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authorKarl Berry <karl@freefriends.org>2008-10-10 23:15:06 +0000
committerKarl Berry <karl@freefriends.org>2008-10-10 23:15:06 +0000
commit41977cc6e6769af289a96d6846be398bdd94d133 (patch)
treee05fceb93f97d08ebc333e21ddc1f1f27c39200e /Master
parenta4e7b650b36655b60114b5bcf614496a9dfcfc31 (diff)
tablor 4.0 (8oct08)
git-svn-id: svn://tug.org/texlive/trunk@10915 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master')
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp4
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.0221
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.1198
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.10558
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.1052
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.11409
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.12326
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.13702
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.14467
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.15383
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.16427
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.17174
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.18447
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.19204
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.2124
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.20133
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.21233
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.2285
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.23146
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.2483
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.25224
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.26220
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.27193
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.28486
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.29132
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.3198
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.30449
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.31129
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.32127
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.33102
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.34169
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.35172
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.36356
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.37263
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.38600
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.39527
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.4229
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.40698
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.41429
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.42564
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.43580
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.44325
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.45325
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.46229
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.47324
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.48240
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.49122
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.5452
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.50116
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.6332
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.7275
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.8384
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.9306
-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp301
-rw-r--r--Master/texmf-dist/doc/latex/tablor/tablor.pdfbin341164 -> 340205 bytes
-rw-r--r--Master/texmf-dist/doc/latex/tablor/tablor.tex579
-rw-r--r--Master/texmf-dist/tex/latex/tablor/tablor.sty418
57 files changed, 9117 insertions, 7784 deletions
diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp b/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp
index d0549eeb9cf..0f84f2a3c09 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/TSav-105.mp
@@ -4,12 +4,12 @@ newLigneVariables(btex $ {x}$ etex);
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moins;
valBarre(btex 0 etex);plus;barre;
plus;barre;plus;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5x^{2}-1}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5 x^{2}-1}$ etex);
plus;barre;
plus;
valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.0 b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.0
index ffbec24f4c8..ae6786f19dc 100644
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diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.1 b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.1
index eb7d268cb39..ae6786f19dc 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.1
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diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.9 b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.9
index 9db7e1ac706..6c89a54adba 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.9
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.9
@@ -1,15 +1,17 @@
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diff --git a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
index 5797a66cf34..fa53635eeb2 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
+++ b/Master/texmf-dist/doc/latex/tablor/Figures/tablor.Tab.mp
@@ -8,7 +8,39 @@ verbatimtex
\renewcommand\cdot{ } % idem pour les cdot
\begin{document}
etex
-beginTableau(0) newLigneVariables(btex $x$ etex);val(btex $-5$ etex);
+beginTableau(0) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
+val(btex $-1$ etex);
+val(btex $0$ etex);
+val(btex $1$ etex);
+val(btex $+\infty $ etex);
+
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex); plus; nonDefBarre;plus;valBarre(btex 0 etex);moins;nonDefBarre;moins;
+newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex
+ $+\infty $
+ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $0$
+ etex,1);limGauche(btex
+ $-\infty$
+ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0);
+
+endTableau;
+
+beginTableau(1) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
+val(btex $-1$ etex);
+val(btex $0$ etex);
+val(btex $1$ etex);
+val(btex $+\infty $ etex);
+
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex); plus; nonDefBarre;plus;valBarre(btex 0 etex);moins;nonDefBarre;moins;
+newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex
+ $+\infty $
+ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $0$
+ etex,1);limGauche(btex
+ $-\infty$
+ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0);
+
+endTableau;
+
+beginTableau(2) newLigneVariables(btex $x$ etex);val(btex $-5$ etex);
val(btex $0$ etex);
val(btex $7$ etex);
@@ -17,7 +49,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
valPos(btex $49$ etex,1);
endTableau;
-beginTableau(1) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(3) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
@@ -29,14 +61,14 @@ endTableau;
-beginTableau(2) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; valBarre(btex 0 etex);plus;
endTableau;
-beginTableau(3) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
+beginTableau(5) newLigneVariables(btex $t$ etex);val(btex $-10$ etex);
val(btex $-1$ etex);
val(btex $0$ etex);
val(btex $1$ etex);
@@ -52,7 +84,20 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);va
endTableau;
-beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(6) newLigneVariables(btex $t$ etex);val(btex $-\pi $ etex);
+val(btex $\frac{(-\pi )}{2}$ etex);
+val(btex $\frac{\pi }{2}$ etex);
+val(btex $\pi $ etex);
+
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex); moins; valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;
+newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);valPos(btex $\frac{1}{2}$ etex,1); valPos(btex $\frac{-1}{2}$
+ etex,0);
+valPos(btex $\frac{3}{2}$
+ etex,1);valPos(btex $\frac{1}{2}$ etex,0);
+
+endTableau;
+
+beginTableau(7) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -61,7 +106,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $0$ etex,0);debutNonDef;finNonDef;limDroite(btex $0$ etex,0);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(5) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(8) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $\frac{5}{2}$ etex);
@@ -73,7 +118,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $-\infty$ etex,0);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex$\ln\left(\frac{441}{16}\right)$etex,1);limGauche(btex $-\infty$ etex,0);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(6) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $\alpha_1$ etex);val(btex $-1$ etex);val(btex $0$ etex);val(btex $1$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
+beginTableau(9) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $\alpha_1$ etex);val(btex $-1$ etex);val(btex $0$ etex);val(btex $1$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$ $ etex);plus; nonDefBarre;plus;valBarre(btex 0 etex);moins;nonDefBarre;moins;valBarre(btex $ $ etex);moins;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
@@ -83,7 +128,7 @@ valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); limGauche(bte
valPos(btex $1$ etex,0);
endTableau;
-beginTableau(7) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);val(btex $+\infty $ etex);
+beginTableau(10) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus; nonDefBarre;plus;valBarre(btex $ $ etex);plus;valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins;nonDefBarre;moins;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
@@ -95,7 +140,7 @@ valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex $+\infty $ etex,1);nonDefB
limGauche(btex $-\infty$ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0);
endTableau;
-beginTableau(9) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(12) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $ 0.212584$ etex);
val(btex $ 0.584635$ etex);
val(btex $+\infty $ etex);
@@ -107,27 +152,27 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);no
valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(10) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
-val(btex $\frac{1}{8} \times \pi $ etex);
-val(btex $\frac{1}{3} \times \pi $ etex);
-val(btex $\frac{3}{8} \times \pi $ etex);
+beginTableau(13) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+val(btex $\frac{\pi }{8}$ etex);
+val(btex $\frac{\pi }{3}$ etex);
+val(btex $\frac{3 \pi }{8}$ etex);
val(btex $\frac{\pi }{2}$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3\sin\left(\frac{3\pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3\sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex);
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex $\cos\left(\frac{3\pi }{8}\right)$
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3 \sin\left(\frac{3 \pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3 \sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex);
+newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex $\cos\left(\frac{3 \pi }{8}\right)$
etex,0.5);valPos(btex $-1$
etex,0);
valPos(btex $-\left(\cos\left(\frac{\pi }{8}\right)\right)$
etex,0.5);valPos(btex $0$ etex,1);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex);valBarre(btex $4$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-2$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $4$ etex);
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);valPos(btex $0$ etex,0);valPos(btex $1$
- etex,1);valPos(btex $-\left(\frac{1}{2} \times \sqrt{3}\right)$
+ etex,1);valPos(btex $\frac{(-\left(\sqrt{3}\right))}{2}$
etex,0.5);valPos(btex $-1$
etex,0);
valPos(btex $0$ etex,1);
endTableau;
-beginTableau(11) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
+beginTableau(14) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex);
val(btex $-4$ etex);
val(btex $-1$ etex);
val(btex $0$ etex);
@@ -155,7 +200,7 @@ valPos(btex $\frac{16}{3}$
endTableau;
- beginTableau(12)
+ beginTableau(15)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty$ etex);val(btex $\frac{3}{2}$ etex);
val(btex $5$etex);
@@ -165,7 +210,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2x+3}$ etex);plus;val
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -x+5}$ etex);plus;barre;plus;valBarre(btex 0 etex);moins;
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle {(-2x+3)(-x+5)}}$ etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
endTableau;
- beginTableau(13)
+ beginTableau(16)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $-\left(\sqrt{2}\right)$ etex);
val(btex $-1$ etex);
@@ -173,7 +218,7 @@ val(btex $1$ etex);
val(btex $\sqrt{2}$ etex);
val(btex $\frac{3}{2}$ etex);
val(btex $+\infty $ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex);
plus;barre;
plus;barre;
plus;barre;
@@ -214,7 +259,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle P(x)}$ etex);
endTableau;
- beginTableau(14)
+ beginTableau(17)
newLigneVariables(btex $ {x}$ etex);
val(btex $-15$ etex);val(btex $-10$ etex);
val(btex $10$ etex);
@@ -231,7 +276,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f(x)}$ etex);
endTableau;
-beginTableau(15)
+beginTableau(18)
newLigneVariables(btex $ {x}$ etex);
val(btex $-\infty $ etex);val(btex $-4$ etex);
val(btex $\frac{5}{4}$ etex);
@@ -239,14 +284,14 @@ val(btex $\frac{3}{2}$ etex);
val(btex $2$ etex);
val(btex $4$ etex);
val(btex $+\infty $ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex);
plus;barre;
plus;barre;
plus;
valBarre(btex 0 etex);moins;barre;
moins;barre;moins;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(4x\right)+5}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(4 x\right)+5}$ etex);
plus;barre;
plus;
valBarre(btex 0 etex);moins;barre;
@@ -266,32 +311,16 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-2}$ etex);
moins;
valBarre(btex 0 etex);plus;barre;plus;
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex);
- moins;nonDefBarre; plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;nonDefBarre;plus;
-endTableau;
-
-
-beginTableau(16)
-newLigneVariables(btex $ {x}$ etex);
- val(btex $-\infty $ etex);val(btex $-10$ etex);
-val(btex $10$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-10}$ etex);
- moins;barre;moins;
-
- valBarre(btex 0 etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+10}$ etex);
- moins;valBarre(btex 0 etex);plus;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex);
- plus;nonDefBarre; moins;
- valBarre(btex 0 etex);
+ moins;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;valBarre(btex 0 etex);plus;
endTableau;
-beginTableau(17)
+beginTableau(19)
newLigneVariables(btex $\displaystyle {x}$ etex);
val(btex $-10$ etex);val(btex $-5$ etex);
val(btex $10$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10)(x+5)}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+5)}$ etex);
plus;valBarre(btex 0 etex); moins;valBarre(btex 0 etex);
endTableau;
@@ -301,12 +330,12 @@ newLigneVariables(btex $ {x}$ etex);
val(btex $-\frac{\sqrt{5}}{5}$ etex);
val(btex $\frac{\sqrt{5}}{5}$ etex);
val(btex $50$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3x+2}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3 x+2}$ etex);
moins;
valBarre(btex 0 etex);plus;barre;
plus;barre;plus;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5x^{2}-1}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 5 x^{2}-1}$ etex);
plus;barre;
plus;
valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
@@ -316,7 +345,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle F(x)}$ etex);
endTableau;
- beginTableau(18) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
+ beginTableau(20) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;moins;valBarre(btex$ $ etex);moins; valBarre(btex 0 etex);plus;valBarre(btex $ $ etex);plus;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPos(btex $-1$
@@ -324,7 +353,7 @@ nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $ 2 $ etex,0.5); valPo
$ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(19) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(21) newLigneVariables(btex $x$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins; valBarre(btex 0 etex);plus;valBarre(btex $ $ etex);plus;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $\frac{1}{4}$ etex,1); valPos(btex $0$
@@ -332,13 +361,13 @@ valPos(btex $\frac{1}{4}$ etex,1); valPos(btex $0$
$ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(20) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(22) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus;valBarre(btex$ $ etex);plus;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(22) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
+beginTableau(24) newLigneVariables(btex $x$ etex);val(btex $1$ etex);
val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins;
@@ -346,7 +375,7 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
endTableau;
-beginTableau(23) newLigneVariables(btex $x$ etex);val(btex $-\pi $ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $\pi $ etex);
+beginTableau(25) newLigneVariables(btex $x$ etex);val(btex $-\pi $ etex);val(btex $\alpha_1$ etex);val(btex $0$ etex);val(btex $\alpha_2$ etex);val(btex $\pi $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);valBarre(btex 0 etex);moins;valBarre(btex$ $ etex);moins; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex $1$
@@ -354,9 +383,9 @@ valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex $1$
$ 1/2 $ etex,0.5);valPos(btex $-1$ etex,0);
endTableau;
-beginTableau(24) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(26) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $\pi $ etex);
-val(btex $2\pi $ etex);
+val(btex $2 \pi $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);valBarre(btex 0 etex);moins; valBarre(btex 0 etex);plus;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $1$ etex,1); valPos(btex $-1$
@@ -364,22 +393,22 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
valPos(btex $1$ etex,1);
endTableau;
-beginTableau(25) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex);
+beginTableau(27) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle h'(t)}$ etex); plus;valBarre(btex$ $ etex);plus; nonDefBarre;plus;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle h}$ etex);
valPos(btex $0$ etex,0);valPos(btex $ 7 $ etex,0.5); limGauche(btex $+\infty $ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $0$ etex,1);
endTableau;
-beginTableau(26) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);
+beginTableau(28) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$ $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
-valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex $\frac{3}{4} \times \sqrt{3}$
+valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex $\frac{3 \sqrt{3}}{4}$
etex,1);valPos(btex
$ 1 $ etex,0.5);valPos(btex $0$ etex,0);
endTableau;
-beginTableau(27) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
+beginTableau(29) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);
val(btex $0$ etex);
val(btex $+\infty $ etex);
@@ -389,15 +418,15 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);no
endTableau;
- beginTableau(28)
+ beginTableau(30)
newLigneVariables(btex $ {x}$ etex);
- val(btex $-10$ etex);val(btex $-\left(\frac{1}{2} \times \sqrt{5}\right)+\frac{-3}{2}$ etex);
+ val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex);
val(btex $-1$ etex);
-val(btex $\frac{1}{2} \times \sqrt{5}+\frac{-3}{2}$ etex);
+val(btex $\frac{(\sqrt{5}-3)}{2}$ etex);
val(btex $1$ etex);
val(btex $\frac{3}{2}$ etex);
val(btex $+\infty $ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2x\right)+3}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(2 x\right)+3}$ etex);
plus;barre;
plus;barre;
plus;barre;
@@ -419,7 +448,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+1}$ etex);
plus;barre;
plus;barre;plus;
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+3x+1}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+3 x+1}$ etex);
plus;
valBarre(btex 0 etex);moins;barre;
moins;
@@ -431,7 +460,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex);
endTableau;
- beginTableau(29) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+ beginTableau(31) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $-3$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; valBarre(btex 0 etex);plus;valBarre(btex $ $ etex);plus;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $-1$ etex,1); valPos(btex $-\left(e^{-4}\right)-1$
@@ -439,7 +468,7 @@ valPos(btex $-1$ etex,1); valPos(btex $-\left(e^{-4}\right)-1$
$ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(30) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
+beginTableau(32) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $1$ etex,0); valPos(btex $2$
@@ -447,7 +476,7 @@ valPos(btex $1$ etex,0); valPos(btex $2$
$ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0);
endTableau;
-beginTableau(32) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
+beginTableau(34) newLigneVariables(btex $x$ etex);val(btex $0$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -457,13 +486,13 @@ newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);va
endTableau;
-beginTableau(33) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex);
+beginTableau(35) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\pi $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); moins;valBarre(btex$ $ etex);moins;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
valPos(btex $1$ etex,1);valPos(btex $ 0 $ etex,0.5);valPos(btex $-\pi -1$ etex,0);
endTableau;
-beginTableau(34) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $e^{\frac{1}{2}}$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
+beginTableau(36) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $e^{\frac{1}{2}}$ etex);val(btex $\alpha_2$ etex);val(btex $+\infty $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus;valBarre(btex$ $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins;
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);
nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ -1 $ etex,0.5); valPos(btex $\frac{1}{4}$
@@ -473,15 +502,15 @@ endTableau;
-beginTableau(35)
+beginTableau(37)
newLigneVariables(btex $\displaystyle {x}$ etex);
val(btex $-10$ etex);val(btex $10$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10)(x+10)}$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+10)}$ etex);
valBarre(btex 0 etex);plus;
valBarre(btex 0 etex);
endTableau;
-beginTableau(36) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(38) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-\left(\sqrt{2}\right)$ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
@@ -492,7 +521,7 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; v
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); valPos(btex$-2$etex,0);limGauche(btex $0$ etex,1);debutNonDef;finNonDef;limDroite(btex $0$ etex,1);valPos(btex$-2$etex,0);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(37) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(39) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $+\infty $ etex);
@@ -501,38 +530,38 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $-\infty$ etex,0);debutNonDef;finNonDef;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(38) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
-val(btex $\frac{1}{8} \times \pi $ etex);
-val(btex $\frac{1}{3} \times \pi $ etex);
-val(btex $\frac{3}{8} \times \pi $ etex);
+beginTableau(40) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+val(btex $\frac{\pi }{8}$ etex);
+val(btex $\frac{\pi }{3}$ etex);
+val(btex $\frac{3 \pi }{8}$ etex);
val(btex $\frac{\pi }{2}$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3\sin\left(\frac{3\pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3\sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex);
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex $\cos\left(\frac{3\pi }{8}\right)$
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3 \sin\left(\frac{3 \pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3 \sin\left(\frac{\pi }{8}\right)$ etex);plus;valBarre(btex $3$ etex);
+newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex $\cos\left(\frac{3 \pi }{8}\right)$
etex,0.5);valPos(btex $-1$
etex,0);
valPos(btex $-\left(\cos\left(\frac{\pi }{8}\right)\right)$
etex,0.5);valPos(btex $0$ etex,1);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex);valBarre(btex $4$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-2$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $4$ etex);
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);valPos(btex $0$ etex,0);valPos(btex $1$
- etex,1);valPos(btex $-\left(\frac{1}{2} \times \sqrt{3}\right)$
+ etex,1);valPos(btex $\frac{(-\left(\sqrt{3}\right))}{2}$
etex,0.5);valPos(btex $-1$
etex,0);
valPos(btex $0$ etex,1);
endTableau;
-beginTableau(39) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
-val(btex $\frac{1}{3} \times \pi $ etex);
+beginTableau(41) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+val(btex $\frac{\pi }{3}$ etex);
val(btex $\pi $ etex);
-val(btex $\frac{5}{3} \times \pi $ etex);
-val(btex $2\pi $ etex);
+val(btex $\frac{5 \pi }{3}$ etex);
+val(btex $2 \pi $ etex);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex);valBarre(btex $-1$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $3$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-1$ etex);
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $0$ etex,1);valPos(btex $-\left(\sqrt{3}\right)-\left(\frac{1}{-3} \times \pi \right)$
+newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $0$ etex,1);valPos(btex $\frac{(\pi +-3 \sqrt{3})}{3}$
etex,0);
valPos(btex $\pi $
- etex,0.5);valPos(btex $\sqrt{3}+\frac{5}{3} \times \pi $
- etex,1);valPos(btex $2\pi $ etex,0);
+ etex,0.5);valPos(btex $\frac{(5 \pi +3 \sqrt{3})}{3}$
+ etex,1);valPos(btex $2 \pi $ etex,0);
newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(\sqrt{3}\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $\sqrt{3}$ etex);plus;valBarre(btex $0$ etex);
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);valPos(btex $1$ etex,1);valPos(btex $0$
@@ -542,7 +571,7 @@ valPos(btex $0$
etex,0.5);valPos(btex $1$ etex,1);
endTableau;
-beginTableau(40) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
+beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
val(btex $-1$ etex);
val(btex $1$ etex);
val(btex $\frac{5}{2}$ etex);
@@ -554,75 +583,51 @@ newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; d
newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $\sqrt{35}$ etex,0);debutNonDef;finNonDef;limDroite(btex $\sqrt{15}$ etex,0);valPos(btex$\sqrt{21}$etex,1);limGauche(btex $\sqrt{15}$ etex,0);debutNonDef;finNonDef;limDroite(btex $\sqrt{35}$ etex,0);valPos(btex $+\infty $ etex,1);
endTableau;
-beginTableau(41) newLigneVariables(btex $x$ etex);val(btex $-5$ etex);
-val(btex $\frac{2}{5}$ etex);
-val(btex $10$ etex);
-
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $\frac{169}{2}$ etex,1); valPos(btex $\frac{58}{5}$
- etex,0);
-valPos(btex $242$ etex,1);
-endTableau;
-
-beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-20$ etex);
-val(btex $-\left(\frac{1}{9} \times \sqrt{7}\right)+\frac{5}{9}$ etex);
-val(btex $\frac{1}{9} \times \sqrt{7}+\frac{5}{9}$ etex);
-val(btex $20$ etex);
-
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-26047$ etex,0); valPos(btex $\frac{14}{243} \times \sqrt{7}+\frac{-1681}{243}$
- etex,1);valPos(btex $-\left(\frac{14}{243} \times \sqrt{7}\right)+\frac{-1681}{243}$
- etex,0);
-valPos(btex $22033$ etex,1);
-endTableau;
+beginTableau(43) newLigneVariables(btex $t$ etex);val(btex $0$ etex);
+val(btex $\frac{\pi }{8}$ etex);
+val(btex $\frac{\pi }{6}$ etex);
+val(btex $\frac{3 \pi }{8}$ etex);
+val(btex $\frac{\pi }{2}$ etex);
-beginTableau(43) newLigneVariables(btex $x$ etex);val(btex $-20$ etex);
-val(btex $-\left(\frac{1}{9} \times \sqrt{7}\right)+\frac{5}{9}$ etex);
-val(btex $\frac{1}{9} \times \sqrt{7}+\frac{5}{9}$ etex);
-val(btex $20$ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(t)}$ etex);valBarre(btex $3$ etex);plus;valBarre(btex $3 \cos\left(\frac{3 \pi }{8}\right)$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-\left(3 \cos\left(\frac{\pi }{8}\right)\right)$ etex);moins;valBarre(btex $0$ etex);
+newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $0$ etex,0);valPos(btex $\sin\left(\frac{3 \pi }{8}\right)$
+ etex,0.5);valPos(btex $1$
+ etex,1);valPos(btex $-\left(\sin\left(\frac{\pi }{8}\right)\right)$
+ etex,0.5);valPos(btex $-1$ etex,0);
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $26047$ etex,1); valPos(btex $-\left(\frac{14}{243} \times \sqrt{7}\right)+\frac{1681}{243}$
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex);valBarre(btex $4$ etex);plus;valBarre(btex $0$ etex);moins;valBarre(btex $-2$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $4$ etex);
+newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);valPos(btex $0$ etex,0);valPos(btex $1$
+ etex,1);valPos(btex $\frac{\sqrt{3}}{2}$
+ etex,0.5);valPos(btex $-1$
etex,0);
-valPos(btex $\frac{14}{243} \times \sqrt{7}+\frac{1681}{243}$
- etex,1);valPos(btex $-22033$ etex,0);
-
+valPos(btex $0$ etex,1);
endTableau;
-
-
-beginTableau(44)
-newLigneVariables(btex $\displaystyle {x}$ etex);
- val(btex $-20$ etex);val(btex $ 1.942052$ etex);
-val(btex $20$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -\left(3x^{3}\right)+5x^{2}-\left(2x\right)+7}$ etex);
- plus;valBarre(btex 0 etex); moins;
+ beginTableau(44)
+newLigneVariables(btex $ {x}$ etex);
+ val(btex $0$ etex);val(btex $\frac{\pi }{3}$ etex);
+val(btex $\frac{\pi }{3}$ etex);
+val(btex $\frac{7 \pi }{6}$ etex);
+val(btex $\frac{5 \pi }{3}$ etex);
+val(btex $\frac{11 \pi }{6}$ etex);
+val(btex $2 \pi $ etex);
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \cos\left(x\right)+\frac{1}{-2}}$ etex);
+ plus;
+ valBarre(btex 0 etex);plus;
+ valBarre(btex 0 etex);moins;barre;
+ moins;
+ valBarre(btex 0 etex);plus;barre;plus;
-endTableau;
-
-
-
-beginTableau(45)
-newLigneVariables(btex $\displaystyle {x}$ etex);
- val(btex $-20$ etex);val(btex $ 1.942052$ etex);
-val(btex $20$ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3x^{3}-\left(5x^{2}\right)+2x-7}$ etex);
- moins;valBarre(btex 0 etex); plus;
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \sin\left(x\right)+\frac{1}{2}}$ etex);
+ plus;barre;
+ plus;barre;
+ plus;
+ valBarre(btex 0 etex);moins;barre;
+ moins;valBarre(btex 0 etex);plus;
+
+newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f (x)}$ etex);
+ plus;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;
endTableau;
-beginTableau(46) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);val(btex $ 0.000000$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex);
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f''(x)}$ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins;
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f'}$ etex);
-valPos(btex $\frac{1}{2}$ etex,0); valPos(btex $ 1.000000$
- etex,1);valPos(btex
- $ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0);
-endTableau;
-
-beginTableau(47) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex);
-val(btex $ 0.639232$ etex);
-val(btex $+\infty $ etex);
-
-newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);plus; valBarre(btex 0 etex);moins;
-newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-\infty$ etex,0); valPos(btex $ 0.967397$
- etex,1);valPos(btex $-\infty$ etex,0);
-
-endTableau;
-
+ \ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.pdf b/Master/texmf-dist/doc/latex/tablor/tablor.pdf
index db5ac600269..e79dbbf0274 100644
--- a/Master/texmf-dist/doc/latex/tablor/tablor.pdf
+++ b/Master/texmf-dist/doc/latex/tablor/tablor.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.tex b/Master/texmf-dist/doc/latex/tablor/tablor.tex
index dcc593424ab..fd514f0f77e 100644
--- a/Master/texmf-dist/doc/latex/tablor/tablor.tex
+++ b/Master/texmf-dist/doc/latex/tablor/tablor.tex
@@ -48,11 +48,11 @@ keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,com
% petits environnements bclogo
\newenvironment{DANGER}[1]{%
-\begin{bclogo}{\attention}{#1}{0.9white}{0.1}}
+\begin{bclogo}{\attention}{#1}{0.9white}{0.1}{0}}
{\end{bclogo}}
\newenvironment{Idee}[1]{%
-\begin{bclogo}{\coeur}{#1}{0.9white}{0.1}}
+\begin{bclogo}{\coeur}{#1}{0.9white}{0.1}{0}}
{\end{bclogo}}
@@ -72,24 +72,6 @@ keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,com
-%%%% Macros pour un Vrai-Faux
-
-\usepackage{pifont}
-
-\newcommand{\Q}{\mbox{\ding{114}\hspace{-.7em}\raisebox{.2ex}[1ex]{\ding{51}}}}
-
-\newcommand{\VF}{%
- \hfill\makebox[1cm][s]{\bf V\hfill F}
- }
-
-\newcommand{\Rep}[1][]{%
- \ifthenelse{\equal{#1}{v}}{%
- \hfill\makebox[1cm][s]{\Q\hfill \ding{114}}}{%
- \ifthenelse{\equal{#1}{f}}{%
- \hfill\makebox[1cm][s]{\ding{114} \hfill\Q}}{%
- \hfill\makebox[1cm][s]{\ding{114} \hfill\ding{114}}}}}
-
-
% titre
\title{\texttt{tablor.sty} \\La machine à créer des tableaux de signes et de variations }
@@ -98,7 +80,7 @@ keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,com
avec l'efficace participation de Jean-Michel \textsc{Boucart}\\
Forum d'aide ~:~\href{http://gconnan.free.fr/punbb/upload/index.php}{http://gconnan.free.fr/punbb/upload/index.php}}
-\date{14 juin 2008 - Version 3.00}
+\date{8 octobre 2008 - Version 4.00}
@@ -129,6 +111,37 @@ Forum d'aide ~:~\href{http://gconnan.free.fr/punbb/upload/index.php}{http://gcon
Il s'agit d'obtenir rapidement un tableau de signe ou un tableau de variation en entrant un
minimum de commandes.
+\section{Nouveautés}
+
+\subsection{Changements depuis la version 3.00}
+
+La version 4.00 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.
+
+
+\subsection{Professor.sty}
+
+
+\texttt{tablor.sty} a fait des petits... Grâce à une efficace
+collaboration avec Denis \textsc{LE FUR}, vous disposez à présent de
+toute une panoplie d'outils similaires pour tracer des courbes, des
+histogrammes, des arbres de probabilités, des graphes probabilistes, des
+lissages par moyennes mobiles et j'en passe et des meilleures... Allez
+découvrir ces trésors sur
+\href{http://mathsp.tuxfamily.org/spip.php?rubrique46}{http://mathsp.tuxfamily.org/spip.php?rubrique46}.
+
+
+
+
+
+
+
+
+
\section{Comment ça marche~?}
\subsection{Principe général}
@@ -200,7 +213,7 @@ fclose(sortie); // on ferme XCasmpfc.mp
-\begin{figure}
+\begin{figure}[!h]
\begin{Idee}{Autres collaborations XCAS/\LaTeX{}}
On peut suivre ce même principe pour créer d'autres associations de
vos outils préférés. Voir par exemple~:
@@ -219,6 +232,17 @@ et
\section{De quoi a-t-on besoin~?}
+\begin{figure}[!h]
+ \begin{Idee}{Conseils en lignes}
+ N'hésitez pas à explorer la page suivante :
+
+\href{http://mathsp.tuxfamily.org/spip.php?article186}{http://mathsp.tuxfamily.org/spip.php?article186}
+
+surtout si vous êtes sur XP :-)
+ \end{Idee}
+ \end{figure}
+
+
\begin{itemize}
\item Il faut avoir installé \texttt{XCAS}, logiciel multi-plateforme de calcul et de programmation~:
@@ -266,7 +290,7 @@ pour installer une nouvelle extension \LaTeX{}.
\end{itemize}
-\begin{figure}
+\begin{figure}[!h]
\begin{Idee}{shell-escape}
Pour les utilisateurs de TeXnicCenter, observez cette
@@ -294,7 +318,7 @@ et là il faut ajouter
\end{figure}
-\begin{figure}
+\begin{figure}[!h]
\begin{DANGER}{Conflit d'extensions}
L'extension \verb+fancybox+ rentre en conflit avec \verb+fancyvrb+ qu'utilise
\verb+tablor+ car elles définissent toutes deux différemment l'environnement \verb+VerbatimOut+.
@@ -314,14 +338,14 @@ et là il faut ajouter
-% \begin{figure}
+% \begin{figure}[!h]
% %\begin{DANGER}
% Le fichier \texttt{tablor.sty} est codé en \texttt{latin-1}. Les utilisateurs de
% \texttt{utf-8} devront donc utiliser \texttt{tablorutf8.sty} à la place.
% %\end{DANGER}
% \end{figure}
-\pagebreak
+%\pagebreak
\section{Comment l'utiliser~?}
@@ -343,7 +367,7 @@ Le préambule sera toujours~:
-% \begin{figure}
+% \begin{figure}[!h]
% \begin{Idee}
% Les fontes utilisées dans les tableaux sont \verb+[upright]{fourier}+. Il est tout à
% fait possible d'utiliser d'autres fontes. Il suffit de modifier le fichier
@@ -581,7 +605,55 @@ ou bien, selon les cas~:
\end{lstlisting}
+\section{Facteur de réduction}
+Si vous trouvez le tableau trop grand, vous pouvez utilisez la commande
+\verb+\ech{nombre}+ où \texttt{nombre} représente le coefficienr de
+réduction ou d'agrandissement du tableau.
+
+Par exemple, comparez~:
+
+ \begin{lstlisting}
+\begin{TV}
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
+\end{TV}
+ \end{lstlisting}
+
+ \begin{center}
+
+
+\begin{TV}
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
+\end{TV}
+
+\end{center}
+
+et
+
+ \begin{lstlisting}
+\ech{0.7}
+\begin{TV}
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
+\end{TV}
+\ech{1}
+ \end{lstlisting}
+
+ \begin{center}
+
+ \ech{0.7}
+\begin{TV}
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
+\end{TV}
+\ech{1}
+
+\end{center}
+
+\begin{figure}[!h]
+ \begin{DANGER}{Remise à l'échelle 1}
+ N'oubliez pas de remettre à l'échelle 1 en entrant à la
+ suite de l'environnement \verb+\ech{1}+
+ \end{DANGER}
+ \end{figure}
\section{Tableaux des variations}
@@ -594,7 +666,7 @@ L'environnement s'appelle \texttt{TV}. On utilise une commande au format \texttt
\xcas
\begin{lstlisting}
-TV([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,t,\tv)
+TV([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,lignes,trigo,\tv)
\end{lstlisting}
\begin{itemize}
@@ -602,16 +674,18 @@ TV([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expr
\item \texttt{[borne inf,borne sup]} désigne les bornes de l'ensemble de définition. On note
$+\infty$~:~\texttt{+infinity} et $-\infty$~:~\texttt{-infinity}. N'oubliez pas
les crochets~!
-\item \texttt{[valeurs interdites]} désigne la liste des valeurs interdites;
+\item \texttt{[valeurs interdites]} désigne la liste des valeurs interdites~;
\item \texttt{"nom fonction"} désigne la lettre représentant la fonction telle que vous voulez
qu'elle apparaisse : $f$, $g$, $\varphi$, etc.
\item \texttt{"nom variable"}~:~même chose pour la variable, selon que vous voulez la désigner par
$x$, $t$, etc. N'oubliez pas les guillemets~!
\item \texttt{expression en fonction de x} désigne l'expression de la fonction. Attention~! Utilisez
- ici toujours $x$ pour désigner la variable;
-\item le paramètre \texttt{t} est à remplacer par 1 si vous voulez voir apparaître une ligne
+ ici toujours $x$ pour désigner la variable~;
+\item le paramètre \texttt{lignes} est à remplacer par 1 si vous voulez voir apparaître une ligne
avec le signe de la dérivée, par 0 si vous ne voulez pas de cette ligne et par 2 si vous ne voulez
- que le signe de la dérivée.
+ que le signe de la dérivée~;
+\item le paramètre \texttt{trigo} est à remplacer par \texttt{t} si la
+ fonction étudiée est trigonométrique et par tout autre symbole sinon~;
\item on termine par \verb+\tv+, une commande permettant de numéroter les tableaux en interne.
\end{itemize}
@@ -627,7 +701,7 @@ Voyons à présent quelques exemples.
On obtient~:
\begin{TV}
-TV([-5,7],[],"f","x",x^2,0,\tv);
+TV([-5,7],[],"f","x",x^2,0,n,\tv);
\end{TV}
@@ -635,7 +709,7 @@ après avoir entré~:
\begin{lstlisting}
\begin{TV}
-TV([-5,7],[],"f","x",x^2,0,\tv)
+TV([-5,7],[],"f","x",x^2,0,n,\tv)
\end{TV}
\end{lstlisting}
@@ -645,12 +719,12 @@ TV([-5,7],[],"f","x",x^2,0,\tv)
\begin{lstlisting}
\begin{TV}
-TV([-infinity,+infinity],[],"f","x",x^2,1,\tv)
+TV([-infinity,+infinity],[],"f","x",x^2,1,n,\tv)
\end{TV}
\end{lstlisting}
\begin{TV}
-TV([-infinity,+infinity],[],"f","x",x^2,1,\tv)
+TV([-infinity,+infinity],[],"f","x",x^2,1,n,\tv)
\end{TV}
\item Avec la même fonction sur \textbf{R} avec uniquement le signe de la dérivée~:
@@ -659,12 +733,12 @@ TV([-infinity,+infinity],[],"f","x",x^2,1,\tv)
\begin{lstlisting}
\begin{TV}
-TV([-infinity,+infinity],[],"f","x",x^2,2,\tv)
+TV([-infinity,+infinity],[],"f","x",x^2,2,n,\tv)
\end{TV}
\end{lstlisting}
\begin{TV}
-TV([-infinity,+infinity],[],"f","x",x^2,2,\tv)
+TV([-infinity,+infinity],[],"f","x",x^2,2,n,\tv)
\end{TV}
@@ -674,7 +748,7 @@ TV([-infinity,+infinity],[],"f","x",x^2,2,\tv)
\begin{lstlisting}
\begin{TV}
-TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,\tv)
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
\end{TV}
\end{lstlisting}
@@ -682,12 +756,30 @@ TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,\tv)
\begin{TV}
-TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,\tv)
+TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv)
\end{TV}
\end{center}
+\item Pour la fonction $x\mapsto \sin(x)+\frac{1}{2}$ on n'oublie pas le
+ paramètre \texttt{t}~:
+
+ \begin{lstlisting}
+\begin{TV}
+TV([-pi,pi],[],"g","t",sin(x)+1/2,1,t,\tv)
+\end{TV}
+ \end{lstlisting}
+
+ \begin{center}
+\begin{TV}
+TV([-pi,pi],[],"g","t",sin(x)+1/2,1,t,\tv)
+\end{TV}
+\end{center}
+
+
+
+
\item Il y aura des problèmes pour des équations $f'(x)=0$ que \texttt{XCAS} ne saurait pas résoudre
de manière formelle. Il faudrait alors utiliser une résolution numérique et remplacer
\texttt{resoudre} par \texttt{fsolve}. Mais dans les études demandées au Bac, l'étude des signes
@@ -710,19 +802,19 @@ On utilise alors l'environnement \texttt{TVZ} (Z comme zone...).
\begin{lstlisting}
\begin{TVZ}
- TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,\tv)
+ TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,\tv)
\end{TVZ}
\end{lstlisting}
\begin{center}
\begin{TVZ}
- TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,\tv)
+ TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,\tv)
\end{TVZ}
\end{center}
-\begin{figure}
+\begin{figure}[!h]
\begin{DANGER}{Listes des intervalles interdits}
Le troisième argument est une liste d'intervalles : la liste des «~zones interdites~»
qui peut éventuellemnt se réduire à un seul intervalle comme dans l'exemple précédent.
@@ -735,7 +827,7 @@ Voici un exemple comportant plusieurs zones in
\begin{lstlisting}
\begin{TVZ}
- TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,\tv)
+ TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,n,\tv)
\end{TVZ}
\end{lstlisting}
@@ -743,7 +835,7 @@ Voici un exemple comportant plusieurs zones in
\begin{center}
\begin{TVZ}
- TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,\tv)
+ TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,n,\tv)
\end{TVZ}
\end{center}
@@ -756,7 +848,7 @@ Si l'on veut mettre en évidence les solutions de l'équation $f(x)=a$, on uti
La syntaxe est~:
\begin{lstlisting}
-TVI([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,t,a,\tv)
+TVI([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,t,a,trigo,\tv)
\end{lstlisting}
Les paramètres sont les mêmes que pour \texttt{TV} mais on ajoute la valeur \texttt{a} bien sûr.
@@ -766,7 +858,7 @@ Par exemple, pour $f~:~x\mapsto \frac{x^2}{x^2-1}$ et l'équation $f(x)=10$ on en
\begin{lstlisting}
\begin{TVI}
-TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,\tv)
+TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,n,\tv)
\end{TVI}
\end{lstlisting}
@@ -774,7 +866,7 @@ TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,\tv)
et on obtient~:
\begin{TVI}
-TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,\tv)
+TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,n,\tv)
\end{TVI}
Les solutions sont notées $\alpha_1$, $\alpha_2$, etc.
@@ -784,7 +876,7 @@ Si l'équation est plutôt $f(x)=-1$~:
\begin{lstlisting}
\begin{TVI}
-TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,\tv)
+TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,n,\tv)
\end{TVI}
\end{lstlisting}
@@ -792,7 +884,7 @@ TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,\tv)
et on obtient~:
\begin{TVI}
-TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,\tv)
+TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,n,\tv)
\end{TVI}
@@ -823,7 +915,7 @@ On étudie d'abord la fonction $x\mapsto g'(x)$~:
% \begin{TVIapp}
-% TVIapp([0,+infinity],[0],"g'","x",diff(ln(x)-x*exp(2-x),x),1,0,\tv)
+% TVIapp([0,+infinity],[0],"g'","x",diff(ln(x)-x*exp(2-x),x),1,0,n,\tv)
% \end{TVIapp}
\stepcounter{TVn}
@@ -860,18 +952,19 @@ La syntaxe est la suivante~:
\begin{lstlisting}
\begin{TVP}
-TVP(IE,VI,["x","y"],"t",[x(t),y(t)],a,trigo,\tv)
+TVP(IE,VI,["x","y"],"t",[x(t),y(t)],a,trigo,n,\tv)
\end{TVP}
\end{lstlisting}
avec \texttt{IE} l'intervalle d'étude, \texttt{VI} la liste des listes de valeurs interdites
respectives pour les deux fonctions, \texttt{a} pour avoir un tableau complet ou partiel comme dans
-les autres "TV", enfin \texttt{trigo} qui vaut 1 si interviennent des fonctions trigonométrqiues, 0
+les autres "TV", enfin \texttt{trigo} qui vaut \texttt{t} si interviennent des
+fonctions trigonométrqiues, autre chose
sinon.
-\begin{figure}[h]
+\begin{figure}[!h]
\begin{DANGER}{Version de XCAS}
L'utilisation de TVP implique l'utilisation d'une version de XCAS d'une date postérieure au 14 juin
2008 !
@@ -892,13 +985,13 @@ sinon.
\begin{lstlisting}
\begin{TVP}
- TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv)
+ TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv)
\end{TVP}
\end{lstlisting}
\begin{TVP}
- TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv)
+ TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv)
\end{TVP}
@@ -919,14 +1012,14 @@ y(t)=\frac{t^2(t+2)}{t+1}
\begin{lstlisting}
\begin{TVP}
-TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,0,\tv)
+TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,\tv)
\end{TVP}
\end{lstlisting}
\begin{TVP}
-TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,0,\tv)
+TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,\tv)
\end{TVP}
@@ -957,7 +1050,7 @@ TSa(-2,3,-1,5,\tv);
-\begin{figure}[h]
+\begin{figure}[!h]
\begin{DANGER}{Nouveauté à partir de la version 2.08}
Par souci de cohérence avec l'environnement TSq, on doit rajouter maintenant en premier argument le
nom de la fonction produit dans l'environnement TS.
@@ -977,7 +1070,7 @@ précisant l'intervalle d'étude~:
\begin{lstlisting}
\begin{TS}
- TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],\tv);
+ TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],n,\tv);
\end{TS}
\end{lstlisting}
@@ -985,7 +1078,7 @@ On obtient~:
\begin{TS}
- TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],\tv);
+ TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],n,\tv);
\end{TS}
@@ -994,13 +1087,13 @@ Ou bien, sur un intervalle borné~:
\begin{lstlisting}
\begin{TS}
-TS("f",[x-10,x+10],[-15,10],\tv)
+TS("f",[x-10,x+10],[-15,10],n,\tv)
\end{TS}
\end{lstlisting}
\begin{TS}
-TS("f",[x-10,x+10],[-15,10],\tv)
+TS("f",[x-10,x+10],[-15,10],n,\tv)
\end{TS}
@@ -1012,7 +1105,7 @@ On entre dans deux listes différentes les facteurs du numérateur et du dénominat
\begin{lstlisting}
\begin{TSq}
-TSq("nom du quotient",[liste des facteurs du numérateur],[liste des facteurs du dénominateur],[inf,sup])
+TSq("nom du quotient",[liste des facteurs du numérateur],[liste des facteurs du dénominateur],[inf,sup],trigo,\tv)
\end{TSq}
\end{lstlisting}
@@ -1020,7 +1113,7 @@ Par exemple, pour étudier le signe de $\frac{(-2x+3)(-4x+5)}{(x^2-16)(x-2)}$ sur
\begin{lstlisting}
\begin{TSq}
-TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],\tv)
+TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],n,\tv)
\end{TSq}
\end{lstlisting}
@@ -1028,21 +1121,21 @@ TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],\tv)
\begin{TSq}
-TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],\tv)
+TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],n,\tv)
\end{TSq}
-Sur un intervalle borné~:
+% Sur un intervalle borné~:
-\begin{lstlisting}
-\begin{TSq}
-TSq("Q",[x-10],[x+10],[-infinity,10],\tv)
-\end{TSq}
-\end{lstlisting}
+% \begin{lstlisting}
+% \begin{TSq}
+% TSq("Q",[x-10],[x+10],[-infinity,10],n,\tv)
+% \end{TSq}
+% \end{lstlisting}
-\begin{TSq}
-TSq("Q",[x-10],[x+10],[-infinity,10],\tv)
-\end{TSq}
+% \begin{TSq}
+% TSq("Q",[x-10],[x+10],[-infinity,10],n,\tv)
+% \end{TSq}
@@ -1055,14 +1148,14 @@ l'expression étudiée et l'intervalle considéré~:
\begin{lstlisting}
\begin{TSc}
-TSc((x-10)*(x+5),[-10,10],\tv)
+TSc((x-10)*(x+5),[-10,10],n,\tv)
\end{TSc}
\end{lstlisting}
\begin{TSc}
-TSc((x-10)*(x+5),[-10,10],\tv)
+TSc((x-10)*(x+5),[-10,10],n,\tv)
\end{TSc}
@@ -1087,7 +1180,7 @@ Si vous tapez~:
\begin{lstlisting}
\begin{TV*}{100}
- TV([-1,+infinity],[],"f","x",x-ln(x+1),1,\tv)
+ TV([-1,+infinity],[],"f","x",x-ln(x+1),1,n,\tv)
\end{TV*}
\end{lstlisting}
@@ -1106,7 +1199,7 @@ Par exemple, je tape~:
\begin{lstlisting}
\begin{TS*}{100}
- TS("F",[3*x+2,5*x^2-1],[-50,50],\tv)
+ TS("F",[3*x+2,5*x^2-1],[-50,50],n,\tv)
\end{TS*}
\end{lstlisting}
@@ -1125,7 +1218,7 @@ automatiquement pour m'afficher le tableau voulu~:
\begin{center}
\begin{TS*}{105}
- TS("F",[3*x+2,5*x^2-1],[-50,50],\tv)
+ TS("F",[3*x+2,5*x^2-1],[-50,50],n,\tv)
\end{TS*}
\end{center}
@@ -1191,6 +1284,7 @@ dans un fichier \texttt{latex-tempo}:
"\""(p "nom de la variable :")"\","
""(p "expression de la fonction (utiliser x) :")","
""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")","
+""(p "trigo ?(t:trigo, n:non trigo) :")","
"\\tv)" n>
"\\end{TV}" n>
"\\end{center}" > % ))
@@ -1203,6 +1297,7 @@ dans un fichier \texttt{latex-tempo}:
"\""(p "nom de la variable :")"\","
""(p "expression de la fonction (utiliser x) :")","
""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")","
+""(p "trigo ?(t:trigo, n:non trigo) :")","
""(p "f(x)=l pour la valeur l :")","
"\\tv)" n>
"\\end{TVI}" n>
@@ -1212,7 +1307,8 @@ dans un fichier \texttt{latex-tempo}:
"\\begin{TS}" n>
"TS(\""(p "nom du produit :")"\","
"["(p "liste des facteurs (,) :")"],"
- "["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"],"
+ "["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"],"
+""(p "trigo ?(t:trigo, n:non trigo) :")","
"\\tv)" n>
"\\end{TS}" n>
"\\end{center}" > % ))
@@ -1223,6 +1319,7 @@ dans un fichier \texttt{latex-tempo}:
"["(p "liste des facteurs du numerateur (,) :")"],"
"["(p "liste des facteurs du denominateur (,) :")"],"
"["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"],"
+""(p "trigo ?(t:trigo, n:non trigo) :")","
"\\tv)" n>
"\\end{TSq}" n>
"\\end{center}" > % ))
@@ -1238,7 +1335,7 @@ dans un fichier \texttt{latex-tempo}:
"["(p "expression de la fonction x (utiliser t) :")","
""(p "expression de la fonction y (utiliser t) :")"],"
""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")","
- ""(p "1 si fonctions trigo, 0 sinon :")","
+ ""(p "t si fonctions trigo, n sinon :")","
"\\tv)" n>
"\\end{TVP}" n>
"\\end{center}" > % ))
@@ -1253,6 +1350,7 @@ dans un fichier \texttt{latex-tempo}:
"\""(p "nom de la variable :")"\","
""(p "expression de la fonction (utiliser x) :")","
""(p "type de tableau (1:complet, 0:sans signe, 2:que le signe) :")","
+""(p "trigo ?(t:trigo, n:non trigo) :")","
"\\tv)" n>
"\\end{TV}" n>
"\\end{center}" > % ))
@@ -1267,133 +1365,127 @@ Voici quelques exemples de tableaux~:
\begin{lstlisting}
\begin{TVI}
-TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,\tv)
+TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,n,\tv)
\end{TVI}
\end{lstlisting}
\begin{TVI}
-TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,\tv)
+TVI([-1,+infinity],[-1],"f","x",x^2/sqrt(x+1)-1,1,2,n,\tv)
\end{TVI}
\begin{lstlisting}
\begin{TVI}
-TVI([-1/2,+infinity],[],"f","x",x^2,1,2,\tv)
+TVI([-1/2,+infinity],[],"f","x",x^2,1,2,n,\tv)
\end{TVI}
\end{lstlisting}
\begin{TVI}
-TVI([-1/2,+infinity],[],"f","x",x^2,1,2,\tv)
+TVI([-1/2,+infinity],[],"f","x",x^2,1,2,n,\tv)
\end{TVI}
\begin{lstlisting}
\begin{TVI}
-TVI([0,+infinity],[0],"f","x",ln(x),1,2,\tv)
+TVI([0,+infinity],[0],"f","x",ln(x),1,2,n,\tv)
\end{TVI}
\end{lstlisting}
\begin{TVI}
-TVI([0,+infinity],[0],"f","x",ln(x),1,2,\tv)
+TVI([0,+infinity],[0],"f","x",ln(x),1,2,n,\tv)
\end{TVI}
\stepcounter{TVn}
\begin{lstlisting}
\begin{TV}
-TV([1,+infinity],[],"f","x",-ln(x),1,\tv)
+TV([1,+infinity],[],"f","x",-ln(x),1,n,\tv)
\end{TV}
\end{lstlisting}
\begin{TV}
-TV([1,+infinity],[],"f","x",-ln(x),1,\tv)
+TV([1,+infinity],[],"f","x",-ln(x),1,n,\tv)
\end{TV}
\begin{lstlisting}
\begin{TVI}
-TVI([-pi,pi],[],"f","x",cos(x),1,1/2,\tv)
+TVI([-pi,pi],[],"f","x",cos(x),1,1/2,t,\tv)
\end{TVI}
\end{lstlisting}
\begin{TVI}
-TVI([-pi,pi],[],"f","x",cos(x),1,1/2,\tv)
+TVI([-pi,pi],[],"f","x",cos(x),1,1/2,t,\tv)
\end{TVI}
\begin{lstlisting}
\begin{TV}
-TV([0,2*pi],[],"f","x",cos(x),1,\tv)
+TV([0,2*pi],[],"f","x",cos(x),1,t,\tv)
\end{TV}
\end{lstlisting}
\begin{TV}
-TV([0,2*Pi],[],"f","x",cos(x),1,\tv)
+TV([0,2*Pi],[],"f","x",cos(x),1,t,\tv)
\end{TV}
-\begin{figure}
- \begin{DANGER}{Fonctions périodiques}
- Il y aura des problèmes si vous demandez un tableau des variations d'une fonction
- périodique sur un intervalle
- d'amplitude supérieure à la période, mais est-ce vraiment utile ?...
- \end{DANGER}
- \end{figure}
+
\begin{lstlisting}
\begin{TVI}
-TVI([0,pi],[pi/2],"h","t",tan(x),1,7,\tv)
+TVI([0,pi],[pi/2],"h","t",tan(x),1,7,t,\tv)
\end{TVI}
\end{lstlisting}
\begin{TVI}
-TVI([0,pi],[pi/2],"h","t",tan(x),1,7,\tv)
+TVI([0,pi],[pi/2],"h","t",tan(x),1,7,t,\tv)
\end{TVI}
\begin{lstlisting}
\begin{TVI}
-TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,\tv)
+TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,n,\tv)
\end{TVI}
\end{lstlisting}
\begin{TVI}
-TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,\tv)
+TVI([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,n,\tv)
\end{TVI}
\begin{lstlisting}
\begin{TV}
-TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,\tv)
+TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,n,\tv)
\end{TV}
\end{lstlisting}
\begin{TV}
-TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,\tv)
+TV([-1,+infinity],[-1],"f","x",ln(1+x)-(x-x^2/2+x^3/3),1,n,\tv)
\end{TV}
\begin{lstlisting}
\begin{TS}
-TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],\tv);
+TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],n,\tv);
\end{TS}
\end{lstlisting}
\begin{TS}
-TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],\tv);
+TS("G",[-2*x+3,x-1,x+1,x^2+3*x+1],[-10,+infinity],n,\tv);
\end{TS}
\begin{lstlisting}
\begin{TVI}
-TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,\tv)
+TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,n,\tv)
\end{TVI}
\end{lstlisting}
\begin{TVI}
-TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,\tv)
+TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,n,\tv)
\end{TVI}
@@ -1401,12 +1493,12 @@ TVI([-infinity,+infinity],[],"f","x",(x+2)*exp(x-1)-1,1,0,\tv)
\begin{lstlisting}
\begin{TVI}
-TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,\tv)
+TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,n,\tv)
\end{TVI}
\end{lstlisting}
\begin{TVI}
-TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,\tv)
+TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,n,\tv)
\end{TVI}
\stepcounter{TVn}
@@ -1414,12 +1506,12 @@ TVI([-infinity,+infinity],[],"f","x",1+(-2*x+1)*exp(2*x),1,0,\tv)
\begin{lstlisting}
\begin{TV}
-TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,\tv)
+TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,n,\tv)
\end{TV}
\end{lstlisting}
\begin{TV}
-TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,\tv)
+TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,n,\tv)
\end{TV}
@@ -1428,91 +1520,91 @@ TV([0,+infinity],[],"f","x",ln(exp(x)+x)-x,1,\tv)
\begin{lstlisting}
\begin{TVI}
-TVI([0,pi],[],"f","x",cos(x)-x,1,0,\tv)
+TVI([0,pi],[],"f","x",cos(x)-x,1,0,n,\tv)
\end{TVI}
\end{lstlisting}
\begin{TVI}
-TVI([0,pi],[],"f","x",cos(x)-x,1,0,\tv)
+TVI([0,pi],[],"f","x",cos(x)-x,1,0,n,\tv)
\end{TVI}
\begin{lstlisting}
\begin{TVI}
-TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,\tv)
+TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,n,\tv)
\end{TVI}
\end{lstlisting}
\begin{TVI}
-TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,\tv)
+TVI([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,n,\tv)
\end{TVI}
\begin{lstlisting}
\begin{TSc}
-TSc((x-10)*(x+10),[-10,10],\tv)
+TSc((x-10)*(x+10),[-10,10],n,\tv)
\end{TSc}
\end{lstlisting}
\begin{TSc}
-TSc((x-10)*(x+10),[-10,10],\tv)
+TSc((x-10)*(x+10),[-10,10],n,\tv)
\end{TSc}
\begin{lstlisting}
\begin{TVZ}
- TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,\tv)
+ TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,n,\tv)
\end{TVZ}
\end{lstlisting}
\begin{TVZ}
- TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,\tv)
+ TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",(sqrt(x^2-1))*(x^2-4),1,n,\tv)
\end{TVZ}
\begin{lstlisting}
\begin{TVZ}
- TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,\tv)
+ TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,n,\tv)
\end{TVZ}
\end{lstlisting}
\begin{TVZ}
- TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,\tv)
+ TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",ln(x^2-1),1,n,\tv)
\end{TVZ}
\begin{lstlisting}
\begin{TVP}
-TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv)
+TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv)
\end{TVP}
\end{lstlisting}
\begin{TVP}
-TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,1,\tv)
+TVP([0,pi/2],[[],[]],["x","y"],"t",[cos(3*t),sin(4*t)],1,t,\tv)
\end{TVP}
\begin{lstlisting}
\begin{TVP}
-TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,1,\tv)
+TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,t,\tv)
\end{TVP}
\end{lstlisting}
\begin{TVP}
-TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,1,\tv)
+TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,t,\tv)
\end{TVP}
\begin{lstlisting}
\begin{TVZ}
- TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,\tv)
+ TVZ([-infinity,+infinity],[-1,1,4,6],[[-1,1],[4,6]],"f","x",ln((x-5)^2-1)+ln(x^2-1),1,n,\tv)
\end{TVZ}
\end{lstlisting}
@@ -1520,175 +1612,212 @@ TVP([0,2*pi],[[],[]],["x","y"],"t",[t-2*sin(t),-1+2*cos(t)],1,1,\tv)
\begin{center}
\begin{TVZ}
- TVZ([-infinity,+infinity],[],[[-1,1],[4,6]],"f","x",sqrt((x-5)^2-1)+sqrt(x^2-1),1,\tv)
+ TVZ([-infinity,+infinity],[],[[-1,1],[4,6]],"f","x",sqrt((x-5)^2-1)+sqrt(x^2-1),1,n,\tv)
\end{TVZ}
\end{center}
-\lat
+
\begin{lstlisting}
-\begin{enumerate}
-\item
+ \begin{TVP}
+ TVP([0,pi/2],[[],[]],["f","g"],"t",[(sin(3*t)),(sin(4*t))],1,t,\tv)
+ \end{TVP}
+\end{lstlisting}
+
+
+\begin{center}
+ \begin{TVP}
+ TVP([0,pi/2],[[],[]],["f","g"],"t",[(sin(3*t)),(sin(4*t))],1,t,\tv)
+ \end{TVP}
+ \end{center}
+
+\begin{lstlisting}
+\begin{TS}
+ TS(" f ",[cos(x)-1/2,sin(x)+1/2],[0,2*pi],t,\tv)
+\end{TS}
+\end{lstlisting}
+
- Selon le tableau de variation de la fonction $f$
- ci-dessous, on peut affirmer que \ldots
+\begin{center}
+\begin{TS}
+ TS(" f ",[cos(x)-1/2,sin(x)+1/2],[0,2*pi],t,\tv)
+\end{TS}
+\end{center}
+
+
+
+
+
+
+
+
+
+
+% \lat
+
+% \begin{lstlisting}
+% \begin{enumerate}
+% \item
+
+% Selon le tableau de variation de la fonction $f$
+% ci-dessous, on peut affirmer que \ldots
-\begin{TV}
- TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,\tv)
-\end{TV}
+% \begin{TV}
+% TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,n,\tv)
+% \end{TV}
-\VF
-\begin{itemize}
+% \VF
+% \begin{itemize}
- \item[\ldots] 5 n'a pas d'antécédent \Rep
- \item[\ldots] 5 n'a pas d'image \Rep
- \item[\ldots] 5 a deux antécédents \Rep
- \item[\ldots] 5 a une image supérieure à celle de $\sqrt{2}$\Rep
+% \item[\ldots] 5 n'a pas d'antécédent \Rep
+% \item[\ldots] 5 n'a pas d'image \Rep
+% \item[\ldots] 5 a deux antécédents \Rep
+% \item[\ldots] 5 a une image supérieure à celle de $\sqrt{2}$\Rep
-\end{itemize}
+% \end{itemize}
-\item Soit $f$ la fonction définie par $f~:~x\mapsto 3x^3-5x^2+2x-7$. Les tableaux suivants peuvent
- correspondre à $f$~:
+% \item Soit $f$ la fonction définie par $f~:~x\mapsto 3x^3-5x^2+2x-7$. Les tableaux suivants peuvent
+% correspondre à $f$~:
-\VF
+% \VF
- \begin{enumerate}
+% \begin{enumerate}
- \item Tableau 1 \Rep
+% \item Tableau 1 \Rep
-\begin{TV}
- TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,\tv)
-\end{TV}
+% \begin{TV}
+% TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,n,\tv)
+% \end{TV}
-\item Tableau 2 \Rep
+% \item Tableau 2 \Rep
-\begin{TV}
- TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,\tv)
-\end{TV}
+% \begin{TV}
+% TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,n,\tv)
+% \end{TV}
-\item Tableau 3 \Rep
+% \item Tableau 3 \Rep
-\begin{TSc}
- TSc(-3*x^3+5*x^2-2*x+7,[-20,20],\tv)
-\end{TSc}
+% \begin{TSc}
+% TSc(-3*x^3+5*x^2-2*x+7,[-20,20],n,\tv)
+% \end{TSc}
-\item Tableau 4 \Rep
+% \item Tableau 4 \Rep
-\begin{TSc}
- TSc(3*x^3-5*x^2+2*x-7,[-20,20],\tv)
-\end{TSc}
+% \begin{TSc}
+% TSc(3*x^3-5*x^2+2*x-7,[-20,20],n,\tv)
+% \end{TSc}
-\end{enumerate}
+% \end{enumerate}
-\end{enumerate}
+% \end{enumerate}
-\end{lstlisting}
+% \end{lstlisting}
-\begin{enumerate}
-\item
+% \begin{enumerate}
+% \item
- Selon le tableau de variation de la fonction $f$
- ci-dessous, on peut affirmer que \ldots
+% Selon le tableau de variation de la fonction $f$
+% ci-dessous, on peut affirmer que \ldots
-\begin{TV}
- TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,\tv)
-\end{TV}
+% \begin{TV}
+% TV([-5,10],[],"f","x",(5/2)*x^2-2*x+12,0,n,\tv)
+% \end{TV}
-\VF
-\begin{itemize}
+% \VF
+% \begin{itemize}
- \item[\ldots] 5 n'a pas d'antécédent \Rep
- \item[\ldots] 5 n'a pas d'image \Rep
- \item[\ldots] 5 a deux antécédents \Rep
- \item[\ldots] 5 a une image supérieure à celle de $\sqrt{2}$\Rep
+% \item[\ldots] 5 n'a pas d'antécédent \Rep
+% \item[\ldots] 5 n'a pas d'image \Rep
+% \item[\ldots] 5 a deux antécédents \Rep
+% \item[\ldots] 5 a une image supérieure à celle de $\sqrt{2}$\Rep
-\end{itemize}
+% \end{itemize}
-\item Soit $f$ la fonction définie par $f~:~x\mapsto 3x^3-5x^2+2x-7$. Les tableaux suivants peuvent-ils
- correspondre à la fonction $f$~:
+% \item Soit $f$ la fonction définie par $f~:~x\mapsto 3x^3-5x^2+2x-7$. Les tableaux suivants peuvent-ils
+% correspondre à la fonction $f$~:
-\VF
+% \VF
- \begin{enumerate}
+% \begin{enumerate}
- \item Tableau 1 \Rep
+% \item Tableau 1 \Rep
-\begin{TV}
- TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,\tv)
-\end{TV}
+% \begin{TV}
+% TV([-20,20],[],"f","x",3*x^3-5*x^2+2*x-7,0,n,\tv)
+% \end{TV}
-\item Tableau 2 \Rep
+% \item Tableau 2 \Rep
-\begin{TV}
- TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,\tv)
-\end{TV}
+% \begin{TV}
+% TV([-20,20],[],"f","x",-3*x^3+5*x^2-2*x+7,0,n,\tv)
+% \end{TV}
-\item Tableau 3 \Rep
+% \item Tableau 3 \Rep
-\begin{TSc}
- TSc(-3*x^3+5*x^2-2*x+7,[-20,20],\tv)
-\end{TSc}
+% \begin{TSc}
+% TSc(-3*x^3+5*x^2-2*x+7,[-20,20],n,\tv)
+% \end{TSc}
-\item Tableau 4 \Rep
+% \item Tableau 4 \Rep
-\begin{TSc}
- TSc(3*x^3-5*x^2+2*x-7,[-20,20],\tv)
-\end{TSc}
+% \begin{TSc}
+% TSc(3*x^3-5*x^2+2*x-7,[-20,20],n,\tv)
+% \end{TSc}
-\end{enumerate}
+% \end{enumerate}
-\end{enumerate}
+% \end{enumerate}
-\begin{lstlisting}
-On considère la fonction $f$ définie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$
+% \begin{lstlisting}
+% On considère la fonction $f$ définie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$
-Étudions sa dérivée~:
+% Étudions sa dérivée~:
-\begin{TVIapp}
- TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv)
- \end{TVIapp}
+% \begin{TVIapp}
+% TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv)
+% \end{TVIapp}
-On en déduit le tableau de variation de $f$
+% On en déduit le tableau de variation de $f$
-\begin{TVapp}
- TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv)
- \end{TVapp}
-\end{lstlisting}
+% \begin{TVapp}
+% TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv)
+% \end{TVapp}
+% \end{lstlisting}
-On considère la fonction $f$ définie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$
+% On considère la fonction $f$ définie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$
-Étudions sa dérivée~:
+% Étudions sa dérivée~:
-\begin{TVIapp}
- TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv)
- \end{TVIapp}
+% \begin{TVIapp}
+% TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv)
+% \end{TVIapp}
-On en déduit le tableau de variation de $f$
+% On en déduit le tableau de variation de $f$
-\begin{TVapp}
- TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv)
- \end{TVapp}
+% \begin{TVapp}
+% TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv)
+% \end{TVapp}
diff --git a/Master/texmf-dist/tex/latex/tablor/tablor.sty b/Master/texmf-dist/tex/latex/tablor/tablor.sty
index ebcb6445802..b759961e1a3 100644
--- a/Master/texmf-dist/tex/latex/tablor/tablor.sty
+++ b/Master/texmf-dist/tex/latex/tablor/tablor.sty
@@ -1,5 +1,5 @@
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
-\ProvidesPackage{tablor}[12/06/2008 v3.00 la machine a creer des tableaux de signes et variations]
+\ProvidesPackage{tablor}[08/10/2008 v4.00 la machine a creer des tableaux de signes et variations]
% \copyleft Connan le Barbare (aka Guillaume Connan) \copyright
% This work may be distributed and/or mofified under the conditions
@@ -18,29 +18,29 @@
% %%%%%% Pour des tableaux de plus de 2 facteurs
%
% \begin{TS}
-% TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[a,b],\tv);
+% TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[a,b],n,\tv);
% \end{TS}
%
% pour les tableaux de signes avec quotient
%\begin{TSq}
-%TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],\tv)
+%TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],n,\tv)
%%\end{TSq}
% un tableau de variation :
%
% \begin{TV}
-% TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,\tv)
+% TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,n,\tv)
% \end{TV}
%
% tableau de variation avec zones interdites
%
% \begin{TVZ}
-% TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,\tv)
+% TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,\tv)
% \end{TVZ}
%
%
% tableau avec valeurs intermediares
%\begin{TVI}
-%TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,\tv)
+%TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,\tv)
%\end{TVI}
%%%
% tableau de variations avec f' sans zero formel
@@ -62,12 +62,12 @@
%
% Courbes parametrees
% \begin{TVP}
-% TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,0,\tv)
+% TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,\tv)
% \end{TVP}
%
%
% \begin{TVP}
-% TVP([0,pi/2],[[],[]],["x","y"],"t",[2*cos(t),sin(2*t)],1,1,\tv)
+% TVP([0,pi/2],[[],[]],["x","y"],"t",[2*cos(t),sin(2*t)],1,t,\tv)
% \end{TVP}
% %
@@ -102,6 +102,7 @@
\newboolean{windows}\setboolean{windows}{false}
+
%% on configure tablor dans un fichier exterieur pour la plateforme
%% et l'editeur
@@ -162,7 +163,7 @@
%% Donne comme prefixe aux tableaux le prefixe courant
%% Peut-être modifie par \initablor
-\newcommand{\Tableaux}{\jobname}
+\newcommand{\nomtravail}{\jobname}
%% initialise les compteurs
@@ -179,17 +180,17 @@
\newcommand{\initablor}[1][\jobname]{%
-\renewcommand{\Tableaux}{#1}% Arret du nom des tableaux
+\renewcommand{\nomtravail}{#1}% Arret du nom des tableaux
\setcounter{TVn}{0}% Initialisation du compteur de tableaux.
\ifthenelse{\boolean{xcas}}% Avec l'option XCas
-{\IfFileExists{\Tableaux.Tab.mp}% Si Tableaux.mp est present...
- {\immediate\write18{\rem \Tableaux.Tab.mp}}% le detruire
+{\IfFileExists{\nomtravail.Tab.mp}% Si Tableaux.mp est present...
+ {\immediate\write18{\rem \nomtravail.Tab.mp}}% le detruire
{}%
- \immediate\write18{\cp enteteMP.cfg \Tableaux.Tab.mp}% Reconstituer l'entête de Tableaux.mp
+ \immediate\write18{\cp enteteMP.cfg \nomtravail.Tab.mp}% Reconstituer l'entête de Tableaux.mp
}
-{\IfFileExists{\Tableaux.Tab.mp}% Sans l'option XCas, si
+{\IfFileExists{\nomtravail.Tab.mp}% Sans l'option XCas, si
% Tableaux.mp existe
-{\immediate\write18{mpost -interaction=batchmode \Tableaux.Tab}}% l'executer pour reconstituer les figures
+{\immediate\write18{mpost -interaction=batchmode \nomtravail.Tab}}% l'executer pour reconstituer les figures
{\PackageWarning{tablor}{Pas de source metapost pour creer les tableaux.}}% sinon message d'erreur
% (mais pas d'arret car les tableaux
% peuvent être presents )
@@ -224,12 +225,52 @@
\begin{VerbatimOut}{XcasTV.cxx}
-TV(L,F,nom,nomv,f,ftt,nmr):={
+TV(L,F,nom,nomv,f,ftt,trigo,nmr):={
nl:=size(L);
f:=unapply(f,x);
fp:=fonction_derivee(f);
Z:=concat(L,F);
+S:=[];
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k<ns;k++){
+m:=0;
+while(evalf(simplifier(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
S:=resoudre(fp(x),x);
+}
+
+
+ si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
+ qq:=member(simplifier(S[j]),Z)==0;
+ kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
+ if(kk==1){if(qq==1){Z:=append(Z,simplifier(S[j]))}};
+ fpour
+ fsi;
+Z:=sort(Z);
+nz:=size(Z);
+
+
+ tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z);
+ ftantque;
+
+
+
+
+
+
+
si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
if(kk==1){Z:=append(Z,simplifier(S[j]))};
@@ -360,7 +401,7 @@ fclose(sortie);
\begin{VerbatimOut}{XcasTVZ.cxx}
-TVZ(L,F,FF,nom,nomv,f,ftt,nmr):={
+TVZ(L,F,FF,nom,nomv,f,ftt,trigo,nmr):={
nl:=size(L);
nf:=size(FF);
Ff:=NULL;IMIN:=NULL;IMAX:=NULL;
@@ -382,7 +423,32 @@ for(k:=0;k<nf;k++){
Z:=concat(Z,FF[k]);
}
+S:=[];
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k<ns;k++){
+m:=0;
+while(evalf(simplifier(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
S:=resoudre(fp(x),x);
+}
+
+
+
+
+
+
si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
for(k:=0;k<nf;k++){
kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
@@ -584,10 +650,22 @@ f:=unapply(f,x);
fp:=fonction_derivee(f);
z0:=concat(L,F);z:=sort(z0);
nz:=size(z);
-if(L==[-infinity,+infinity]){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..100);}
-else{if(L[0]==-infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..L[1]);}
-else{if(L[1]==+infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=L[0]..100);}
-else{S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=z[0]..z[nz-1])}}};
+
+
+
+
+
+
+S:=NULL;
+if(L==[-infinity,+infinity]){j:=[seq(-100+k,k=0..200)]minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[0]==-infinity){j:=[seq(k,k=100..floor(L[1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[1]==+infinity){j:=[seq(k,k=floor(L[0])..100)] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for;}
+else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for; }}};
+
+
+
+
+
si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]);
if(kk==1){if(kok==1){z:=append(z,simplifier(S[j]))}};
@@ -746,12 +824,32 @@ fclose(sortie);
\begin{VerbatimOut}{XcasTVI.cxx}
-TVI(L,F,nom,nomv,f,ftt,ao,nmr):={
+TVI(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={
nl:=size(L);
f:=unapply(f,x);
fp:=fonction_derivee(f);
Z:=concat(L,F);
+S:=[];
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(fp(x))),x);
+ns:=size(SS);
+for(k:=0;k<ns;k++){
+m:=0;
+while(evalf(simplifier(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m-1;
+}
+}
+}else{
S:=resoudre(fp(x),x);
+}
+
si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
if(kk==1){Z:=append(Z,simplifier(S[j]))};
@@ -963,10 +1061,24 @@ f:=unapply(f,x);
fp:=fonction_derivee(f);
z0:=concat(L,F);z:=sort(z0);
nz:=size(z);
-if(L==[-infinity,+infinity]){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..100);}
-else{if(L[0]==-infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..L[1]);}
-else{if(L[1]==+infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=L[0]..100);}
-else{S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=z[0]..z[nz-1])}}};
+
+
+
+
+
+S:=NULL;
+if(L==[-infinity,+infinity]){j:=[seq(-100+k,k=0..200)]minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[0]==-infinity){j:=[seq(k,k=100..floor(L[1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[1]==+infinity){j:=[seq(k,k=floor(L[0])..100)] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for;}
+else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for; }}};
+
+
+
+
+
+
+
+
si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]);
if(kk==1){if(kok==1){z:=append(z,simplifier(S[j]))}};
@@ -1186,8 +1298,6 @@ fclose(sortie);
\begin{VerbatimOut}{XcasTVP.cxx}
-
-
TVP(L,F,nom,nomv,ff,ftt,trigo,nmr):={
//local Z,LLL,FFF,nl,fp,f,S,d,t,ns,k,m,x,j,kk,nz,u,l0;
nl:=size(L);
@@ -1196,61 +1306,71 @@ S:=[];
f:=ff;
Z:=[];
LLL:=[];
+
+
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+
for(d:=0;d<=1;d++){
f:=subst(f,f[d]=unapply(f[d],t));
fp:=append(fp,fonction_derivee(f[d]));
LLL:=concat(L,F[d]);
Z:=LLL union Z;
+SS:=resoudre(factor(simplifier(fp[d](t))),t);
+ns:=size(SS);
-ns:=size(resoudre(factor(simplifier(fp[d](t))),t));
-reset_solve_counter(0);
for(k:=0;k<ns;k++){
-if(trigo==1){
-all_trig_solutions:=1;
-reset_solve_counter(-1,-1);m:=0;
-while(simplifier(subst(resoudre(factor(simplifier(fp[d](t))),t)[k],n_1=m))<=evalf(L[nl-1])){
-reset_solve_counter(-1,-1);
-S:=concat(S,simplifier(subst(resoudre(factor(simplifier(fp[d](t))),t)[k],n_1=m)));m:=m+1;
-reset_solve_counter(-1,-1);
+if(trigo==t){
+m:=0;
+while(evalf(simplifier(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
+
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m+1;
+
};m:=-1;
-while(evalf(subst(resoudre(factor(simplifier(fp[d](t))),t)[k],n_1=m))>=L[0]){
-reset_solve_counter(-1,-1);
-S:=concat(S,simplifier(subst(resoudre(factor(simplifier(fp[d](t))),t)[k],n_1=m)));m:=m-1;
-reset_solve_counter(-1,-1);
+while(evalf(subst(SS[k],n_1=m))>=L[0]){
+
+S:=concat(S,simplifier(subst(SS[k],n_1=m)));m:=m-1;
+
}
}else{
-S:=concat(S,resoudre(factor(simplifier(fp[d](x))),x));
+S:=concat(S,SS);
}
}
- si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
+
+
+ si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
qq:=member(simplifier(S[j]),Z)==0;
kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
if(kk==1){if(qq==1){Z:=append(Z,simplifier(S[j]))}};
fpour
fsi;
-
-Z:=sort(Z);
+Z:=sort(Z);
nz:=size(Z);
-
- tantque simplifier(Z[0])==simplifier(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z);
+ tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z);
ftantque;
+
+
+
nz:=size(Z);
u:=1;
tantque (u<nz-2) and (nz>2) faire
- tantque Z[u]==Z[u+1] faire
+ tantque evalf(Z[u])==evalf(Z[u+1]) faire
Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=size(Z);
ftantque;
u:=u+1;
ftantque;
- };
-Z:=sort(Z);
+ };
+
+Z:=sort(Z);
nz:=size(Z);
+
+
l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:="",""; lf:="","";lsp:="","";
pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
";fpour;
@@ -1263,14 +1383,15 @@ for(d:=0;d<=1;d++){
FFF[d]:=concat(F[d],[-infinity,+infinity]);
k0:= evalf(limite(f[d](x),x=Z[0],1))> evalf(limite(f[d](x),x=Z[1],-1));
kz:=evalf(limite(f[d](x),x=Z[nz-1],-1))> evalf(limite(f[d](x),x=Z[nz-2],1));
-
+//}
+//$
lsi[d]:=lsic+nom[d]+"'("+nomv+")}$ etex);"+if(member(Z[0],FFF[d])==0){"valBarre(btex $"+latex(simplifier(fp[d](Z[0])))+"$ etex);"}else{if(Z[0]==-infinity){" "}else{"nonDefBarre;
"}}+
if(Z[0]==-infinity){if(sign(evalf(fp[d](if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F[d])==0){
if(sign(fp[d](Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{
if(sign(fp[d]((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}
-
-if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp[d](Z[r]+0.01))>0;
+
+if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp[d](Z[r]+0.01))>0;
lsp[d]:=lsp[d]+if(member(Z[r],F[d])==0){"valBarre(btex $"+latex(simplifier(fp[d](Z[r])))+"$ etex);"}else{"nonDefBarre;"}+
if(ksp==1){"plus;"}else{"moins;"}
}; }
@@ -1298,15 +1419,17 @@ lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex $"+latex(simplifier(fp[d](Z
for(d:=0;d<=1;d++){
K0[d]:= evalf(limite(f[d](x),x=Z[0],1))> evalf(limite(f[d](x),x=Z[1],-1));
Kz[d]:=evalf(limite(f[d](x),x,Z[nz-1],-1))> evalf(limite(f[d](x),x,Z[nz-2],1));
+//{
+//$
lm0[d]:=limite(f[d](x),x,Z[0],1)==-infinity;
li[d]:=lvic+nom[d]+"}$ etex);"+
if(member(Z[0],F[d])==0){"valPos(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[0],1)))}+"$ etex,"}
- else{"nonDefBarre;limDroite(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[0],1)))}+"$ etex,"}+
+ else{"nonDefBarre;limDroite(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[0],1)))}+"$ etex,"}+
if(K0[d]==1){"1"}else{"0"}+
");";
-
+
if(nz>2){ for(r:=1; r<=nz-2;r++){ krm[d]:=evalf(limite(f[d](x),x=Z[r-1],1))< evalf(limite(f[d](x),x=Z[r],-1));
- krp[d]:=evalf(limite(f[d](x),x=Z[r],1))> evalf(limite(f[d](x),x,Z[r+1],-1)) ;
+ krp[d]:=evalf(limite(f[d](x),x=Z[r],1))> evalf(limite(f[d](x),x,Z[r+1],-1)) ;
lmrm[d]:=limite(f[d](x),x,Z[r],-1)==-infinity;lmrp[d]:=limite(f[d](x),x,Z[r],1)==-infinity;
lp[d]:=lp[d]+if(member(Z[r],F[d])){
"limGauche(btex
@@ -1318,9 +1441,9 @@ lm0[d]:=limite(f[d](x),x,Z[0],1)==-infinity;
}; }
lnz[d]:=limite(f[d](x),x=Z[nz-1],-1)==-infinity;
- lf[d]:=if(member(Z[nz-1],F[d])==0){"valPos(btex $"+if(lnz[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[nz-1],-1)))}+"$ etex,"}+
+ lf[d]:=if(member(Z[nz-1],F[d])==0){"valPos(btex $"+if(lnz[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz[d]==1){"-\\infty"}else{latex(simplifier(limite(f[d](x),x,Z[nz-1],-1)))}+"$ etex,"}+
if(Kz[d]==1){"1);"}else{"0);
-"};
+"};
@@ -1403,8 +1526,6 @@ fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);
}:;
-
-
\end{VerbatimOut}
@@ -1420,22 +1541,58 @@ fclose(sortie);
\begin{VerbatimOut}{XcasTabSignL.cxx}
-TS(nomf,L,D,nmr):={
+TS(nomf,L,D,trigo,nmr):={
L:=apply(f->unapply(f,x),L)
n:=size(L);
Z:=NULL;
-
+nl:=size(L);
+S:=[];
mini:=D[0]; maxi:=D[1];
pour k de 0 jusque n-1 faire
- S:=resoudre(L[k](x),x);
+
+
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(L[k](x))),x);
+ns:=size(SS);
+for(j:=0;j<ns;j++){
+m:=0;
+while(evalf(simplifier(subst(SS[j],n_1=m)))<=evalf(maxi)){
+S:=concat(S,simplifier(subst(SS[j],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){
+S:=concat(S,simplifier(subst(SS[j],n_1=m)));m:=m-1;
+}
+}
+
+}else{
+S:=resoudre(L[k](x),x);
+}
+
+
+
+
si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
if(S[j]>mini and S[j]<maxi){Z:=Z,simplifier(S[j]);}
fpour;
fsi;
fpour;
+
+
+
+
+
Z:=sort(Z);
nz:=size(Z);
+
+
+
+
+
if(nz>2){pour u de 1 jusque nz-2 faire
si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1;
fsi;
@@ -1537,7 +1694,7 @@ fclose(sortie);
\begin{VerbatimOut}{XcasTabSignQ.cxx}
-TSq(nomf,L,Fo,D,nmr):={
+TSq(nomf,L,Fo,D,trigo,nmr):={
L:=apply(f->unapply(f,x),L);
Fo:=apply(f->unapply(f,x),Fo);
L:=concat(L,Fo);
@@ -1546,10 +1703,36 @@ Z:=NULL;
m:=size(Fo);
F:=NULL;FF:=NULL;
mini:=D[0]; maxi:=D[1];
-
+S:=[];
+SF:=[];
pour k de 0 jusque n-1 faire
- S:=resoudre(L[k](x),x);
+
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(L[k](x))),x);
+ns:=size(SS);
+for(j:=0;j<ns;j++){
+mm:=0;
+while(evalf(simplifier(subst(SS[j],n_1=mm)))<=evalf(maxi)){
+S:=concat(S,simplifier(subst(SS[j],n_1=mm)));mm:=mm+1;
+};mm:=-1;
+while(evalf(subst(SS[j],n_1=mm))>=evalf(mini)){
+S:=concat(S,simplifier(subst(SS[j],n_1=mm)));mm:=mm-1;
+}
+}
+
+}else{
+S:=resoudre(L[k](x),x);
+}
+
+
+
+
+
si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
if(S[j]>mini and S[j]<maxi){Z:=Z,simplifier(S[j]);}
fpour;
@@ -1558,7 +1741,28 @@ fpour;
pour k de 0 jusque m-1 faire
- SF:=resoudre(Fo[k](x),x);
+
+
+
+if(trigo==1){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SSF:=resoudre(factor(simplifier(Fo[k](x))),x);
+nsf:=size(SSF);
+for(j:=0;j<nsf;j++){
+mm:=0;
+while(evalf(simplifier(subst(SSF[j],n_1=mm)))<=evalf(maxi)){
+SF:=concat(SF,simplifier(subst(SSF[j],n_1=mm)));mm:=mm+1;
+};mm:=-1;
+while(evalf(subst(SSF[j],n_1=mm))>=evalf(mini)){
+SF:=concat(SF,simplifier(subst(SSF[j],n_1=mm)));mm:=mm-1;
+}
+}
+
+}else{
+SF:=resoudre(Fo[j](x),x);
+}
+
si size(SF)>0 alors pour j de 0 jusque size(SF)-1 faire
FF:=FF,simplifier(SF[j]);
if(SF[j]>mini and SF[j]<maxi){F:=F,simplifier(SF[j]);}
@@ -1756,7 +1960,7 @@ fclose(sortie);
-%%
+%%$
%% Code giac/Xcas pour les Tableaux de Signes d'expression ne contenant
%% qu'un seul terme
@@ -1764,11 +1968,38 @@ fclose(sortie);
\begin{VerbatimOut}{XcasTSc.cxx}
-TSc(g,D,nmr):={
+TSc(g,D,trigo,nmr):={
f:=unapply(g,x);
Z:=NULL;
mini:=D[0]; maxi:=D[1];lm:=" ";
+
+S:=[];
+
+
+
+if(trigo==t){
+all_trig_solutions:=1;
+reset_solve_counter(-1,-1);
+SS:=resoudre(factor(simplifier(f(x))),x);
+ns:=size(SS);
+for(j:=0;j<ns;j++){
+m:=0;
+while(evalf(simplifier(subst(SS[j],n_1=m)))<=evalf(maxi)){
+S:=concat(S,simplifier(subst(SS[j],n_1=m)));m:=m+1;
+};m:=-1;
+while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){
+S:=concat(S,simplifier(subst(SS[j],n_1=m)));m:=m-1;
+}
+}
+
+}else{
S:=resoudre(f(x),x);
+}
+
+
+
+
+
if(size(S)==0){
l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
li:=if(mini!=-infinity and f(mini)==0){"
@@ -1856,14 +2087,16 @@ fclose(sortie);
-%%
+%%$
%%
%% traitement des fichiers produits par giac/xcas
%%
%%
+% pour l'échelle des tableaux taper \ech{facteur de réduction}
-
+\newcommand\echelle{1}
+\newcommand\ech[1]{\renewcommand\echelle{#1}}
\newcommand{\dresse}[1]{%
@@ -1872,24 +2105,25 @@ fclose(sortie);
% exporter le source mp
% puis lancer metapost pour creer
% l'image du tableau
- \immediate\write18{\cat XCasmpfc.mp >> \Tableaux.Tab.mp}
- \immediate\write18{\cat enteteMP.cfg >> \Tableaux.Tab#1.mp}
- \immediate\write18{\cat XCasmpfc.mp >> \Tableaux.Tab#1.mp}
- \immediate\write18{\cat queue.mp >> \Tableaux.Tab#1.mp}
- \immediate\write18{mpost -jobname=\Tableaux.Tab \Tableaux.Tab#1.mp}
- \immediate\write18{\rem \Tableaux.Tab#1.mp}
+ \immediate\write18{\cat XCasmpfc.mp >> \nomtravail.Tab.mp}
+ \immediate\write18{\cat enteteMP.cfg >> \nomtravail.Tab#1.mp}
+ \immediate\write18{\cat XCasmpfc.mp >> \nomtravail.Tab#1.mp}
+ \immediate\write18{\cat queue.mp >> \nomtravail.Tab#1.mp}
+ \immediate\write18{mpost -jobname=\nomtravail.Tab \nomtravail.Tab#1.mp}
+ \immediate\write18{\rem \nomtravail.Tab#1.mp}
}%
{% sinon, si le tableau est absent, alerte.
- \IfFileExists{\Tableaux.Tab.\theTVn}{}{%
+ \IfFileExists{\nomtravail.Tab.\theTVn}{}{%
\PackageError{tablor}{Tableau absent non
reconstituable.}{Pour compiler il faut, soit les fichiers de
- tableaux, soit le fichier \Tableaux.Tab.mp, soit disposer de
+ tableaux, soit le fichier \nomtravail.Tab.mp, soit disposer de
XCas.}}}
\begin{center}
- \includegraphics{\Tableaux.Tab.\theTVn}
+ \includegraphics[scale=\echelle]{\nomtravail.Tab.\theTVn}
\end{center}
-\stepcounter{TVn}}
+\stepcounter{TVn}
+}
%%
@@ -1900,34 +2134,34 @@ fclose(sortie);
\newcommand{\dressetoile}[1]{%
-\IfFileExists{\Tableaux.Tab.\theTVn}{% Test sur l'existence du tableau
+\IfFileExists{\nomtravail.Tab.\theTVn}{% Test sur l'existence du tableau
% Si oui, inclusion du fichier source de sauvegarde mp dans Tableaux
-\immediate\write18{\cat TSav-\theTVn.mp >> \Tableaux.Tab.mp}}
+\immediate\write18{\cat TSav-\theTVn.mp >> \nomtravail.Tab.mp}}
% Si non, lancement des operations de fabrication
{\executGiacmp{XCas#1.giac}%
\immediate\write18{\editeur XCasmpfc.mp }
% Modification avec l'editeur choisi
-\immediate\write18{\cat XCasmpfc.mp >> \Tableaux.Tab.mp}
+\immediate\write18{\cat XCasmpfc.mp >> \nomtravail.Tab.mp}
\immediate\write18{\cp XCasmpfc.mp TSav-\theTVn.mp} % Sauvegarde du
% source mp sur le disque pour une
% inclusion ulterieure dans Tableaux.mp.
-\immediate\write18{\cat enteteMP.cfg >> \Tableaux.Tab#1.mp}
-\immediate\write18{\cat XCasmpfc.mp >> \Tableaux.Tab#1.mp}} % Inclusion du
+\immediate\write18{\cat enteteMP.cfg >> \nomtravail.Tab#1.mp}
+\immediate\write18{\cat XCasmpfc.mp >> \nomtravail.Tab#1.mp}} % Inclusion du
% source dans le
% fichier
% Tableaux
-\immediate\write18{\cat queue.mp >> \Tableaux.Tab#1.mp}
-\immediate\write18{mpost -jobname=\Tableaux.Tab \Tableaux.Tab#1.mp}% Reconstitution des tableaux
+\immediate\write18{\cat queue.mp >> \nomtravail.Tab#1.mp}
+\immediate\write18{mpost -jobname=\nomtravail.Tab \nomtravail.Tab#1.mp}% Reconstitution des tableaux
% et creation du dernier. L'option
% pallie l'absence de end en fin de
% fichier
-\immediate\write18{\rem \Tableaux.Tab#1.mp}
+\immediate\write18{\rem \nomtravail.Tab#1.mp}
\begin{center}
- \includegraphics{\Tableaux.Tab.\theTVn}
+ \includegraphics[scale=\echelle]{\nomtravail.Tab.\theTVn}
\end{center}
-
+\ech{1}
\setcounter{TVn}{\theTVnbis} % Restauration du compteur TVn
}
@@ -2182,7 +2416,7 @@ read("XCasTVIapp.user");
%% pour nettoyer les fichiers auxiliaires
-\AtEndDocument{\immediate\write18{\cat queue.mp >> \Tableaux.Tab.mp}
+\AtEndDocument{\immediate\write18{\cat queue.mp >> \nomtravail.Tab.mp}
}