="comment">% Restauration du compteur TVn
+<span class="font-latex-sedate">\ech</span>{1}
+<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVnbis</span></span><span class="variable-name">}</span>    <span class="comment">% Restauration du compteur </span><span class="comment"><span class="flyspell-duplicate">TVn</span></span><span class="comment">
 </span>}
 
 
@@ -2032,7 +2535,7 @@ fclose(sortie);
 
 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasa.giac}
-maple_mode(0);
+<span class="flyspell-duplicate">maple</span>_mode(0);
 read("config.cxx");
 read("XcasTabSigna.cxx");
 read("XCasa.user");
@@ -2056,7 +2559,7 @@ read("XCasa.user");
 maple_mode(0);
 read("config.cxx");
 read("XcasTabSignQ.cxx");
-read("XCasQ.user");
+<span class="flyspell-duplicate">read</span>("XCasQ.user");
 <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
 
 <span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSq}</span><span class="comment">%
@@ -2067,19 +2570,19 @@ read("XCasQ.user");
 
 <span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSq*}</span>[1]<span class="comment">%
 </span>{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
-<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
+<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{</span><span class="variable-name"><span class="flyspell-duplicate">TVn</span></span><span class="variable-name">}{#1}</span>
 <span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasQ.user}}
 {<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{Q}}
 
 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasL.giac}
 maple_mode(0);
-read("config.cxx");
+<span class="flyspell-duplicate">read</span>("config.cxx");
 read("XcasTabSignL.cxx");
 read("XCasL.user");
 <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
 
-<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TS}</span><span class="comment">%
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TS</span></span><span class="function-name">}</span><span class="comment">%
 </span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasL.user}}
 {<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{L}}
 
@@ -2092,7 +2595,7 @@ read("XCasL.user");
 
 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTSc.giac}
-maple_mode(0);
+<span class="flyspell-duplicate">maple</span>_mode(0);
 read("config.cxx");
 read("XcasTSc.cxx");
 read("XCasTSc.user");
@@ -2101,11 +2604,11 @@ read("XCasTSc.user");
 
 
 
-<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSc*}</span>[1]<span class="comment">%
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TSc</span></span><span class="function-name">*}</span>[1]<span class="comment">%
 </span>{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
-<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
+<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{</span><span class="variable-name"><span class="flyspell-duplicate">TVn</span></span><span class="variable-name">}{#1}</span>
 <span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTSc.user}}
-{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{TSc}}
+{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="flyspell-duplicate">TSc</span>}}
 
 
 <span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSc}</span><span class="comment">%
@@ -2116,7 +2619,7 @@ read("XCasTSc.user");
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTV.giac}
 maple_mode(0);
 read("config.cxx");
-read("XcasTV.cxx");
+<span class="flyspell-duplicate">read</span>("XcasTV.cxx");
 read("XCasTV.user");
 <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
 
@@ -2127,9 +2630,9 @@ read("XCasTV.user");
 
 <span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TV*}</span>[1]{<span class="comment">%
 </span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
-<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
+<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{</span><span class="variable-name"><span class="flyspell-duplicate">TVn</span></span><span class="variable-name">}{#1}</span>
 <span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTV.user}}<span class="comment">%
-</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{TV}}
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="flyspell-duplicate">TV</span>}}
 
 
 
@@ -2140,20 +2643,20 @@ read("XCasTV.user");
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVP.giac}
 maple_mode(0);
 read("config.cxx");
-read("XcasTVP.cxx");
+<span class="flyspell-duplicate">read</span>("XcasTVP.cxx");
 read("XCasTVP.user");
 <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
 
-<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVP}</span><span class="comment">%
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVP</span></span><span class="function-name">}</span><span class="comment">%
 </span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVP.user}}<span class="comment">%
 </span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
-<span class="font-latex-sedate">\dresse</span>{TVP}}
+<span class="font-latex-sedate">\dresse</span>{<span class="flyspell-duplicate">TVP</span>}}
 
 <span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVP*}</span>[1]{<span class="comment">%
 </span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
-<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
+<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{</span><span class="variable-name"><span class="flyspell-duplicate">TVn</span></span><span class="variable-name">}{#1}</span>
 <span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVP.user}}<span class="comment">%
-</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{TVP}}
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="flyspell-duplicate">TVP</span>}}
 
 
 
@@ -2166,21 +2669,21 @@ read("XCasTVP.user");
 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVZ.giac}
 maple_mode(0);
-read("config.cxx");
+<span class="flyspell-duplicate">read</span>("config.cxx");
 read("XcasTVZ.cxx");
 read("XCasTVZ.user");
 <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
 
-<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVZ}</span><span class="comment">%
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVZ</span></span><span class="function-name">}</span><span class="comment">%
 </span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVZ.user}}<span class="comment">%
 </span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
-<span class="font-latex-sedate">\dresse</span>{TVZ}}
+<span class="font-latex-sedate">\dresse</span>{<span class="flyspell-duplicate">TVZ</span>}}
 
 <span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVZ*}</span>[1]{<span class="comment">%
 </span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
 <span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
 <span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVZ.user}}<span class="comment">%
-</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{TVZ}}
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="flyspell-duplicate">TVZ</span>}}
 
 
 
@@ -2194,20 +2697,20 @@ read("XCasTVZ.user");
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVapp.giac}
 maple_mode(0);
 read("config.cxx");
-read("XcasTVapp.cxx");
+<span class="flyspell-duplicate">read</span>("XcasTVapp.cxx");
 read("XCasTVapp.user");
 <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
 
 <span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVapp}</span><span class="comment">%
 </span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVapp.user}}<span class="comment">%
 </span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
-<span class="font-latex-sedate">\dresse</span>{TVapp}}
+<span class="font-latex-sedate">\dresse</span>{<span class="flyspell-duplicate">TVapp</span>}}
 
 <span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVapp*}</span>[1]{<span class="comment">%
 </span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
-<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
+<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{</span><span class="variable-name"><span class="flyspell-duplicate">TVn</span></span><span class="variable-name">}{#1}</span>
 <span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVapp.user}}<span class="comment">%
-</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{TVapp}}
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="flyspell-duplicate">TVapp</span>}}
 
 
 
@@ -2220,7 +2723,7 @@ read("XCasTVapp.user");
 
 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVI.giac}
-maple_mode(0);
+<span class="flyspell-duplicate">maple</span>_mode(0);
 read("config.cxx");
 read("XcasTVI.cxx");
 read("XCasTVI.user");
@@ -2228,14 +2731,14 @@ read("XCasTVI.user");
 
 <span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVI}</span><span class="comment">%
 </span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVI.user}}<span class="comment">%
-</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{TVI}}
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{<span class="flyspell-duplicate">TVI</span>}}
 
 
-<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVI*}</span>[1]<span class="comment">%
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVI</span></span><span class="function-name">*}</span>[1]<span class="comment">%
 </span>{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
 <span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
 <span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVI.user}}<span class="comment">%
-</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{TVI}}
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="flyspell-duplicate">TVI</span>}}
 
 
 
@@ -2244,34 +2747,65 @@ read("XCasTVI.user");
 
 <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVIapp.giac}
 maple_mode(0);
-read("config.cxx");
+<span class="flyspell-duplicate">read</span>("config.cxx");
 read("XcasTVIapp.cxx");
 read("XCasTVIapp.user");
 <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
 
-<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVIapp}</span><span class="comment">%
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVIapp</span></span><span class="function-name">}</span><span class="comment">%
 </span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVIapp.user}}<span class="comment">%
-</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{TVIapp}}
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{<span class="flyspell-duplicate">TVIapp</span>}}
 
 
 <span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVIapp*}</span>[1]<span class="comment">%
 </span>{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
 <span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
 <span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVIapp.user}}<span class="comment">%
-</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{TVIapp}}
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="flyspell-duplicate">TVIapp</span>}}
+
+
+
+
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{<span class="flyspell-incorrect">XCasTVPC</span>.<span class="flyspell-duplicate">giac</span>}
+maple_mode(0);
+read("config.<span class="flyspell-duplicate">cxx</span>");
+read("<span class="flyspell-duplicate">XcasTVPC</span>.<span class="flyspell-duplicate">cxx</span>");
+read("<span class="flyspell-duplicate">XCasTVPC</span>.user");
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVPC</span></span><span class="function-name">}</span><span class="comment">%
+</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[<span class="flyspell-duplicate">commandchars</span>=<span class="font-latex-warning">\\</span>??]{<span class="flyspell-duplicate">XCasTVPC</span>.user}}<span class="comment">%
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+<span class="font-latex-sedate">\dresse</span>{<span class="flyspell-duplicate">TVPC</span>}}
+
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVPC</span></span><span class="function-name">*}</span>[1]{<span class="comment">%
+</span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{</span><span class="variable-name"><span class="flyspell-duplicate">TVnbis</span></span><span class="variable-name">}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
+<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
+<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[<span class="flyspell-duplicate">commandchars</span>=<span class="font-latex-warning">\\</span>??]{<span class="flyspell-duplicate">XCasTVPC</span>.user}}<span class="comment">%
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="flyspell-duplicate">TVPC</span>}}
+
+
+
+
+
+
+
+
+
 
 
 
 <span class="comment-delimiter">%% </span><span class="comment">pour nettoyer les fichiers auxiliaires
 </span>
-<span class="font-latex-sedate">\AtEndDocument</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span>  queue.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab.mp}
+<span class="font-latex-sedate">\AtEndDocument</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span>  queue.mp &gt;&gt; <span class="font-latex-sedate">\nomtravail</span>.Tab.<span class="flyspell-duplicate">mp</span>}
                          }
 
 
 
 
 <span class="comment-delimiter">%%</span><span class="comment">
-</span><span class="comment-delimiter">%% </span><span class="comment">Zi end -&gt; enjoy :)
+</span><span class="comment-delimiter">%% </span><span class="comment">Zi end -&gt; </span><span class="comment"><span class="flyspell-incorrect">enjoy</span></span><span class="comment"> :)
 </span></pre>
   </body>
 </html>
diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.pdf b/Master/texmf-dist/doc/latex/tablor/tablor.pdf
index e79dbbf0274..2a75ee1a1e6 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 fd514f0f77e..210154ce647 100644
--- a/Master/texmf-dist/doc/latex/tablor/tablor.tex
+++ b/Master/texmf-dist/doc/latex/tablor/tablor.tex
@@ -76,11 +76,11 @@ keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,com
 
 \title{\texttt{tablor.sty} \\La machine à créer des tableaux de signes et de variations }
 
-\author{Guillaume \textsc{Connan} \\ \href{http://gconnan.free.fr}{http://gconnan.free.fr}\\
+\author{Guillaume \textsc{Connan} \\ \href{http://tehessin.tuxfamily.org/}{http://tehessin.tuxfamily.org/}\\
 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{8 octobre 2008 - Version 4.00}
+\date{21 octobre 2008 - Version 4.02}
 
 
 
@@ -115,13 +115,25 @@ minimum de commandes.
 
 \subsection{Changements depuis la version 3.00}
 
-La version 4.00 n'est  malheureusement plus compatible avec les versions
+La version 4.01 n'est  malheureusement plus compatible avec les versions
 antérieures car une option supplémentaire a été ajoutée pour traiter les
 fonctions trigonométriques.
 
 Une  possibilité  a de  plus  été ajoutée  pour  réduire  la taille  des
 tableaux.
 
+Les tableaux de signes courts (TSc) ont un argument de plus pour traiter
+les valeurs interdites (version 4.01).
+
+
+Une extension pour une compilation via Xe\TeX{} a été
+créé~:~\verb+tablor-xetex.sty+ (version  4.01) ne fonctionnant  que sous
+unix.
+
+
+
+Un   environnement  TVPC  a   été  créé   pour  traiter   les  fonctions
+prolongeables par continuité (version 4.02).
 
 \subsection{Professor.sty}
 
@@ -656,6 +668,63 @@ TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
                \end{figure}
 
 
+
+
+
+
+\section{Utilisation du moteur Xe\LaTeX}
+
+
+On peut à présent compiler  via Xe\LaTeX{} en utilisant l'extension dédiée
+\verb+tablor-xetex.sty+  qui ne fonctionnera  que dans  un environnement
+UNIX  puisqu'elle utilise  un script  \texttt{shell} pour  convertir les
+sorties MetaPOST en \texttt{pdf} :
+
+
+\begin{lstlisting}
+  
+\ifxetex
+
+\begin{filecontents*}{convert-mp-pdf.sh}
+#!/bin/sh
+mpost -interaction nonstopmode $1 ;
+
+cat>$1.tex<<EOF
+\documentclass{article}
+\usepackage[T1]{fontenc}
+\usepackage[frenchb]{babel}
+\usepackage{graphicx}
+\usepackage{pst-eps}
+\thispagestyle{empty}
+\begin{document}
+\begin{TeXtoEPS}
+\includegraphics{$1.0}
+\end{TeXtoEPS}
+\end{document}
+EOF
+latex $1
+dvips -o $1.eps -E $1.dvi
+epstopdf $1.eps;
+## Fin de convert-mp-pdf.sh
+\end{filecontents*}
+
+%$>>
+
+
+\immediate\write18{chmod 775 ./convert-mp-pdf.sh}
+
+\fi
+
+\end{lstlisting}
+
+
+
+Il  n'y a  rien à  faire.  Cette version  peut même  être utilisée  avec
+pdf\LaTeX{} ou pdf\TeX{}~!
+
+
+
+
 \section{Tableaux des variations}
 
 \subsection{Tableau standard}
@@ -900,7 +969,7 @@ amené à rechercher une  approximation numérique de ces zéros. Cela est  possible
 
 Voyons sur un exemple.
 
-\paragraph*{Exemple}
+\subsubsection*{Exemple}
 
 
 Soit $g$ la fonction $x\mapsto \ln(x)-x e^{2-x} $.
@@ -936,6 +1005,32 @@ TVapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,\tv)
 \end{TVapp}
 
 
+\subsection{Tableaux de variations de fonctions prolongeables par continuité}
+
+On  peut avoir prolongée  une fonction  par continuité  et donc  ne plus
+avoir de double barre sur la  ligne des variations mais toujours une sur
+la ligne du signe de la dérivée.
+
+On entre trois listes~:
+\begin{enumerate}
+\item les bornes de l'intervalle d'étude, comme toujours~;
+\item les valeurs où la fonction sera prolongée par continuité~;
+\item les valeurs où la fonction n'est pas dérivable.
+\end{enumerate}
+
+Cela donne pour $x\mapsto {\rm e}^{-1/x^2}$~:
+
+
+\begin{lstlisting}
+\begin{TVPC}
+TVPC([-infinity,+infinity],[0],[0],"g","t",e^(-1/x^2),1,n,\tv); 
+\end{TVPC}
+\end{lstlisting}
+
+
+\begin{TVPC}
+TVPC([-infinity,+infinity],[0],[0],"g","t",e^(-1/x^2),1,n,\tv); 
+\end{TVPC}
 
 
 
@@ -1024,10 +1119,10 @@ TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+
 
 
 
-\subsection{Tableaux de signes}
+\section{Tableaux de signes}
 
 
-\subsubsection*{Cas du produit de deux facteurs affines}
+\subsection{Cas du produit de deux facteurs affines}
 
 Pour étudier le signe de $(-2x+3)(-x+5)$ sur \textbf{R}, on entre~:
 
@@ -1045,7 +1140,7 @@ TSa(-2,3,-1,5,\tv);
 \end{TSa}
 
 
-\subsubsection*{Cas du produit d'un nombre quelconque de facteurs quelconques sur un intervalle quelconque}
+\subsection{Cas du produit d'un nombre quelconque de facteurs quelconques sur un intervalle quelconque}
 
 
 
@@ -1098,7 +1193,7 @@ TS("f",[x-10,x+10],[-15,10],n,\tv)
 
 
 
-\subsubsection*{Signe d'un quotient}
+\subsection{Signe d'un quotient}
 
 On entre dans deux listes différentes les facteurs du numérateur et du dénominateur~:
 
@@ -1140,29 +1235,49 @@ TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],n,\tv)
 
 
 
-\subsubsection*{Signe d'une seule expression}
+\subsection{Signe d'une seule expression}
 
 
 On  utilise  l'environnement   \texttt{TSc}  comme  \emph{Tableau  de  Signe   court}  en  précisant
-l'expression étudiée et l'intervalle considéré~:
+l'expression étudiée, l'intervalle considéré et les valeurs interdites~:
 
 \begin{lstlisting}
 \begin{TSc}
-TSc((x-10)*(x+5),[-10,10],n,\tv)
+TSc((x-10)*(x+5),[-10,10],[],n,\tv)
 \end{TSc}
 \end{lstlisting}
 
 
 
 \begin{TSc}
-TSc((x-10)*(x+5),[-10,10],n,\tv)
+TSc((x-10)*(x+5),[-10,10],[],n,\tv)
 \end{TSc}
 
+avec valeurs interdites~:
 
+\begin{lstlisting}
+\begin{TSc}
+TSc((x+10)/((x-5)*(x-2)),[-10,5],[2,5],n,\tv)
+\end{TSc}
+\end{lstlisting}
 
 
+\begin{TSc}
+TSc((x+10)/((x-5)*(x-2)),[-10,5],[2,5],n,\tv)
+\end{TSc}
 
+valeurs interdites et fonction trigonométrique~:
 
+\begin{lstlisting}
+\begin{TSc}
+TSc(tan(x),[0,2*pi],[pi/2,3*pi/2],t,\tv)
+\end{TSc}
+\end{lstlisting}
+
+
+\begin{TSc}
+TSc(tan(x),[0,2*pi],[pi/2,3*pi/2],t,\tv)
+\end{TSc}
 
 
 \section{Comment modifier les tableaux à partir des fichiers MetaPOST~?}\label{modif}
@@ -1544,14 +1659,14 @@ TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,n,\tv)
 
 \begin{lstlisting}
 \begin{TSc}
-TSc((x-10)*(x+10),[-10,10],n,\tv)
+TSc((x-10)*(x+10),[-10,10],[],n,\tv)
 \end{TSc}
 \end{lstlisting}
 
 
 
 \begin{TSc}
-TSc((x-10)*(x+10),[-10,10],n,\tv)
+TSc((x-10)*(x+10),[-10,10],[],n,\tv)
 \end{TSc}
 
 
diff --git a/Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty b/Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty
new file mode 100644
index 00000000000..21605a4d10b
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty
@@ -0,0 +1,2836 @@
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+\ProvidesPackage{tablor-xetex}[24/10/2008 v4.02  la machine a  creer des
+tableaux de signes et variations compatible xetex]
+
+% \copyleft Connan le Barbare (aka Guillaume Connan) \copyright
+% This work may be distributed and/or mofified under the conditions
+% or the LaTeX Project Public Licence, either v1.3 or (at your option)
+% any later version. The latest version is in
+%   http://www.latex-project.org/lppl/
+% This work consists of the files tablor.sty, tablor-xetex.sty, tablor.cfg, tablor.tex,
+% tablor.pdf and tablor.html
+
+
+%% Cree 16 environnements :
+%% tableau de signes de 2 facteurs affines
+% \begin{TSa}
+% TSa(-2,3,-1,5,\tv);
+% \end{TSa}
+% %%%%%% 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],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],n,\tv)
+%%\end{TSq}
+% un tableau de variation :
+%
+% pour les tableaux de signes �à une seule ligne
+% \begin{TSc}
+% TSc((x+10)/((x-5)*(x-2)),[-10,5],[2,5],n,0)
+% \end{TSc}
+%
+%
+% \begin{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,n,\tv)
+% \end{TVZ}
+%
+%
+% tableau avec valeurs intermediares
+%\begin{TVI}
+%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
+%\begin{TVapp}
+% TVapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,\tv)
+% \end{TVapp}
+%
+%
+% tableau de variations avec f' sans zero formel
+%\begin{TVIapp}
+% TVIapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,0,\tv)
+% \end{TVIapp}
+%
+%
+%%%
+% et leurs pendants etoiles qui permettent l'affichage intermediaire du 
+% fichier metapost pour le modifier
+%
+%
+% 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,n,\tv)
+%  \end{TVP}
+%
+%
+% \begin{TVP}
+%  TVP([0,pi/2],[[],[]],["x","y"],"t",[2*cos(t),sin(2*t)],1,t,\tv)
+%  \end{TVP}
+% %
+% %
+% Fonctions prolongeables par continuit�é
+% TVPC([intervalles d'�étude],[valeurs prolongeables],[valeurs interdites pour f'],"g","t",e^(-1/x^2),1,n,\tv); 
+% \begin{TVPC}
+% TVPC([-infinity,+infinity],[0],[0],"g","t",e^(-1/x^2),1,n,\tv); 
+% \end{TVPC}
+
+
+
+
+%% extensions requises
+%% Il faudra rajouter dans le preambule \usepackage{graphicx} si vous 
+%% ne l'avez pas de base 
+
+
+\RequirePackage{filecontents}
+\RequirePackage{ifthen}
+\RequirePackage{fancyvrb}
+\RequirePackage{ifpdf}
+\RequirePackage{ifxetex}
+\fvset{gobble=0}
+
+% option xcas present 
+
+
+\newboolean{xcas}\setboolean{xcas}{false}
+\DeclareOption{xcas}{\setboolean{xcas}{true}}
+
+
+\ProcessOptions\relax
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% pour xelatex (ne marche que sur unix....)
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\ifxetex
+
+\begin{filecontents*}{convert-mp-pdf.sh}
+#!/bin/sh
+mpost -interaction nonstopmode $1 ;
+
+cat>$1.tex<<EOF
+\documentclass{article}
+\usepackage[T1]{fontenc}
+\usepackage[frenchb]{babel}
+\usepackage{graphicx}
+\usepackage{pst-eps}
+\thispagestyle{empty}
+\begin{document}
+\begin{TeXtoEPS}
+\includegraphics{$1.$2}
+\end{TeXtoEPS}
+\end{document}
+EOF
+latex $1
+dvips -o $1.eps -E $1.dvi
+epstopdf $1.eps;
+## Fin de convert-mp-pdf.sh
+\end{filecontents*}
+
+%$>>
+
+
+\immediate\write18{chmod 775 ./convert-mp-pdf.sh}
+
+\fi
+
+%% Initialisation du choix d'OS
+\newboolean{windows}\setboolean{windows}{false}
+
+
+
+%% on configure  tablor  dans un fichier exterieur pour la plateforme
+%% et l'editeur
+
+\IfFileExists{tablor.cfg}{\input{tablor.cfg}}%\typeout{pas de fichier tablor.cfg}}
+
+
+%% Definit des commandes disque selon l'OS utilise
+\ifthenelse{\boolean{windows}}%
+    {\newcommand{\rem}{DEL } \newcommand{\cat}{TYPE }
+      \newcommand{\cp}{COPY }}%
+    {\newcommand{\rem}{rm }\newcommand{\cat}{cat }
+      \newcommand{\cp}{cp }}
+
+
+
+
+
+
+
+%% pour ceux compilant via pdflatex
+
+\ifpdf
+\DeclareGraphicsRule{*}{mps}{*}{}
+\fi
+
+%% pour nettoyer les fichiers auxiliaires
+
+\AtEndDocument{\immediate\write18{\rem *.user XCas* Xcas* *.mpx}
+                         }
+
+
+
+
+%% Pour clore les fichiers metapost 
+
+
+  \begin{VerbatimOut}{queue.mp}
+  
+  end
+
+  \end{VerbatimOut}
+
+
+
+%% Nettoie les fichiers log dont le nom depend du choix de l'utilisateur
+%% Par defaut, c'est le nom du fichier tex courant (\jobname)
+%% Cl�ôt le fichier metapost contenant le recapitulatif de tous les tableaux
+
+
+
+\newcommand{\nettoyer}[1][\jobname]%
+{\immediate\write18{\rem #1.Tab.log  queue.mp enteteMP.cfg session.tex config.cxx}
+}
+
+
+
+
+%% Donne comme prefixe aux tableaux le prefixe courant
+%% Peut-�être modifie par \initablor
+
+\newcommand{\nomtravail}{\jobname}
+
+%% initialise les compteurs
+
+\newcounter{TVn}
+\newcommand{\tv}{\theTVn}
+
+\newcounter{TVnbis}
+\newcommand{\tvbis}{\theTVnbis}
+
+
+
+%% permet de donner un prefixe aux tableaux produits (\jobname par defaut)
+%% effectue quelques verifications :
+
+
+\newcommand{\initablor}[1][\jobname]{%
+\renewcommand{\nomtravail}{#1}%     Arret du nom des tableaux
+\setcounter{TVn}{0}%     Initialisation du compteur de tableaux.
+\ifthenelse{\boolean{xcas}}%    Avec l'option XCas
+{\IfFileExists{\nomtravail.Tab.mp}%      Si Tableaux.mp est present...
+        {\immediate\write18{\rem \nomtravail.Tab.mp}}%  le detruire
+        {}%   
+ \immediate\write18{\cp  enteteMP.cfg \nomtravail.Tab.mp}% Reconstituer l'ent�ête de Tableaux.mp
+} 
+{\IfFileExists{\nomtravail.Tab.mp}%      Sans l'option XCas, si
+                                %      Tableaux.mp existe
+{\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 �être presents )
+}}%
+
+
+
+%% commande pour lancer giac selon l'OS
+
+\makeatletter
+\newcommand{\executGiacmp}[1]{%
+\ifthenelse{\boolean{windows}}%
+{\immediate\write18{giac #1 }}%
+{\immediate\write18{giac  <#1 }}}
+\makeatother
+
+
+
+
+%%%
+%
+%%% LES SCRIPTS GIAC/XCAS
+%
+%%%
+
+
+
+
+
+
+%%
+%% Code giac/Xcas pour les Tableaux de Variations
+%%
+
+
+\begin{VerbatimOut}{XcasTV.cxx}
+TV(L,F,nom,nomv,f,ftt,trigo,nmr):={
+nl:=size(L);
+f:=unapply(f,x);
+fp:=function_diff(f);
+Z:=concat(L,F);
+S:=[];
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=solve(factor(simplify(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k<ns;k++){
+m:=0;
+while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
+S:=solve(fp(x),x);
+}
+
+
+  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire
+                             qq:=member(simplify(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,simplify(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,simplify(S[j]))};
+                          fpour
+  fsi;
+
+Z:=sort(Z); 
+nz:=size(Z);
+ si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1; 
+     fsi;
+pour u de 1 jusque nz-2 faire 
+     si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1; 
+     fsi;
+fpour;
+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; 
+
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
+                          
+lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
+     if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
+                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+                                                    if(sign(fp(Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
+                                                         if(sign(fp((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}
+ 
+if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.1))>0;                     
+                                               lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                                if(ksp==1){"plus;"}else{"moins;"}
+                                                  }; }
+
+lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;
+"}
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
+     li:=lvic+nom+"}$ etex);"+
+           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+           if(k0==1){"1"}else{"0"}+
+                         ");";
+            
+                     if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
+                                                  lp:=lp+if(member(Z[r],F)){
+                                    "limGauche(btex
+                                    $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$
+                                    etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
+                                            etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+"}}}
+                                                   }; }
+
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+                          
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
+    
+
+
+
+
+MetaLfc:=if(ftt==2){if(nz>2){"
+
+beginTableau("+nmr+")"+
+        l0+lsi+lsp+lsf+"
+endTableau;
+
+";}else{
+intro+"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+"
+endTableau;
+
+";
+}
+}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+li+
+lf
++"
+endTableau;
+
+";}}else{
+if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+lsi+lsp+lsf+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+
+li+
+lf
++"
+endTableau;
+
+";}
+}}
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+
+ }:;
+
+\end{VerbatimOut}
+
+
+
+%
+%
+%  TVPC : pour les fonctions prolongeables par continuit�é.
+%%
+%%
+
+
+
+
+\begin{VerbatimOut}{XcasTVPC.cxx}
+TVPC(L,F,FP,nom,nomv,f,ftt,trigo,nmr):={
+nl:=size(L);
+f:=unapply(f,x);
+fp:=function_diff(f);
+Z:=concat(L,F);
+Z:=concat(Z,FP);
+S:=[];
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=solve(factor(simplify(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k<ns;k++){
+m:=0;
+while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
+S:=solve(fp(x),x);
+}
+
+
+  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire
+                             qq:=member(simplify(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,simplify(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,simplify(S[j]))};
+                          fpour
+  fsi;
+
+Z:=sort(Z); 
+nz:=size(Z);
+ si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1; 
+     fsi;
+pour u de 1 jusque nz-2 faire 
+     si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1; 
+     fsi;
+fpour;
+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; 
+
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
+                          
+lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
+     if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],FP)==0){
+                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+                                                    if(sign(fp(Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
+                                                         if(sign(fp((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}
+ 
+if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.1))>0;                     
+                                               lsp:=lsp+if(member(Z[r],FP)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                                if(ksp==1){"plus;"}else{"moins;"}
+                                                  }; }
+
+lsf:=if(member(Z[nz-1],FP)==0){""}else{"nonDefBarre;
+"}
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
+     li:=lvic+nom+"}$ etex);"+
+           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+           if(k0==1){"1"}else{"0"}+
+                         ");";
+            
+                     if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
+                                                  lp:=lp+if(member(Z[r],F)){ 
+                                    "valPos(btex
+                                    $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$
+                                    etex,"+if(krm==1){"1);"}else{"0);"} }
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
+                                            etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+"}}}
+                                                   }; }
+
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+                          
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);"}else{"0);"}};    
+    
+
+
+
+
+MetaLfc:=if(ftt==2){if(nz>2){"
+
+beginTableau("+nmr+")"+
+        l0+lsi+lsp+lsf+"
+endTableau;
+
+";}else{
+intro+"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+"
+endTableau;
+
+";
+}
+}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+li+
+lf
++"
+endTableau;
+
+";}}else{
+if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+lsi+lsp+lsf+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+
+li+
+lf
++"
+endTableau;
+
+";}
+}}
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+
+ }:;
+
+\end{VerbatimOut}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+%%
+%%
+%% TV avec une zone interdite : on rajoute comme argument la liste des intervalles interdits
+%% par exemple, pour sqrt(x^2-1) : TVZ([-infinity,100],[],[[-1,1]],"f","x",sqrt(x^2-1),1,1)
+%%
+
+\begin{VerbatimOut}{XcasTVZ.cxx}
+
+
+TVZ(L,F,FF,nom,nomv,f,ftt,trigo,nmr):={
+nl:=size(L);
+nf:=size(FF);
+ Ff:=NULL;IMIN:=NULL;IMAX:=NULL;
+for(k:=0;k<nf;k++){
+if(FF[k][0]>L[0]){Imin[k]:=FF[k][0];LL:=L}else{Imin[k]:=L[0];LL:=[L[1]]};
+if(FF[k][1]<L[1]){Imax[k]:=FF[k][1];LL:=L}else{Imax[k]:=L[1];LL:=[L[0]]};
+ Ff:=Ff,[Imin[k],Imax[k]];
+ IMIN:=IMIN,Imin[k];
+ IMAX:=IMAX,Imax[k];
+ }
+ FF:=[Ff];
+ IMIN:=[IMIN];
+ IMAX:=[IMAX];
+ f:=unapply(f,x);
+fp:=function_diff(f);
+Z:=concat(LL,F);
+
+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:=solve(factor(simplify(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k<ns;k++){
+m:=0;
+while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
+S:=solve(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]));
+                             kK:=(evalf(S[j])<evalf(Imin[k])) or (evalf(S[j])>evalf(Imax[k]));
+                             Kk:=(kk) and kK;
+                          if(Kk==1){Z:=append(Z,simplify(S[j]))};
+                          }
+                        fpour
+  fsi;
+
+Z:=sort(Z); 
+nz:=size(Z);
+
+
+
+ si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1; 
+     fsi;
+pour u de 1 jusque nz-2 faire 
+     si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1; 
+     fsi;
+fpour;
+nz:=size(Z);
+
+for(j:=0;j<nf;j++){
+ for(k:=1;k<nz;k++){
+   if ((Z[k]>Imin[j])and(Z[k]<Imax[j])){Z:=augment(Z[0..k-1],Z[k+1..nz-1]);nz:=nz-1;
+   }
+  }
+}
+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; 
+
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
+                          
+lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
+if(member(Z[0],IMIN)!=0){"debutNonDef;"}else{if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
+                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+                                                    if(sign(fp(Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
+                                                         if(sign(fp((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}}
+
+
+
+if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0; 
+                                               lsp:=lsp+if(member(Z[r],IMIN)!=0){"debutNonDef;"}else{
+                                                       if(member(Z[r],IMAX)!=0){"finNonDef;"+
+                                                if(ksp==1){"plus;"}else{"moins;"}}else{
+                                                 if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                                if(ksp==1){"plus;"}else{"moins;"}
+                                                  }}}}; 
+
+
+
+lsf:=if(member(Z[0],IMAX)!=0){"finNonDef;"}else{if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;
+"}}
+
+
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
+     li:=lvic  +nom+"}$ etex);"+
+           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+           if(k0==1){"1"}else{"0"}+
+                         ");";
+            
+if(nz>2){ 
+   for(r:=1; r<=nz-2;r++){ 
+     krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+     krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+     lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
+
+     lp:=lp+if(member(Z[r],IMIN)!=0){"limGauche(btex $"+if(lmrm==1){
+             "-\\infty"}else{
+                latex(simplify(limit(f(x),x=Z[r],-1)))}
+         +"$ etex,"+if(krm==1){
+             "1);"}else{"0);"}
+         +"debutNonDef;"
+       }//fsi Zr=Imin
+      else{
+        if (member(Z[r],IMAX)!=0) {"finNonDef;limDroite(btex $"+if(lmrp==1){
+             "-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}
+         +"$ etex,"+if(krp==1){
+             "1);"}else{"0);"}          
+       }
+        else {
+          if(member(Z[r],F)){
+         "limGauche(btex $"+if(lmrm==1){
+             "-\\infty"}else{
+                latex(simplify(limit(f(x),x=Z[r],-1)))}
+         +"$ etex,"+if(krm==1){
+             "1);"}else{"0);"}
+         +"nonDefBarre;limDroite(btex $"+if(lmrp==1){
+             "-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}
+         +"$ etex,"+if(krp==1){
+             "1);"}else{"0);"}
+         }//fsi (member Zr F)
+          else{"valPos(btex$"+latex(simplify(f(Z[r])))+"$etex,"+
+             if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){
+               "0.5);"}else{
+                    if(krp==1){
+                       "1);"}else{"0);"}//felse(krp)
+                    }//felse(valpos)
+               }//felse(member Zr F)
+               } //felse(Zr=Imax)
+              }//felse(Zr=Imin)
+           };//ffor 
+         }//fsi nz
+
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
+    
+
+
+    
+
+MetaLfc:=if(ftt==2){if(nz>2){"
+
+beginTableau("+nmr+")"+
+        l0+lsi+lsp+lsf+"
+endTableau;
+
+";}else{
+intro+"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+"
+endTableau;
+
+";
+}
+}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+li+
+lf
++"
+endTableau;
+
+";}}else{
+if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+lsi+lsp+lsf+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+
+li+
+lf
++"
+endTableau;
+
+";}
+}}
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+ }
+:;
+
+
+\end{VerbatimOut}
+
+
+%%
+%%
+%% Quand les solutions formelles de f'(x)=0 ne sont pas calculables
+%%
+
+
+
+\begin{VerbatimOut}{XcasTVapp.cxx}
+
+
+
+
+
+
+
+TVapp(L,F,nom,nomv,f,ftt,nmr):={
+
+
+nl:=size(L);
+f:=unapply(f,x);
+fp:=function_diff(f);
+z0:=concat(L,F);z:=sort(z0);
+nz:=size(z);
+
+
+
+
+
+
+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,simplify(S[j]))}};
+                          fpour;
+fsi;
+
+
+S:=NULL;
+S:=S,z[0];
+for(j:=1;j<size(z);j++){
+ if(z[j]!=undef and (abs(z[j])>1e-15 or z[j]==0)){
+   S:=S,z[j]};
+}
+z:=[S];
+
+Z:=sort(z);
+nz:=size(Z);
+
+S:=NULL;
+S:=S,Z[0];
+for(j:=1;j<nz;j++){
+ if(Z[j]!=S[size(S)-1]){
+   S:=S,Z[j]};
+}
+Z:=[S]; 
+
+
+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; 
+
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
+                          
+lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
+     if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
+                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+                                                    if(sign(fp(Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
+                                                         if(sign(fp((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}
+ 
+if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.01))>0;                     
+                                               lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                                if(ksp==1){"plus;"}else{"moins;"}
+                                                  }; }
+
+lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;
+"}
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
+     li:=lvic+nom+"}$ etex);"+
+           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+           if(k0==1){"1"}else{"0"}+
+                         ");";
+            
+                     if(nz>2){ for(r:=1; r<=nz-2;r++){  krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
+                                                  lp:=lp+if(member(Z[r],F)){
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
+                                            etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+"}}}
+                                                   }; }
+
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+ 
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
+    
+
+
+MetaLfc:=if(ftt==2){if(nz>2){"
+
+beginTableau("+nmr+")"+
+        l0+lsi+lsp+lsf+"
+endTableau;
+
+";}else{
+intro+"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+"
+endTableau;
+
+";
+}
+}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+li+
+lf
++"
+endTableau;
+
+";}}else{
+if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+lsi+lsp+lsf+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+
+li+
+lf
++"
+endTableau;
+
+";}
+}}
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+
+ }:;
+
+
+
+
+
+
+
+\end{VerbatimOut}
+
+
+
+
+
+
+
+%%
+%% Code giac/Xcas pour les Tableaux de Variations avec 
+%% Valeurs intermediaires
+%%
+
+
+
+
+
+\begin{VerbatimOut}{XcasTVI.cxx}
+
+
+TVI(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={
+nl:=size(L);
+f:=unapply(f,x);
+fp:=function_diff(f);
+Z:=concat(L,F);
+S:=[];
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=solve(factor(simplify(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k<ns;k++){
+m:=0;
+while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
+S:=solve(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,simplify(S[j]))};
+                          fpour
+  fsi;
+
+Z:=sort(Z); 
+nz:=size(Z);
+ si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1; 
+     fsi;
+pour u de 1 jusque nz-2 faire 
+     si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1; 
+     fsi;
+fpour;
+nz:=size(Z);
+l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";
+
+
+
+LI:=limit(f(x),x,Z[0],1);
+LF:=limit(f(x),x,Z[nz-1],-1);
+LP:=NULL;
+if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}}};
+if(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
+      
+NL:=size(LL);
+A:=NULL;aa:=1;kk:=0;
+
+if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
+if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}}
+l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"};
+
+if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
+TestL:=(abs(LL[k])==abs(LL[k+1]));
+if(TestS==0){ if( TestL==1 ){l0:=l0}else{
+A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;kk:=kk+1}}else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}}
+l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);
+"};
+
+
+
+TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
+                          
+lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
+     if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
+                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+                                                    if(sign(fp((Z[0]+10^(-10))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
+                                                         if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$  $ etex);"+ if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "}; 
+
+
+
+
+ 
+if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
+                                                 ksp:=evalf(fp(Z[r]+0.01))>0;  
+                                                 TestL:=(abs(LL[r])==abs(LL[r+1]));
+                                 lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                  if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $  $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "};
+                                             }}
+else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+                                          TestL:=(abs(LL[r])==abs(LL[r+1]));
+                      if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                  if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $  $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
+                                   } else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                  if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}        
+}}     
+  }; 
+
+
+
+lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;"}
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
+
+TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
+
+     li:=lvic+nom+"}$ etex);
+"+  if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+           if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; 
+                         
+            
+                     if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
+                                                 krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
+                                                  lp:=lp+if(member(Z[r],F)) {
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
+                                            etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
+                                            $ "+ao+" $ etex,0.5);"
+                                                           }else{" "}; 
+};//for
+}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
+                                                 krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
+if(TestS==0){if( TestL==1 ){lp:=lp}else{  lp:=lp+if(member(Z[rr],F)) {
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
+                                            etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
+                                            $ "+ao+" $ etex,0.5);
+                                                                 ";rr:=rr+1;
+}// else testL==1
+}//testS==0
+else{lp:=lp+if(member(Z[rr],F)){
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
+                                            etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+                                                            "}}};rr:=rr+1;
+}//else testS==0
+}//for nz<NL
+}// else nz<NL
+//if nz=NL
+};//if nz>2
+
+
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
+    
+
+
+
+MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+
+        l0+lsi+lsp+lsf+"
+endTableau;
+
+";}else{
+"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+"
+endTableau;
+
+";
+}
+}else{
+if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+li+
+lf
++"
+endTableau;
+";}}else{
+if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+lsi+lsp+lsf+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+
+li+
+lf
++"
+endTableau;
+
+";}
+}};
+
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+
+ }:;
+
+
+
+\end{VerbatimOut}
+
+
+
+
+
+
+
+%%
+%%
+%% Quand les solutions de f'(x)=0 ne sont pas formellement calculables
+%%
+
+
+
+
+\begin{VerbatimOut}{XcasTVIapp.cxx}
+
+
+TVIapp(L,F,nom,nomv,f,ftt,ao,nmr):={
+
+
+nl:=size(L);
+f:=unapply(f,x);
+fp:=function_diff(f);
+z0:=concat(L,F);z:=sort(z0);
+nz:=size(z);
+
+
+
+
+
+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,simplify(S[j]))}};
+                          fpour;
+fsi;
+
+
+S:=NULL;
+S:=S,z[0];
+for(j:=1;j<size(z);j++){
+ if(z[j]!=undef and (abs(z[j])>1e-15 or z[j]==0)){
+   S:=S,z[j]};
+}
+z:=[S];
+
+
+
+Z:=sort(z);
+nz:=size(Z);
+
+S:=NULL;
+S:=S,Z[0];
+for(j:=1;j<nz;j++){
+ if(Z[j]!=S[size(S)-1]){
+   S:=S,Z[j]};
+}
+Z:=[S]; 
+
+
+nz:=size(Z);
+l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";
+
+
+
+LI:=limit(f(x),x,Z[0],1);
+LF:=limit(f(x),x,Z[nz-1],-1);
+LP:=NULL;
+if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}}};
+if(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
+      
+NL:=size(LL);
+A:=NULL;aa:=1;kk:=0;
+
+if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
+if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}}
+l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"};
+
+if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
+TestL:=(abs(LL[k])==abs(LL[k+1]));
+if(TestS==0){ if( TestL==1 ){l0:=l0}else{
+A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;kk:=kk+1}}else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}}
+l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);
+"};
+
+
+
+TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
+                          
+lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
+     if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
+                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+                                                    if(sign(fp((Z[0]+10^(-10))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
+                                                         if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$  $ etex);"+ if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "}; 
+
+
+
+
+ 
+if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
+                                                 ksp:=evalf(fp(Z[r]+0.01))>0;  
+                                                 TestL:=(abs(LL[r])==abs(LL[r+1]));
+                                 lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                  if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $  $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "};
+                                             }}
+else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+                                          TestL:=(abs(LL[r])==abs(LL[r+1]));
+                      if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                  if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $  $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
+                                   } else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                  if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}        
+}}     
+  }; 
+
+
+
+lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;"}
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
+
+TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
+
+     li:=lvic+nom+"}$ etex);
+"+  if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+           if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; 
+                         
+            
+                     if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
+                                                 krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
+                                                  lp:=lp+if(member(Z[r],F)) {
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
+                                            etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
+                                            $ "+ao+" $ etex,0.5);"
+                                                           }else{" "}; 
+};//for
+}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
+                                                 krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
+if(TestS==0){if( TestL==1 ){lp:=lp}else{  lp:=lp+if(member(Z[rr],F)) {
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
+                                            etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
+                                            $ "+ao+" $ etex,0.5);
+                                                                 ";rr:=rr+1;
+}// else testL==1
+}//testS==0
+else{lp:=lp+if(member(Z[rr],F)){
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
+                                            etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+                                                            "}}};rr:=rr+1;
+}//else testS==0
+}//for nz<NL
+}// else nz<NL
+//if nz=NL
+};//if nz>2
+
+
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
+    
+
+
+
+
+
+
+MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+
+        l0+lsi+lsp+lsf+"
+endTableau;
+
+";}else{
+"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+"
+endTableau;
+
+";
+}
+}else{
+if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+li+
+lf
++"
+endTableau;
+";}}else{
+if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+lsi+lsp+lsf+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+
+li+
+lf
++"
+endTableau;
+
+";}
+}};
+
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+
+ }:;
+
+
+
+\end{VerbatimOut}
+
+
+
+
+
+
+
+
+%%
+%% Code giac/Xcas pour les Tableaux de variations de courbes parametrees
+%%
+
+
+
+
+
+
+
+\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);
+fp:=[];
+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,function_diff(f[d]));
+LLL:=concat(L,F[d]);
+Z:=LLL union Z;
+SS:=solve(factor(simplify(fp[d](t))),t);
+ns:=size(SS);
+
+for(k:=0;k<ns;k++){
+if(trigo==t){
+m:=0;
+while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
+
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
+
+}
+}else{
+S:=concat(S,SS);
+}
+}
+
+
+  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire
+                             qq:=member(simplify(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,simplify(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;
+
+
+
+
+nz:=size(Z);
+u:=1;
+ tantque (u<nz-2) and (nz>2) 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);
+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;
+
+ lsi:="","";
+
+FFF:=[[],[]];
+
+for(d:=0;d<=1;d++){
+FFF[d]:=concat(F[d],[-infinity,+infinity]);
+       k0:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1));
+       kz:=evalf(limit(f[d](x),x=Z[nz-1],-1))> evalf(limit(f[d](x),x=Z[nz-2],1));
+//}
+//$
+ lsi[d]:=lsic+nom[d]+"'("+nomv+")}$ etex);"+if(member(Z[0],FFF[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[0])))+"$ 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;
+                                               lsp[d]:=lsp[d]+if(member(Z[r],F[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[r])))+"$ etex);"}else{"nonDefBarre;"}+
+                                                if(ksp==1){"plus;"}else{"moins;"}
+                                                  }; }
+
+lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[nz-1])))+"$ etex);"}else{if(Z[nz-1]==+infinity){" "}else{"nonDefBarre;"}}
+
+
+
+
+ }
+
+
+
+
+
+
+
+
+
+
+
+ lm0:=1,2; li:=1,2; krm:=1,2; krp:=1,2; lmrm:=1,2; lmrp:=1,2; lp:="",""; lnz:=1,2; lf:=1,2; Kz:=1,2;K0:=1,2;
+
+
+for(d:=0;d<=1;d++){
+   K0[d]:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1));
+  Kz[d]:=evalf(limit(f[d](x),x,Z[nz-1],-1))> evalf(limit(f[d](x),x,Z[nz-2],1));
+//{
+//$
+lm0[d]:=limit(f[d](x),x,Z[0],1)==-infinity;
+     li[d]:=lvic+nom[d]+"}$ etex);"+
+           if(member(Z[0],F[d])==0){"valPos(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$ etex,"}+
+           if(K0[d]==1){"1"}else{"0"}+
+                         ");";
+
+                     if(nz>2){ for(r:=1; r<=nz-2;r++){ krm[d]:=evalf(limit(f[d](x),x=Z[r-1],1))< evalf(limit(f[d](x),x=Z[r],-1));
+                                                 krp[d]:=evalf(limit(f[d](x),x=Z[r],1))> evalf(limit(f[d](x),x,Z[r+1],-1)) ;
+                         lmrm[d]:=limit(f[d](x),x,Z[r],-1)==-infinity;lmrp[d]:=limit(f[d](x),x,Z[r],1)==-infinity;
+                                                  lp[d]:=lp[d]+if(member(Z[r],F[d])){
+                                    "limGauche(btex
+                                    $"+if(lmrm[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],-1)))}+"$
+                                    etex,"+if(krm[d]==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],1)))}+"$ etex,"+if(krp[d]==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f[d](Z[r])))+"$
+                                            etex,"+if(sign(evalf(fp[d](Z[r]-0.001)))==sign(evalf((fp[d](Z[r]+0.001))) )){"0.5);"}else{if(krp[d]==1){"1);"}else{"0);
+"}}}
+                                                   }; }
+
+lnz[d]:=limit(f[d](x),x=Z[nz-1],-1)==-infinity;
+
+
+lf[d]:=if(member(Z[nz-1],F[d])==0){"valPos(btex $"+
+           if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(Kz[d]==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(Kz[d]==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
+    
+
+
+
+
+
+}
+
+
+
+
+
+
+
+
+MetaLfc:=if(ftt==2){if(nz>2){"
+
+beginTableau("+nmr+")"+
+        l0+lsi[0]+lsp[0]+lsf[0]+lsi[1]+lsp[1]+lsf[1]+"
+endTableau;
+
+";}else{
+intro+"beginTableau("+nmr+")"+
+        l0+
+lsi[0]+lsf[0]+lsi[1]+lsf[1]+"
+endTableau;
+
+";
+}
+}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+li[0]+
+lp[0]+
+lf[0]+
+li[1]+
+lp[1]+
+lf[1]
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+li[0]+
+lf[0]+
+li[1]+
+lf[1]
++"
+endTableau;
+
+";}}else{
+if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+lsi[0]+lsp[0]+lsf[0]+
+li[0]+
+lp[0]+
+lf[0]+
+lsi[1]+lsp[1]+lsf[1]+
+li[1]+
+lp[1]+
+lf[1]
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+lsi[0]+lsf[0]+
+li[0]+
+lf[0]+
+lsi[1]+lsf[1]+
+li[1]+
+lf[1]
++"
+endTableau;
+
+";}
+}
+}
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+}:;
+\end{VerbatimOut}
+
+
+
+
+%%
+%% Code giac/Xcas pour les Tableaux de signes de produits
+%%
+
+
+
+
+\begin{VerbatimOut}{XcasTabSignL.cxx}
+
+
+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 
+
+
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=solve(factor(simplify(L[k](x))),x);
+ns:=size(SS);
+for(j:=0;j<ns;j++){
+m:=0;
+while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){
+S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){
+S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1;
+}
+}
+
+}else{
+S:=solve(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,simplify(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;
+fpour;};
+nz:=size(Z);
+
+if(nz==0){li:="";l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
+          for(p:=0;p<=n-1;p++){li:=li+lsic+latex(L[p](x))+"}$ etex);"+
+if(mini!=-infinity and L[p](mini)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}+ 
+if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}
+
+}
+           lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"};
+
+
+MetaLfc:="    beginTableau("+nmr+")
+newLigneVariables(btex $ {x}$ etex);
+   "+l0+li+ lsic+nomf+"(x)}$ etex);"+
+               if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}+  lf+
+                               if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}+"
+endTableau;
+"
+;
+
+}else{
+
+l0:="val(btex $"+latex(D[0])+"$ etex);";li:=" ";lr:=" "; 
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
+";fpour; 
+l0:=l0+"val(btex $"+latex(D[1])+"$ etex);";
+
+
+for(p:=0;p<=n-1;p++){lp:="";                                     
+     li:=li+lsic+latex(L[p](x))+"}$ etex);"+
+           if(mini!=-infinity and L[p](mini)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}+ 
+           if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"};
+                               
+                           for(r:=0; r<=nz-2;r++){  
+                             lp:=lp+if(simplify(L[p](Z[r]))==0){"
+                                valBarre(btex 0 etex);"}else{"barre;
+                              "}+ 
+                             if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}};
+ 
+                li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
+                          if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins;
+    "}+if(maxi!=+infinity and L[p](maxi)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}
+    };  
+
+
+pour t de 0 jusque nz-2 faire 
+                           lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"                    
+                         fpour
+
+MetaLfc:="  beginTableau("+nmr+")
+newLigneVariables(btex $ {x}$ etex);
+   "+l0+
+                     li
+                     + lsic+nomf+"(x)}$ etex);"+
+               if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}+  
+                         if(product(L[s](Z[0]-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"+
+                         lr+
+                         if(product(L[s](Z[nz-1]+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+
+                               if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}+"
+endTableau;
+
+ ";
+}
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+ }:;
+
+\end{VerbatimOut}
+
+
+
+
+%%
+%% Code giac/Xcas pour les Tableaux de signes de quotients
+%%
+
+
+
+\begin{VerbatimOut}{XcasTabSignQ.cxx}
+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);
+n:=size(L);
+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 
+
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=solve(factor(simplify(L[k](x))),x);
+ns:=size(SS);
+for(j:=0;j<ns;j++){
+mm:=0;
+while(evalf(simplify(subst(SS[j],n_1=mm)))<=evalf(maxi)){
+S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm+1;
+};mm:=-1;
+while(evalf(subst(SS[j],n_1=mm))>=evalf(mini)){
+S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm-1;
+}
+}
+
+}else{
+S:=solve(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,simplify(S[j]);}
+                      fpour;
+  fsi;
+fpour;
+
+
+pour k de 0 jusque m-1 faire 
+
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SSF:=solve(factor(simplify(Fo[k](x))),x);
+nsf:=size(SSF);
+for(j:=0;j<nsf;j++){
+mm:=0;
+while(evalf(simplify(subst(SSF[j],n_1=mm)))<=evalf(maxi)){
+SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm+1;
+};mm:=-1;
+while(evalf(subst(SSF[j],n_1=mm))>=evalf(mini)){
+SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm-1;
+}
+}
+
+}else{
+SF:=solve(Fo[j](x),x);
+}
+
+  si size(SF)>0 alors pour j de 0 jusque size(SF)-1 faire 
+                          FF:=FF,simplify(SF[j]);
+                          if(SF[j]>mini and SF[j]<maxi){F:=F,simplify(SF[j]);}
+                      fpour;
+  fsi;
+fpour;
+
+
+
+Z:=sort(Z); // on classe les zeros dans l'ordre croissant 
+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; // pour les zeros en double
+     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;
+fpour;};
+nz:=size(Z);
+
+if(nz==0){li:="";l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
+          for(p:=0;p<=n-1;p++){li:=li+lsic+latex(L[p](x))+"}$ etex);"+
+if(mini!=-infinity and L[p](mini)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}+ 
+if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}
+
+}
+           lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"};
+
+
+
+
+MetaLfc:=" 
+beginTableau("+nmr+")
+newLigneVariables(btex $ {x}$ etex);
+   "+l0+li+
+   lsic+nomf+"(x)}$ etex);"+
+              if(member(mini,FF)==0){if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}}else{"nonDefBarre;"}+  lf+
+                               if(member(maxi,FF)==0){if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}}else{"nonDefBarre;"}+"
+endTableau;
+
+"
+;
+
+
+
+
+}else{
+
+
+l0:="val(btex $"+latex(D[0])+"$ etex);";li:=" ";lr:=" "; 
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
+";fpour; 
+l0:=l0+"val(btex $"+latex(D[1])+"$ etex);";
+
+
+for(p:=0;p<=n-1;p++){lp:="";                                     
+     li:=li+lsic+latex(L[p](x))+"}$ etex);"+
+           if(mini!=-infinity and L[p](mini)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}+ 
+           if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"};
+                               
+                           for(r:=0; r<=nz-2;r++){  
+                             lp:=lp+if(simplify(L[p](Z[r]))==0){"
+                                valBarre(btex 0 etex);"}else{"barre;
+                              "}+ 
+                             if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}};
+ 
+                li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
+                          if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins;
+    "}+if(maxi!=+infinity and L[p](maxi)==0){"
+                                valBarre(btex 0 etex);"}else{" "}
+                              
+    };  
+
+
+pour t de 0 jusque nz-2 faire 
+                           lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+
+                                      if(member(Z[t+1],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"}                   
+                         fpour
+
+
+
+
+MetaLfc:="
+beginTableau("+nmr+")
+newLigneVariables(btex $ {x}$ etex);
+   "+l0+
+                     li
+                     +
+   lsic+nomf+"(x)}$ etex);"+
+               if(member(mini,FF)==0){if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}}else{"nonDefBarre;"}+  
+                         if(product(L[s](Z[0]-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+
+                         if(member(Z[0],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"}+
+                         lr+
+                         if(product(L[s](Z[nz-1]+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+
+                               if(member(maxi,FF)==0){if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
+                                valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+"
+endTableau;
+
+"
+
+
+}
+
+
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+
+
+
+
+ }:;
+
+\end{VerbatimOut}
+
+
+
+
+%% Code giac/Xcas pour les Tableaux de signes du produit
+%% de 2 facteurs affines
+%%
+
+
+
+
+\begin{VerbatimOut}{XcasTabSigna.cxx}
+TSa(a,b,c,d,nmr):={
+zA:=solve(a*x+b=0,x)[0];
+zB:=solve(c*x+d=0,x)[0];
+zmin:=min(zA,zB);
+zmax:=max(zA,zB);
+  Meta:= " 
+          beginTableau("+nmr+")
+   newLigneVariables(btex $ {x}$ etex);
+   val(btex $-\\infty$ etex);val(btex $"+latex(zmin)+"$ etex);
+val(btex $"+latex(zmax)+"$etex);
+val(btex $+\\infty$ etex); 
+  "+lsic+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+"}$ etex);"
+        +   if(a>0){"moins;"}else{"plus;"}+
+                                 if(zmin==zA){"valBarre(btex 0 etex);"}else{"barre;"}+
+                                 if(zmin==zA){si a>0 alors "plus;"; sinon "moins;";fsi}
+                                             else{si a>0 alors "moins;"; sinon "plus;"; fsi}+
+                                 if(zmin==zA){"barre;"}else{"valBarre(btex 0 etex);"}+
+                                 if(a>0){"plus;"}else{"moins;"}
+     +lsic+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+"}$ etex);"
+        +     if(c>0){"moins"}else{"plus"}+";"+
+                                 if(zmin==zB){"valBarre(btex 0 etex);"}else{"barre;"}+
+                                 if(zmin==zB){si c>0 alors "plus;"; sinon "moins;";fsi}
+                                             else{si c>0 alors "moins;"; sinon "plus;"; fsi}+
+                                 if(zmin==zB){"barre;"}else{"valBarre(btex 0 etex);"}+
+                                 if(c>0){"plus;"}else{"moins;"}  
+     
+   +lsic+"{("+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+")("+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+")}}$ etex);"
+        +   si a*c>0 alors plus; sinon moins;fsi+";"+
+                                 "valBarre(btex 0 etex);"+
+                                 si a*c>0 alors moins; sinon plus;fsi+";"+
+                                 "valBarre(btex 0 etex);"+
+                                 si a*c>0 alors plus; sinon moins;fsi+";"+"
+endTableau;
+"
+;
+
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,Meta);
+fclose(sortie);
+
+
+ }:;
+\end{VerbatimOut}
+
+
+
+
+
+
+%%$
+%% Code giac/Xcas pour les Tableaux de Signes d'expression ne contenant 
+%% qu'un seul terme
+
+
+
+
+\begin{VerbatimOut}{XcasTSc.cxx}
+TSc(g,D,F,trigo,nmr):={
+f:=unapply(g,x);
+mini:=D[0]; maxi:=D[1];lm:=" ";
+Z:=mini,maxi;
+S:=[];
+
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=solve(factor(simplify(f(x))),x);
+ns:=size(SS);
+for(j:=0;j<ns;j++){
+m:=0;
+while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){
+S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){
+S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1;
+}
+}
+
+}else{
+S:=solve(f(x),x);
+}
+
+
+
+
+
+if(size(S)==0){
+l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
+li:=if(member(mini,F)!=0){"nonDefBarre;"}else{if(mini!=-infinity and f(mini)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}}+ 
+if(mini!=-infinity or maxi!=+infinity){if(f((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}}else{if(f(0)>0){"plus;"}else{"moins;"}};
+lf:=if(member(maxi,F)!=0){"nonDefBarre;"}else{if(maxi!=+infinity and f(maxi)==0){"
+                                valBarre(btex 0 etex);"}else{"
+                              "}};
+}
+else{pour j de 0 jusque size(S)-1 faire 
+                           if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j])};
+                      fpour;
+
+Z:=concat([Z],F);
+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:=concat(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1;
+     fsi;
+fpour;}
+
+if(Z[0]==Z[1]){Z:=Z[1..nz-1];nz:=nz-1;}
+if(Z[nz-2]==Z[nz-1]){Z:=Z[0..nz-2];nz:=nz-1;}
+
+nz:=size(Z);
+l0:=" ";li:=" ";lr:=" "; 
+if(nz==2){l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
+li:=if(mini!=-infinity and f(mini)==0){"
+                                valBarre(btex 0 etex);"}else{if(member(mini,F)==0){"
+                              "}else{"nonDefBarre;"}}+ 
+if(f((mini+maxi)*0.5)>0){"plus;"}else{"moins;"};
+lf:=if(maxi!=+infinity and f(maxi)==0){"
+                                valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){"
+                              "}else{"nonDefBarre;"}
+                              };
+
+}else{
+l0:="val(btex $"+latex(Z[0])+"$ etex);";li:=" ";
+pour m de 1 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
+";
+fpour; 
+
+                                     
+li:= if(mini!=-infinity and f(mini)==0){"
+                                valBarre(btex 0 etex);"}else{if(member(mini,F)==0){"
+                              "}else{"nonDefBarre;"}
+                              }                         
+
+lm:=if(nz>2){for(r:=0; r<nz-2;r++){lm:=lm+if(f((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}+
+            if(member(Z[r+1],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"} 
+                           }}else{" "}; 
+
+lf:=if(f(Z[nz-2]+0.1)>0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){"
+                              "}else{"nonDefBarre;"}
+                              };
+}};  
+
+
+
+
+MetaLfc:="
+
+beginTableau("+nmr+")
+newLigneVariables(btex $\\displaystyle  {x}$ etex);
+   "+l0+lsic+latex(f(x))+"}$ etex);"+
+                     li+lm+lf
+                     +"
+endTableau;
+
+"
+;
+
+
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+ }:;
+\end{VerbatimOut}
+
+
+
+
+
+
+
+%%$
+
+
+
+
+
+
+
+
+%%$
+%%
+%% traitement des fichiers produits par giac/xcas
+%%
+%%
+
+% pour l'�échelle des tableaux taper \ech{facteur de r�éduction}
+
+\newcommand\echelle{1}
+\newcommand\ech[1]{\renewcommand\echelle{#1}}
+
+
+\newcommand{\dresse}[1]{%
+
+
+
+\ifxetex
+
+
+
+\ifthenelse{\boolean{xcas}}{%        Avec l'option "XCas present"
+         \executGiacmp{XCas#1.giac}% reconstituer le tableau
+                                   % exporter le source mp
+                                   % puis lancer metapost pour creer
+                                   % l'image du tableau
+         \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{./convert-mp-pdf.sh \nomtravail.Tab#1 \theTVn}
+          \immediate\write18{\cp \nomtravail.Tab#1.pdf \nomtravail_Tab\theTVn.pdf}
+         \immediate\write18{\rem \nomtravail.Tab#1.mp}  
+           }%
+         {% sinon, si le tableau est absent, alerte.
+         \IfFileExists{\nomtravail.Tab.\theTVn}{}{% 
+         \PackageError{tablor}{Tableau absent non
+         reconstituable.}{Pour compiler il faut, soit les fichiers de
+         tableaux, soit le fichier \nomtravail.Tab.mp, soit disposer de
+         XCas.}}}
+                
+\begin{center}
+  \includegraphics[scale=\echelle]{\nomtravail_Tab\theTVn.pdf}
+\end{center}
+\stepcounter{TVn}
+
+
+
+\else
+
+\ifthenelse{\boolean{xcas}}{%        Avec l'option "XCas present"
+         \executGiacmp{XCas#1.giac}% reconstituer le tableau
+                                   % exporter le source mp
+                                   % puis lancer metapost pour creer
+                                   % l'image du tableau
+         \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{\nomtravail.Tab.\theTVn}{}{% 
+         \PackageError{tablor}{Tableau absent non
+         reconstituable.}{Pour compiler il faut, soit les fichiers de
+         tableaux, soit le fichier \nomtravail.Tab.mp, soit disposer de
+         XCas.}}}
+                
+\begin{center}
+  \includegraphics[scale=\echelle]{\nomtravail.Tab.\theTVn}
+\end{center}
+\stepcounter{TVn}
+
+\fi
+
+}
+
+
+%%
+%% traitement des fichiers produits par giac/xcas avec possibilite
+%% de modifier le fichier metapost (environnement etoile))
+%%
+
+
+
+\newcommand{\dressetoile}[1]{%
+
+
+
+\ifxetex
+
+\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 >> \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 >> \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 >> \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 >> \nomtravail.Tab#1.mp}
+ \immediate\write18{./convert-mp-pdf.sh \nomtravail.Tab#1 \theTVn}
+ \immediate\write18{\cp \nomtravail.Tab#1.pdf \nomtravail_Tab\theTVn.pdf}% Reconstitution des tableaux
+                                % et creation du dernier. L'option
+                                % pallie l'absence de end en fin de
+                                % fichier 
+\immediate\write18{\rem \nomtravail.Tab#1.mp}  
+
+\begin{center}
+  \includegraphics[scale=\echelle]{\nomtravail_Tab\theTVn.pdf}
+\end{center}
+\ech{1}
+\setcounter{TVn}{\theTVnbis}    % Restauration du compteur TVn
+
+
+\else
+
+
+\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 >> \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 >> \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 >> \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 >> \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 \nomtravail.Tab#1.mp}  
+
+\begin{center}
+  \includegraphics[scale=\echelle]{\nomtravail.Tab.\theTVn}
+\end{center}
+\ech{1}
+\setcounter{TVn}{\theTVnbis}    % Restauration du compteur TVn
+
+\fi
+
+}
+
+
+
+
+
+
+
+%%
+%%
+%%%
+%%%
+%%% les "giac" qui permettent d'executer la commande rentree dans le fichier tex
+%%% suivis des environnements qui permettront la saisie du code giac/xcas
+%%% Les versions etoilees permettent de modifier le code metapost produit initialement
+%%%
+
+
+
+
+\begin{VerbatimOut}{XCasa.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTabSigna.cxx");
+read("XCasa.user");
+\end{VerbatimOut}
+
+\newenvironment{TSa}
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasa.user}}
+{\end{VerbatimOut}
+          \dresse{a}
+}
+
+
+
+
+
+
+
+
+
+\begin{VerbatimOut}{XCasQ.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTabSignQ.cxx");
+read("XCasQ.user");
+\end{VerbatimOut}
+
+\newenvironment{TSq}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasQ.user}}
+{\end{VerbatimOut}\dresse{Q}}
+
+
+
+\newenvironment{TSq*}[1]%
+{\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasQ.user}}
+{\end{VerbatimOut}\dressetoile{Q}}
+
+
+\begin{VerbatimOut}{XCasL.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTabSignL.cxx");
+read("XCasL.user");
+\end{VerbatimOut}
+
+\newenvironment{TS}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasL.user}}
+{\end{VerbatimOut}\dresse{L}}
+
+
+\newenvironment{TS*}[1]
+{\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasL.user}}
+{\end{VerbatimOut}\dressetoile{L}}
+
+
+\begin{VerbatimOut}{XCasTSc.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTSc.cxx");
+read("XCasTSc.user");
+\end{VerbatimOut}
+
+
+
+
+\newenvironment{TSc*}[1]%
+{\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTSc.user}}
+{\end{VerbatimOut}\dressetoile{TSc}}
+
+
+\newenvironment{TSc}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTSc.user}}
+{\end{VerbatimOut}\dresse{TSc}}
+
+
+\begin{VerbatimOut}{XCasTV.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTV.cxx");
+read("XCasTV.user");
+\end{VerbatimOut}
+
+\newenvironment{TV}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTV.user}}%
+{\end{VerbatimOut}
+\dresse{TV}}
+
+\newenvironment{TV*}[1]{%
+\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTV.user}}%
+{\end{VerbatimOut}\dressetoile{TV}}
+
+
+
+
+
+
+
+\begin{VerbatimOut}{XCasTVP.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTVP.cxx");
+read("XCasTVP.user");
+\end{VerbatimOut}
+
+\newenvironment{TVP}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVP.user}}%
+{\end{VerbatimOut}
+\dresse{TVP}}
+
+\newenvironment{TVP*}[1]{%
+\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVP.user}}%
+{\end{VerbatimOut}\dressetoile{TVP}}
+
+
+
+
+
+
+
+
+
+
+\begin{VerbatimOut}{XCasTVZ.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTVZ.cxx");
+read("XCasTVZ.user");
+\end{VerbatimOut}
+
+\newenvironment{TVZ}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVZ.user}}%
+{\end{VerbatimOut}
+\dresse{TVZ}}
+
+\newenvironment{TVZ*}[1]{%
+\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVZ.user}}%
+{\end{VerbatimOut}\dressetoile{TVZ}}
+
+
+
+
+
+
+
+
+
+
+\begin{VerbatimOut}{XCasTVapp.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTVapp.cxx");
+read("XCasTVapp.user");
+\end{VerbatimOut}
+
+\newenvironment{TVapp}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVapp.user}}%
+{\end{VerbatimOut}
+\dresse{TVapp}}
+
+\newenvironment{TVapp*}[1]{%
+\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVapp.user}}%
+{\end{VerbatimOut}\dressetoile{TVapp}}
+
+
+
+
+
+
+
+
+
+
+
+\begin{VerbatimOut}{XCasTVI.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTVI.cxx");
+read("XCasTVI.user");
+\end{VerbatimOut}
+
+\newenvironment{TVI}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVI.user}}%
+{\end{VerbatimOut}\dresse{TVI}}
+
+
+\newenvironment{TVI*}[1]%
+{\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVI.user}}%
+{\end{VerbatimOut}\dressetoile{TVI}}
+
+
+
+
+
+
+\begin{VerbatimOut}{XCasTVIapp.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTVIapp.cxx");
+read("XCasTVIapp.user");
+\end{VerbatimOut}
+
+\newenvironment{TVIapp}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIapp.user}}%
+{\end{VerbatimOut}\dresse{TVIapp}}
+
+
+\newenvironment{TVIapp*}[1]%
+{\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIapp.user}}%
+{\end{VerbatimOut}\dressetoile{TVIapp}}
+
+
+
+\begin{VerbatimOut}{XCasTVPC.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTVPC.cxx");
+read("XCasTVPC.user");
+\end{VerbatimOut}
+
+\newenvironment{TVPC}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVPC.user}}%
+{\end{VerbatimOut}
+\dresse{TVPC}}
+
+\newenvironment{TVPC*}[1]{%
+\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVPC.user}}%
+{\end{VerbatimOut}\dressetoile{TVPC}}
+
+
+
+
+%% pour nettoyer les fichiers auxiliaires
+
+\AtEndDocument{\immediate\write18{\cat  queue.mp >> \nomtravail.Tab.mp}
+                         }
+
+
+
+
+%%
+%% Zi end -> enjoy :)
diff --git a/Master/texmf-dist/tex/latex/tablor/tablor.sty b/Master/texmf-dist/tex/latex/tablor/tablor.sty
index b759961e1a3..bbcc38c8837 100644
--- a/Master/texmf-dist/tex/latex/tablor/tablor.sty
+++ b/Master/texmf-dist/tex/latex/tablor/tablor.sty
@@ -1,12 +1,12 @@
 \NeedsTeXFormat{LaTeX2e}[1995/12/01]
-\ProvidesPackage{tablor}[08/10/2008 v4.00 la machine a creer des tableaux de signes et variations]
+\ProvidesPackage{tablor}[21/10/2008 v4.02 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
 % or the LaTeX Project Public Licence, either v1.3 or (at your option)
 % any later version. The latest version is in
 %   http://www.latex-project.org/lppl/
-% This work consists of the files tablor.sty, tablor.cfg, tablor.tex,
+% This work consists of the files tablor.sty, tablor-xetex.sty,  tablor.cfg, tablor.tex,
 % tablor.pdf and tablor.html
 
 
@@ -27,6 +27,12 @@
 %%\end{TSq}
 % un tableau de variation :
 %
+% pour les tableaux de signes �à une seule ligne
+% \begin{TSc}
+% TSc((x+10)/((x-5)*(x-2)),[-10,5],[2,5],n,0)
+% \end{TSc}
+%
+%
 % \begin{TV}
 % TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,n,\tv)
 % \end{TV}
@@ -71,6 +77,15 @@
 %  \end{TVP}
 % %
 
+% Fonctions prolongeables par continuit�é
+% TVPC([intervalles d'�étude],[valeurs prolongeables],[valeurs interdites pour f'],"g","t",e^(-1/x^2),1,n,\tv); 
+
+
+% \begin{TVPC}
+% TVPC([-infinity,+infinity],[0],[0],"g","t",e^(-1/x^2),1,n,\tv); 
+% \end{TVPC}
+
+
 
 
 
@@ -228,7 +243,7 @@
 TV(L,F,nom,nomv,f,ftt,trigo,nmr):={
 nl:=size(L);
 f:=unapply(f,x);
-fp:=fonction_derivee(f);
+fp:=function_diff(f);
 Z:=concat(L,F);
 S:=[];
 
@@ -236,26 +251,26 @@ S:=[];
 if(trigo==t){
 all_trig_solutions:=1;
 reset_solve_counter(-1,-1);
-SS:=resoudre(factor(simplifier(fp(x))),x);
+SS:=solve(factor(simplify(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;
+while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplify(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;
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
 }
 }
 }else{
-S:=resoudre(fp(x),x);
+S:=solve(fp(x),x);
 }
 
 
   si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire
-                             qq:=member(simplifier(S[j]),Z)==0;
+                             qq:=member(simplify(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]))}};
+                          if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}};
                           fpour
   fsi;
 Z:=sort(Z);
@@ -273,7 +288,7 @@ nz:=size(Z);
 
   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]))};
+                          if(kk==1){Z:=append(Z,simplify(S[j]))};
                           fpour
   fsi;
 
@@ -290,8 +305,8 @@ 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; 
 
-       k0:= evalf(limite(f(x),x=Z[0],1))> evalf(limite(f(x),x=Z[1],-1));
-       kz:=evalf(limite(f(x),x=Z[nz-1],-1))> evalf(limite(f(x),x=Z[nz-2],1));
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                           
 lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
      if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
@@ -299,38 +314,47 @@ lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
                                                     if(sign(fp(Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
                                                          if(sign(fp((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}
  
-if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.01))>0;                     
+if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.1))>0;                     
                                                lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                                 if(ksp==1){"plus;"}else{"moins;"}
                                                   }; }
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;
+lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;
 "}
-lm0:=limite(f(x),x=Z[0],1)==-infinity;
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
      li:=lvic+nom+"}$ etex);"+
-           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}
-             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
            if(k0==1){"1"}else{"0"}+
                          ");";
             
-                     if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limite(f(x),x=Z[r-1],1))< evalf(limite(f(x),x=Z[r],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[r],1))> evalf(limite(f(x),x=Z[r+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+                     if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                   lp:=lp+if(member(Z[r],F)){
                                     "limGauche(btex
-                                    $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$
-                                    etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          $"+latex(simplifier(f(Z[r])))+"$
+                                    $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$
+                                    etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
                                             etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
 "}}}
                                                    }; }
 
-lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
-                           lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}+                               
-           if(kz==1){"1);"}else{"0);
-"};    
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+                          
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
     
 
+
+
+
 MetaLfc:=if(ftt==2){if(nz>2){"
 
 beginTableau("+nmr+")"+
@@ -392,6 +416,210 @@ fclose(sortie);
 \end{VerbatimOut}
 
 
+
+
+
+
+%%%%
+
+
+%
+%
+%  TVPC : pour les fonctions prolongeables par continuit�é.
+%%
+%%
+
+
+
+
+\begin{VerbatimOut}{XcasTVPC.cxx}
+TVPC(L,F,FP,nom,nomv,f,ftt,trigo,nmr):={
+nl:=size(L);
+f:=unapply(f,x);
+fp:=function_diff(f);
+Z:=concat(L,F);
+Z:=concat(Z,FP);
+S:=[];
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=solve(factor(simplify(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k<ns;k++){
+m:=0;
+while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
+S:=solve(fp(x),x);
+}
+
+
+  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire
+                             qq:=member(simplify(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,simplify(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,simplify(S[j]))};
+                          fpour
+  fsi;
+
+Z:=sort(Z); 
+nz:=size(Z);
+ si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1; 
+     fsi;
+pour u de 1 jusque nz-2 faire 
+     si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1; 
+     fsi;
+fpour;
+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; 
+
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
+                          
+lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
+     if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],FP)==0){
+                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+                                                    if(sign(fp(Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
+                                                         if(sign(fp((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}
+ 
+if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.1))>0;                     
+                                               lsp:=lsp+if(member(Z[r],FP)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                                                if(ksp==1){"plus;"}else{"moins;"}
+                                                  }; }
+
+lsf:=if(member(Z[nz-1],FP)==0){""}else{"nonDefBarre;
+"}
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
+     li:=lvic+nom+"}$ etex);"+
+           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+           if(k0==1){"1"}else{"0"}+
+                         ");";
+            
+                     if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
+                                                  lp:=lp+if(member(Z[r],F)){ 
+                                    "valPos(btex
+                                    $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$
+                                    etex,"+if(krm==1){"1);"}else{"0);"} }
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
+                                            etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+"}}}
+                                                   }; }
+
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+                          
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);"}else{"0);"}};    
+    
+
+
+
+
+MetaLfc:=if(ftt==2){if(nz>2){"
+
+beginTableau("+nmr+")"+
+        l0+lsi+lsp+lsf+"
+endTableau;
+
+";}else{
+intro+"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+"
+endTableau;
+
+";
+}
+}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+li+
+lf
++"
+endTableau;
+
+";}}else{
+if(nz>2){"beginTableau("+nmr+")"+
+        l0+
+lsi+lsp+lsf+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+        l0+
+lsi+lsf+
+li+
+lf
++"
+endTableau;
+
+";}
+}}
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+
+ }:;
+
+\end{VerbatimOut}
+
+
+
+
+
+
+
+
+
+
+
+
 %%
 %%
 %% TV avec une zone interdite : on rajoute comme argument la liste des intervalles interdits
@@ -416,7 +644,7 @@ if(FF[k][1]<L[1]){Imax[k]:=FF[k][1];LL:=L}else{Imax[k]:=L[1];LL:=[L[0]]};
  IMIN:=[IMIN];
  IMAX:=[IMAX];
  f:=unapply(f,x);
-fp:=fonction_derivee(f);
+fp:=function_diff(f);
 Z:=concat(LL,F);
 
 for(k:=0;k<nf;k++){
@@ -429,19 +657,19 @@ S:=[];
 if(trigo==t){
 all_trig_solutions:=1;
 reset_solve_counter(-1,-1);
-SS:=resoudre(factor(simplifier(fp(x))),x);
+SS:=solve(factor(simplify(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;
+while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplify(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;
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
 }
 }
 }else{
-S:=resoudre(fp(x),x);
+S:=solve(fp(x),x);
 }
 
 
@@ -454,7 +682,7 @@ S:=resoudre(fp(x),x);
                            kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                              kK:=(evalf(S[j])<evalf(Imin[k])) or (evalf(S[j])>evalf(Imax[k]));
                              Kk:=(kk) and kK;
-                          if(Kk==1){Z:=append(Z,simplifier(S[j]))};
+                          if(Kk==1){Z:=append(Z,simplify(S[j]))};
                           }
                         fpour
   fsi;
@@ -484,8 +712,8 @@ 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; 
 
-       k0:= evalf(limite(f(x),x=Z[0],1))> evalf(limite(f(x),x=Z[1],-1));
-       kz:=evalf(limite(f(x),x=Z[nz-1],-1))> evalf(limite(f(x),x=Z[nz-2],1));
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                           
 lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
 if(member(Z[0],IMIN)!=0){"debutNonDef;"}else{if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
@@ -505,33 +733,33 @@ if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0;
 
 
 
-lsf:=if(member(Z[0],IMAX)!=0){"finNonDef;"}else{if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;
+lsf:=if(member(Z[0],IMAX)!=0){"finNonDef;"}else{if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;
 "}}
 
 
-lm0:=limite(f(x),x=Z[0],1)==-infinity;
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
      li:=lvic  +nom+"}$ etex);"+
-           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}
-             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
            if(k0==1){"1"}else{"0"}+
                          ");";
             
 if(nz>2){ 
    for(r:=1; r<=nz-2;r++){ 
-     krm:=evalf(limite(f(x),x=Z[r-1],1))< evalf(limite(f(x),x=Z[r],-1));
-     krp:=evalf(limite(f(x),x=Z[r],1))> evalf(limite(f(x),x=Z[r+1],-1)) ;  
-     lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+     krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+     krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+     lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
 
      lp:=lp+if(member(Z[r],IMIN)!=0){"limGauche(btex $"+if(lmrm==1){
              "-\\infty"}else{
-                latex(simplifier(limite(f(x),x=Z[r],-1)))}
+                latex(simplify(limit(f(x),x=Z[r],-1)))}
          +"$ etex,"+if(krm==1){
              "1);"}else{"0);"}
          +"debutNonDef;"
        }//fsi Zr=Imin
       else{
         if (member(Z[r],IMAX)!=0) {"finNonDef;limDroite(btex $"+if(lmrp==1){
-             "-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}
+             "-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}
          +"$ etex,"+if(krp==1){
              "1);"}else{"0);"}          
        }
@@ -539,15 +767,15 @@ if(nz>2){
           if(member(Z[r],F)){
          "limGauche(btex $"+if(lmrm==1){
              "-\\infty"}else{
-                latex(simplifier(limite(f(x),x=Z[r],-1)))}
+                latex(simplify(limit(f(x),x=Z[r],-1)))}
          +"$ etex,"+if(krm==1){
              "1);"}else{"0);"}
          +"nonDefBarre;limDroite(btex $"+if(lmrp==1){
-             "-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}
+             "-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}
          +"$ etex,"+if(krp==1){
              "1);"}else{"0);"}
          }//fsi (member Zr F)
-          else{"valPos(btex$"+latex(simplifier(f(Z[r])))+"$etex,"+
+          else{"valPos(btex$"+latex(simplify(f(Z[r])))+"$etex,"+
              if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){
                "0.5);"}else{
                     if(krp==1){
@@ -559,10 +787,19 @@ if(nz>2){
            };//ffor 
          }//fsi nz
 
-lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
-                           lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}+                               
-           if(kz==1){"1);"}else{"0);
-"};    
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
+    
+
+
     
 
 MetaLfc:=if(ftt==2){if(nz>2){"
@@ -647,7 +884,7 @@ TVapp(L,F,nom,nomv,f,ftt,nmr):={
 
 nl:=size(L);
 f:=unapply(f,x);
-fp:=fonction_derivee(f);
+fp:=function_diff(f);
 z0:=concat(L,F);z:=sort(z0);
 nz:=size(z);
 
@@ -668,7 +905,7 @@ else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;for k in j do S:=S,fsolv
 
 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]))}};
+                          if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}};
                           fpour;
 fsi;
 
@@ -698,8 +935,8 @@ 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; 
 
-       k0:= evalf(limite(f(x),x=Z[0],1))> evalf(limite(f(x),x=Z[1],-1));
-       kz:=evalf(limite(f(x),x=Z[nz-1],-1))> evalf(limite(f(x),x=Z[nz-2],1));
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                           
 lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
      if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
@@ -712,32 +949,35 @@ if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.01))>0;
                                                 if(ksp==1){"plus;"}else{"moins;"}
                                                   }; }
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;
+lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;
 "}
-lm0:=limite(f(x),x=Z[0],1)==-infinity;
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
      li:=lvic+nom+"}$ etex);"+
-           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}
-             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
            if(k0==1){"1"}else{"0"}+
                          ");";
             
-                     if(nz>2){ for(r:=1; r<=nz-2;r++){  krm:=evalf(limite(f(x),x=Z[r-1],1))< evalf(limite(f(x),x=Z[r],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[r],1))> evalf(limite(f(x),x=Z[r+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+                     if(nz>2){ for(r:=1; r<=nz-2;r++){  krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                   lp:=lp+if(member(Z[r],F)){
-                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          $"+latex(simplifier(f(Z[r])))+"$
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
                                             etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
 "}}}
                                                    }; }
 
-lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
-                           lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}+                               
-           if(kz==1){"1);"}else{"0);
-"};    
-    
-
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+ 
 
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
+    
 
 
 MetaLfc:=if(ftt==2){if(nz>2){"
@@ -827,7 +1067,7 @@ fclose(sortie);
 TVI(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={
 nl:=size(L);
 f:=unapply(f,x);
-fp:=fonction_derivee(f);
+fp:=function_diff(f);
 Z:=concat(L,F);
 S:=[];
 
@@ -835,24 +1075,24 @@ S:=[];
 if(trigo==t){
 all_trig_solutions:=1;
 reset_solve_counter(-1,-1);
-SS:=resoudre(factor(simplifier(fp(x))),x);
+SS:=solve(factor(simplify(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;
+while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplify(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;
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
 }
 }
 }else{
-S:=resoudre(fp(x),x);
+S:=solve(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]))};
+                          if(kk==1){Z:=append(Z,simplify(S[j]))};
                           fpour
   fsi;
 
@@ -869,10 +1109,10 @@ l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";
 
 
 
-LI:=limite(f(x),x,Z[0],1);
-LF:=limite(f(x),x,Z[nz-1],-1);
+LI:=limit(f(x),x,Z[0],1);
+LF:=limit(f(x),x,Z[nz-1],-1);
 LP:=NULL;
-if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limite(f(x),x,Z[r],-1),limite(f(x),x,Z[r],1)}else{f(Z[r])}}};
+if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}}};
 if(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
       
 NL:=size(LL);
@@ -892,8 +1132,8 @@ l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);
 
 
 TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
-       k0:= evalf(limite(f(x),x=Z[0],1))> evalf(limite(f(x),x=Z[1],-1));
-       kz:=evalf(limite(f(x),x=Z[nz-1],-1))> evalf(limite(f(x),x=Z[nz-2],1));
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                           
 lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
      if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
@@ -922,43 +1162,43 @@ else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(sign(evalf(LL[
 
 
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;"}
-lm0:=limite(f(x),x=Z[0],1)==-infinity;
+lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;"}
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
 
 TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
 
      li:=lvic+nom+"}$ etex);
-"+  if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}
-             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+"+  if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
            if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; 
                          
             
                      if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
-                                                 krm:=evalf(limite(f(x),x=Z[r-1],1))< evalf(limite(f(x),x=Z[r],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[r],1))> evalf(limite(f(x),x=Z[r+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+                                                 krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                   lp:=lp+if(member(Z[r],F)) {
-                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          $"+latex(simplifier(f(Z[r])))+"$
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
                                             etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
                                             $ "+ao+" $ etex,0.5);"
                                                            }else{" "}; 
 };//for
 }else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
-                                                 krm:=evalf(limite(f(x),x=Z[rr-1],1))< evalf(limite(f(x),x=Z[rr],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[rr],1))> evalf(limite(f(x),x=Z[rr+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[rr],-1)==-infinity;lmrp:=limite(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
+                                                 krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
 if(TestS==0){if( TestL==1 ){lp:=lp}else{  lp:=lp+if(member(Z[rr],F)) {
-                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          $"+latex(simplifier(f(Z[rr])))+"$
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
                                             etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
                                             $ "+ao+" $ etex,0.5);
                                                                  ";rr:=rr+1;
 }// else testL==1
 }//testS==0
 else{lp:=lp+if(member(Z[rr],F)){
-                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          $"+latex(simplifier(f(Z[rr])))+"$
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
                                             etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
                                                             "}}};rr:=rr+1;
 }//else testS==0
@@ -968,9 +1208,15 @@ else{lp:=lp+if(member(Z[rr],F)){
 };//if nz>2
 
 
-lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
-                           lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}+                               
-           if(kz==1){"1);"}else{"0);"};    
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
     
 
 
@@ -1058,7 +1304,7 @@ TVIapp(L,F,nom,nomv,f,ftt,ao,nmr):={
 
 nl:=size(L);
 f:=unapply(f,x);
-fp:=fonction_derivee(f);
+fp:=function_diff(f);
 z0:=concat(L,F);z:=sort(z0);
 nz:=size(z);
 
@@ -1081,7 +1327,7 @@ else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;for k in j do S:=S,fsolv
 
 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]))}};
+                          if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}};
                           fpour;
 fsi;
 
@@ -1113,10 +1359,10 @@ l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";
 
 
 
-LI:=limite(f(x),x,Z[0],1);
-LF:=limite(f(x),x,Z[nz-1],-1);
+LI:=limit(f(x),x,Z[0],1);
+LF:=limit(f(x),x,Z[nz-1],-1);
 LP:=NULL;
-if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limite(f(x),x,Z[r],-1),limite(f(x),x,Z[r],1)}else{f(Z[r])}}};
+if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}}};
 if(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
       
 NL:=size(LL);
@@ -1136,8 +1382,8 @@ l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);
 
 
 TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
-       k0:= evalf(limite(f(x),x=Z[0],1))> evalf(limite(f(x),x=Z[1],-1));
-       kz:=evalf(limite(f(x),x=Z[nz-1],-1))> evalf(limite(f(x),x=Z[nz-2],1));
+       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
+       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                           
 lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
      if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
@@ -1166,43 +1412,43 @@ else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(sign(evalf(LL[
 
 
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;"}
-lm0:=limite(f(x),x=Z[0],1)==-infinity;
+lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;"}
+lm0:=limit(f(x),x=Z[0],1)==-infinity;
 
 TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
 
      li:=lvic+nom+"}$ etex);
-"+  if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}
-             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}+                               
+"+  if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
            if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; 
                          
             
                      if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
-                                                 krm:=evalf(limite(f(x),x=Z[r-1],1))< evalf(limite(f(x),x=Z[r],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[r],1))> evalf(limite(f(x),x=Z[r+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+                                                 krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                   lp:=lp+if(member(Z[r],F)) {
-                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          $"+latex(simplifier(f(Z[r])))+"$
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
                                             etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
                                             $ "+ao+" $ etex,0.5);"
                                                            }else{" "}; 
 };//for
 }else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); 
-                                                 krm:=evalf(limite(f(x),x=Z[rr-1],1))< evalf(limite(f(x),x=Z[rr],-1));
-                                                 krp:=evalf(limite(f(x),x=Z[rr],1))> evalf(limite(f(x),x=Z[rr+1],-1)) ;  
-                         lmrm:=limite(f(x),x=Z[rr],-1)==-infinity;lmrp:=limite(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
+                                                 krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1));
+                                                 krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ;  
+                         lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
 if(TestS==0){if( TestL==1 ){lp:=lp}else{  lp:=lp+if(member(Z[rr],F)) {
-                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          $"+latex(simplifier(f(Z[rr])))+"$
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
                                             etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
                                             $ "+ao+" $ etex,0.5);
                                                                  ";rr:=rr+1;
 }// else testL==1
 }//testS==0
 else{lp:=lp+if(member(Z[rr],F)){
-                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          $"+latex(simplifier(f(Z[rr])))+"$
+                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
                                             etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
                                                             "}}};rr:=rr+1;
 }//else testS==0
@@ -1212,13 +1458,23 @@ else{lp:=lp+if(member(Z[rr],F)){
 };//if nz>2
 
 
-lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
-                           lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}+                               
-           if(kz==1){"1);"}else{"0);"};    
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
+
+
+
+lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
+           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(kz==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
     
 
 
 
+
+
+
 MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+
         l0+lsi+lsp+lsf+"
 endTableau;
@@ -1313,23 +1569,23 @@ 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]));
+fp:=append(fp,function_diff(f[d]));
 LLL:=concat(L,F[d]);
 Z:=LLL union Z;
-SS:=resoudre(factor(simplifier(fp[d](t))),t);
+SS:=solve(factor(simplify(fp[d](t))),t);
 ns:=size(SS);
 
 for(k:=0;k<ns;k++){
 if(trigo==t){
 m:=0;
-while(evalf(simplifier(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
 
-S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m+1;
+S:=concat(S,simplify(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;
+S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
 
 }
 }else{
@@ -1339,9 +1595,9 @@ S:=concat(S,SS);
 
 
   si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire
-                             qq:=member(simplifier(S[j]),Z)==0;
+                             qq:=member(simplify(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]))}};
+                          if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}};
                           fpour
   fsi;
 Z:=sort(Z);
@@ -1381,22 +1637,22 @@ FFF:=[[],[]];
 
 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));
+       k0:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1));
+       kz:=evalf(limit(f[d](x),x=Z[nz-1],-1))> evalf(limit(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;
+ lsi[d]:=lsic+nom[d]+"'("+nomv+")}$ etex);"+if(member(Z[0],FFF[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[0])))+"$ 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;
-                                               lsp[d]:=lsp[d]+if(member(Z[r],F[d])==0){"valBarre(btex $"+latex(simplifier(fp[d](Z[r])))+"$ etex);"}else{"nonDefBarre;"}+
+                                               lsp[d]:=lsp[d]+if(member(Z[r],F[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[r])))+"$ etex);"}else{"nonDefBarre;"}+
                                                 if(ksp==1){"plus;"}else{"moins;"}
                                                   }; }
 
-lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex $"+latex(simplifier(fp[d](Z[nz-1])))+"$ etex);"}else{if(Z[nz-1]==+infinity){" "}else{"nonDefBarre;"}}
+lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[nz-1])))+"$ etex);"}else{if(Z[nz-1]==+infinity){" "}else{"nonDefBarre;"}}
 
 
 
@@ -1417,33 +1673,39 @@ 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));
+   K0[d]:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1));
+  Kz[d]:=evalf(limit(f[d](x),x,Z[nz-1],-1))> evalf(limit(f[d](x),x,Z[nz-2],1));
 //{
 //$
-lm0[d]:=limite(f[d](x),x,Z[0],1)==-infinity;
+lm0[d]:=limit(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,"}+
+           if(member(Z[0],F[d])==0){"valPos(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$ etex,"}
+             else{"nonDefBarre;limDroite(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$ 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)) ;
-                         lmrm[d]:=limite(f[d](x),x,Z[r],-1)==-infinity;lmrp[d]:=limite(f[d](x),x,Z[r],1)==-infinity;
+                     if(nz>2){ for(r:=1; r<=nz-2;r++){ krm[d]:=evalf(limit(f[d](x),x=Z[r-1],1))< evalf(limit(f[d](x),x=Z[r],-1));
+                                                 krp[d]:=evalf(limit(f[d](x),x=Z[r],1))> evalf(limit(f[d](x),x,Z[r+1],-1)) ;
+                         lmrm[d]:=limit(f[d](x),x,Z[r],-1)==-infinity;lmrp[d]:=limit(f[d](x),x,Z[r],1)==-infinity;
                                                   lp[d]:=lp[d]+if(member(Z[r],F[d])){
                                     "limGauche(btex
-                                    $"+if(lmrm[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[r],-1)))}+"$
-                                    etex,"+if(krm[d]==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[r],1)))}+"$ etex,"+if(krp[d]==1){"1);"}else{"0);"}}
-                                          else{"valPos(btex          $"+latex(simplifier(f[d](Z[r])))+"$
+                                    $"+if(lmrm[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],-1)))}+"$
+                                    etex,"+if(krm[d]==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],1)))}+"$ etex,"+if(krp[d]==1){"1);"}else{"0);"}}
+                                          else{"valPos(btex          $"+latex(simplify(f[d](Z[r])))+"$
                                             etex,"+if(sign(evalf(fp[d](Z[r]-0.001)))==sign(evalf((fp[d](Z[r]+0.001))) )){"0.5);"}else{if(krp[d]==1){"1);"}else{"0);
 "}}}
                                                    }; }
 
-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,"}+
-           if(Kz[d]==1){"1);"}else{"0);
-"};
+lnz[d]:=limit(f[d](x),x=Z[nz-1],-1)==-infinity;
+
+
+lf[d]:=if(member(Z[nz-1],F[d])==0){"valPos(btex $"+
+           if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$ etex,"+
+             if(Kz[d]==1){"1);"}else{"0);"}}
+    else{"limGauche(btex $"+
+         if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$ etex,"+ 
+           if(Kz[d]==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
+    
 
 
 
@@ -1557,27 +1819,27 @@ pour k de 0 jusque n-1 faire
 if(trigo==t){
 all_trig_solutions:=1;
 reset_solve_counter(-1,-1);
-SS:=resoudre(factor(simplifier(L[k](x))),x);
+SS:=solve(factor(simplify(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;
+while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){
+S:=concat(S,simplify(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;
+S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1;
 }
 }
 
 }else{
-S:=resoudre(L[k](x),x);
+S:=solve(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]);}
+                          if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j]);}
                       fpour;
   fsi;
 fpour;
@@ -1641,12 +1903,12 @@ for(p:=0;p<=n-1;p++){lp:="";
            if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"};
                                
                            for(r:=0; r<=nz-2;r++){  
-                             lp:=lp+if(simplifier(L[p](Z[r]))==0){"
+                             lp:=lp+if(simplify(L[p](Z[r]))==0){"
                                 valBarre(btex 0 etex);"}else{"barre;
                               "}+ 
                              if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}};
  
-                li:=li+lp+ if(simplifier(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
+                li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
                           if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins;
     "}+if(maxi!=+infinity and L[p](maxi)==0){"
                                 valBarre(btex 0 etex);"}else{"
@@ -1713,20 +1975,20 @@ pour k de 0 jusque n-1 faire
 if(trigo==t){
 all_trig_solutions:=1;
 reset_solve_counter(-1,-1);
-SS:=resoudre(factor(simplifier(L[k](x))),x);
+SS:=solve(factor(simplify(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;
+while(evalf(simplify(subst(SS[j],n_1=mm)))<=evalf(maxi)){
+S:=concat(S,simplify(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;
+S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm-1;
 }
 }
 
 }else{
-S:=resoudre(L[k](x),x);
+S:=solve(L[k](x),x);
 }
 
 
@@ -1734,7 +1996,7 @@ 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]);}
+                          if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j]);}
                       fpour;
   fsi;
 fpour;
@@ -1744,28 +2006,28 @@ pour k de 0 jusque m-1 faire
 
 
 
-if(trigo==1){
+if(trigo==t){
 all_trig_solutions:=1;
 reset_solve_counter(-1,-1);
-SSF:=resoudre(factor(simplifier(Fo[k](x))),x);
+SSF:=solve(factor(simplify(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;
+while(evalf(simplify(subst(SSF[j],n_1=mm)))<=evalf(maxi)){
+SF:=concat(SF,simplify(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;
+SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm-1;
 }
 }
 
 }else{
-SF:=resoudre(Fo[j](x),x);
+SF:=solve(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]);}
+                          FF:=FF,simplify(SF[j]);
+                          if(SF[j]>mini and SF[j]<maxi){F:=F,simplify(SF[j]);}
                       fpour;
   fsi;
 fpour;
@@ -1839,12 +2101,12 @@ for(p:=0;p<=n-1;p++){lp:="";
            if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"};
                                
                            for(r:=0; r<=nz-2;r++){  
-                             lp:=lp+if(simplifier(L[p](Z[r]))==0){"
+                             lp:=lp+if(simplify(L[p](Z[r]))==0){"
                                 valBarre(btex 0 etex);"}else{"barre;
                               "}+ 
                              if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}};
  
-                li:=li+lp+ if(simplifier(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
+                li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
                           if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins;
     "}+if(maxi!=+infinity and L[p](maxi)==0){"
                                 valBarre(btex 0 etex);"}else{" "}
@@ -1910,8 +2172,8 @@ fclose(sortie);
 
 \begin{VerbatimOut}{XcasTabSigna.cxx}
 TSa(a,b,c,d,nmr):={
-zA:=resoudre(a*x+b=0,x)[0];
-zB:=resoudre(c*x+d=0,x)[0];
+zA:=solve(a*x+b=0,x)[0];
+zB:=solve(c*x+d=0,x)[0];
 zmin:=min(zA,zB);
 zmax:=max(zA,zB);
   Meta:= " 
@@ -1968,11 +2230,10 @@ fclose(sortie);
 
 
 \begin{VerbatimOut}{XcasTSc.cxx}
-TSc(g,D,trigo,nmr):={
+TSc(g,D,F,trigo,nmr):={
 f:=unapply(g,x);
-Z:=NULL;
 mini:=D[0]; maxi:=D[1];lm:=" ";
-
+Z:=mini,maxi;
 S:=[];
 
 
@@ -1980,20 +2241,20 @@ S:=[];
 if(trigo==t){
 all_trig_solutions:=1;
 reset_solve_counter(-1,-1);
-SS:=resoudre(factor(simplifier(f(x))),x);
+SS:=solve(factor(simplify(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;
+while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){
+S:=concat(S,simplify(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;
+S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1;
 }
 }
 
 }else{
-S:=resoudre(f(x),x);
+S:=solve(f(x),x);
 }
 
 
@@ -2002,56 +2263,60 @@ 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){"
+li:=if(member(mini,F)!=0){"nonDefBarre;"}else{if(mini!=-infinity and f(mini)==0){"
                                 valBarre(btex 0 etex);"}else{"
-                              "}+ 
+                              "}}+ 
 if(mini!=-infinity or maxi!=+infinity){if(f((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}}else{if(f(0)>0){"plus;"}else{"moins;"}};
-lf:=if(maxi!=+infinity and f(maxi)==0){"
+lf:=if(member(maxi,F)!=0){"nonDefBarre;"}else{if(maxi!=+infinity and f(maxi)==0){"
                                 valBarre(btex 0 etex);"}else{"
-                              "};
+                              "}};
 }
 else{pour j de 0 jusque size(S)-1 faire 
-                           if(S[j]>mini and S[j]<maxi){Z:=Z,simplifier(S[j])};
+                           if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j])};
                       fpour;
 
-
+Z:=concat([Z],F);
 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;
+     si Z[u]==Z[u+1] alors Z:=concat(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1;
      fsi;
 fpour;}
 
+if(Z[0]==Z[1]){Z:=Z[1..nz-1];nz:=nz-1;}
+if(Z[nz-2]==Z[nz-1]){Z:=Z[0..nz-2];nz:=nz-1;}
 
 nz:=size(Z);
 l0:=" ";li:=" ";lr:=" "; 
-if(nz==0){l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
+if(nz==2){l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
 li:=if(mini!=-infinity and f(mini)==0){"
-                                valBarre(btex 0 etex);"}else{"
-                              "}+ 
-if(f((mini+maxi)*0.5>0)){"plus;"}else{"moins;"};
+                                valBarre(btex 0 etex);"}else{if(member(mini,F)==0){"
+                              "}else{"nonDefBarre;"}}+ 
+if(f((mini+maxi)*0.5)>0){"plus;"}else{"moins;"};
 lf:=if(maxi!=+infinity and f(maxi)==0){"
-                                valBarre(btex 0 etex);"}else{"
-                              "};
+                                valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){"
+                              "}else{"nonDefBarre;"}
+                              };
 
 }else{
-l0:="val(btex $"+latex(D[0])+"$ etex);";li:=" ";
-pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
+l0:="val(btex $"+latex(Z[0])+"$ etex);";li:=" ";
+pour m de 1 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
 ";
 fpour; 
-l0:=l0+"val(btex $"+latex(D[1])+"$ etex);";
+
                                      
 li:= if(mini!=-infinity and f(mini)==0){"
-                                valBarre(btex 0 etex);"}else{"
-                              "}+ 
-if(f(Z[0]-0.01)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);";                               
+                                valBarre(btex 0 etex);"}else{if(member(mini,F)==0){"
+                              "}else{"nonDefBarre;"}
+                              }                         
 
-lm:=if(nz>=2){for(r:=0; r<=nz-2;r++){lm:=lm+if(f((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}+
-                                      "valBarre(btex 0 etex);" 
+lm:=if(nz>2){for(r:=0; r<nz-2;r++){lm:=lm+if(f((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}+
+            if(member(Z[r+1],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"} 
                            }}else{" "}; 
 
-lf:=if(f(Z[nz-1]+1.0)>0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}else{"
-                              "};
+lf:=if(f(Z[nz-2]+0.1)>0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){"
+                              "}else{"nonDefBarre;"}
+                              };
 }};  
 
 
@@ -2076,8 +2341,6 @@ sortie:=fopen("XCasmpfc.mp");
 fprint(sortie,Unquoted,MetaLfc);
 fclose(sortie);
 
-
-
  }:;
 \end{VerbatimOut}
 
@@ -2414,6 +2677,37 @@ read("XCasTVIapp.user");
 
 
 
+
+
+\begin{VerbatimOut}{XCasTVPC.giac}
+maple_mode(0);
+read("config.cxx");
+read("XcasTVPC.cxx");
+read("XCasTVPC.user");
+\end{VerbatimOut}
+
+\newenvironment{TVPC}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVPC.user}}%
+{\end{VerbatimOut}
+\dresse{TVPC}}
+
+\newenvironment{TVPC*}[1]{%
+\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVPC.user}}%
+{\end{VerbatimOut}\dressetoile{TVPC}}
+
+
+
+
+
+
+
+
+
+
+
+
 %% pour nettoyer les fichiers auxiliaires
 
 \AtEndDocument{\immediate\write18{\cat  queue.mp >> \nomtravail.Tab.mp}