diff options
author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
---|---|---|
committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/tablor |
Initial commit
Diffstat (limited to 'macros/latex/contrib/tablor')
70 files changed, 24889 insertions, 0 deletions
diff --git a/macros/latex/contrib/tablor/Figures/TSav-105.mp b/macros/latex/contrib/tablor/Figures/TSav-105.mp new file mode 100644 index 0000000000..0f84f2a3c0 --- /dev/null +++ b/macros/latex/contrib/tablor/Figures/TSav-105.mp @@ -0,0 +1,22 @@ + beginTableau(105) +newLigneVariables(btex $ {x}$ etex); + val(btex $-50$ etex);val(btex $-\frac{2}{3}$ etex); +val(btex $-\frac{\sqrt{5}}{5}$ etex); +val(btex $\frac{\sqrt{5}}{5}$ etex); +val(btex $50$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3 x+2}$ etex); + moins; + valBarre(btex 0 etex);plus;barre; + plus;barre;plus; + +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; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle F(x)}$ etex); + moins;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus; + +endTableau; + +
\ No newline at end of file diff --git a/macros/latex/contrib/tablor/Figures/capture.eps b/macros/latex/contrib/tablor/Figures/capture.eps new file mode 100644 index 0000000000..7cf5b460c5 --- /dev/null +++ b/macros/latex/contrib/tablor/Figures/capture.eps @@ -0,0 +1,1509 @@ +%!PS-Adobe-1.0 EPSF-3.0 +%%BoundingBox: 0 1 1384 842 +%%Creator: KDE 3.5.5 +%%CreationDate: sam fv 2 19:51:19 2008 +%%Orientation: Portrait +%%Pages: 1 +%%DocumentFonts: + +%%EndComments +%%BeginProlog +% Prolog copyright 1994-2005 Trolltech. You may copy this prolog in any way +% that is directly related to this document. For other use of this prolog, +% see your licensing agreement for Qt. +/d/def load def/D{bind d}bind d/d2{dup dup}D/B{0 d2}D/W{255 d2}D/ED{exch d}D +/D0{0 ED}D/LT{lineto}D/MT{moveto}D/S{stroke}D/F{setfont}D/SW{setlinewidth}D +/CP{closepath}D/RL{rlineto}D/NP{newpath}D/CM{currentmatrix}D/SM{setmatrix}D +/TR{translate}D/SD{setdash}D/SC{aload pop setrgbcolor}D/CR{currentfile read +pop}D/i{index}D/bs{bitshift}D/scs{setcolorspace}D/DB{dict dup begin}D/DE{end +d}D/ie{ifelse}D/sp{astore pop}D/BSt 0 d/LWi 1 d/PSt 1 d/Cx 0 d/Cy 0 d/WFi +false d/OMo false d/BCol[1 1 1]d/PCol[0 0 0]d/BkCol[1 1 1]d/BDArr[0.94 0.88 +0.63 0.50 0.37 0.12 0.06]d/defM matrix d/nS 0 d/GPS{PSt 1 ge PSt 5 le and{{ +LArr PSt 1 sub 2 mul get}{LArr PSt 2 mul 1 sub get}ie}{[]}ie}D/QS{PSt 0 ne{ +gsave LWi SW true GPS 0 SD S OMo PSt 1 ne and{BkCol SC false GPS dup 0 get +SD S}if grestore}if}D/r28{{CR dup 32 gt{exit}if pop}loop 3{CR}repeat 0 4{7 +bs exch dup 128 gt{84 sub}if 42 sub 127 and add}repeat}D/rA 0 d/rL 0 d/rB{rL +0 eq{/rA r28 d/rL 28 d}if dup rL gt{rA exch rL sub rL exch/rA 0 d/rL 0 d rB +exch bs add}{dup rA 16#fffffff 3 -1 roll bs not and exch dup rL exch sub/rL +ED neg rA exch bs/rA ED}ie}D/uc{/rL 0 d 0{dup 2 i length ge{exit}if 1 rB 1 +eq{3 rB dup 3 ge{1 add dup rB 1 i 5 ge{1 i 6 ge{1 i 7 ge{1 i 8 ge{128 add}if +64 add}if 32 add}if 16 add}if 3 add exch pop}if 3 add exch 10 rB 1 add{dup 3 +i lt{dup}{2 i}ie 4 i 3 i 3 i sub 2 i getinterval 5 i 4 i 3 -1 roll +putinterval dup 4 -1 roll add 3 1 roll 4 -1 roll exch sub dup 0 eq{exit}if 3 +1 roll}loop pop pop}{3 rB 1 add{2 copy 8 rB put 1 add}repeat}ie}loop pop}D +/sl D0/QCIgray D0/QCIcolor D0/QCIindex D0/QCI{/colorimage where{pop false 3 +colorimage}{exec/QCIcolor ED/QCIgray QCIcolor length 3 idiv string d 0 1 +QCIcolor length 3 idiv 1 sub{/QCIindex ED/x QCIindex 3 mul d QCIgray +QCIindex QCIcolor x get 0.30 mul QCIcolor x 1 add get 0.59 mul QCIcolor x 2 +add get 0.11 mul add add cvi put}for QCIgray image}ie}D/di{gsave TR 1 i 1 eq +{false eq{pop true 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NP BSt 9 eq BSt 11 eq or{0 4 h{dup 0 +exch MT w exch LT}for}if BSt 10 eq BSt 11 eq or{0 4 w{dup 0 MT h LT}for}if +BSt 12 eq BSt 14 eq or{w h gt{0 6 w h add{dup 0 MT h sub h LT}for}{0 6 w h +add{dup 0 exch MT w sub w exch LT}for}ie}if BSt 13 eq BSt 14 eq or{w h gt{0 +6 w h add{dup h MT h sub 0 LT}for}{0 6 w h add{dup w exch MT w sub 0 exch LT +}for}ie}if S}if BSt 24 eq{}if grestore}D/mat matrix d/ang1 D0/ang2 D0/w D0/h +D0/x D0/y D0/ARC{/ang2 ED/ang1 ED/h ED/w ED/y ED/x ED mat CM pop x w 2 div +add y h 2 div add TR 1 h w div neg scale ang2 0 ge{0 0 w 2 div ang1 ang1 +ang2 add arc}{0 0 w 2 div ang1 ang1 ang2 add arcn}ie mat SM}D/C D0/P{NP MT +0.5 0.5 rmoveto 0 -1 RL -1 0 RL 0 1 RL CP fill}D/M{/Cy ED/Cx ED}D/L{NP Cx Cy +MT/Cy ED/Cx ED Cx Cy LT QS}D/DL{NP MT LT QS}D/HL{1 i DL}D/VL{2 i exch DL}D/R +{/h ED/w ED/y ED/x ED NP x y MT 0 h RL w 0 RL 0 h neg RL CP BF QS}D/ACR{/h +ED/w ED/y ED/x ED x y MT 0 h RL w 0 RL 0 h neg RL CP}D/xr D0/yr D0/rx D0/ry +D0/rx2 D0/ry2 D0/RR{/yr ED/xr ED/h ED/w 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0000000000..260b9b876d --- /dev/null +++ b/macros/latex/contrib/tablor/Figures/tablor_Tab.mp @@ -0,0 +1,727 @@ +input tableauVariation; +verbatimtex +%&latex +\documentclass{article} +\usepackage[upright]{kpfonts}% ou mathpazo, lmodern, etc. ou rien ! +%\usepackage{amsmath} +\renewcommand\mbox[1]{ #1 } % pour les mbox intempestifs de xcas +\renewcommand\cdot{ } % idem pour les cdot +\begin{document} +\catcode`\@=0 % pour utiliser le @ +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 $0$ etex); +val(btex $2$ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);valBarre(btex 0 etex);plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $0$ etex,0);valPos(btex $4$ etex,1); +endTableau; + + +beginTableau(3) +newLigneVariables(btex $ {x}$ etex); + val(btex $-\infty $ etex);val(btex $\frac{-3}{5}$ etex); +val(btex $2$ etex); +val(btex $+\infty $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -45 x-27}$ etex); plus; valBarre(btex 0 etex);moins;barre;moins; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 2-x}$ etex); plus;barre;plus;valBarre(btex 0 etex);moins; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @varphi(x)}$ etex); plus;valBarre(btex 0 etex); moins;nonDefBarre;plus; +endTableau; + +beginTableau(4) newLigneVariables(btex $x$ etex);val(btex $-5$ etex); +val(btex $0$ etex); +val(btex $7$ etex); + +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $25$ etex,1); valPos(btex $0$ + etex,0); +valPos(btex $49$ etex,1); +endTableau; + +beginTableau(5) 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; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); valPos(btex $0$ + etex,0); +valPos(btex $+\infty $ etex,1); +endTableau; + + + +beginTableau(6) 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(7) 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(8) 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(9) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex); +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-1$ etex,0); valPos(btex $5$etex,1);valPos(btex $2$etex,0);valPos(btex $9$ etex,1); +endTableau; + +beginTableau(10) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex); +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $-1$ etex,1); limGauche(btex$-\infty $etex,0);nonDefBarre;limDroite(btex$+\infty $etex,1);valPos(btex $2$etex,0);valPos(btex $9$ etex,1); +endTableau; + +beginTableau(11) newLigneVariables(btex $x$ etex);val(btex $1$ etex);val(btex $2$ etex);val(btex $3$ etex);val(btex $4$ etex); +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);nonDefBarre;limDroite(btex $-1$ etex,1); limGauche(btex$-\infty $etex,0);nonDefBarre;limDroite(btex$+\infty $etex,1);valPos(btex $2$etex,0);limGauche(btex $+\infty $ etex,1);nonDefBarre; +endTableau; + +beginTableau(12) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +val(btex $-1$ etex); +val(btex $1$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @varphi'(x)}$ etex);moins; debutNonDefStrict;finNonDefStrict;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @varphi}$ 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(13) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +val(btex $-1$ etex); +val(btex $1$ etex); +val(btex $\frac{5}{2}$ etex); +val(btex $4$ etex); +val(btex $6$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; debutNonDefStrict;finNonDefStrict;plus;valBarre(btex 0 etex);moins;debutNonDefStrict;finNonDefStrict;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $-\infty$ etex,0);debutNonDefStrict;finNonDefStrict;limDroite(btex $-\infty$ etex,0);valPos(btex$\ln\left(\frac{441}{16}\right)$etex,1);limGauche(btex $-\infty$ etex,0);debutNonDefStrict;finNonDefStrict;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(14) 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); +valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); 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 + $ 10 $ etex,0.5); + valPos(btex $1$ etex,0); +endTableau; + +beginTableau(15) 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); +valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex $+\infty $ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex + $ -1 $ etex,0.5); + valPos(btex $0$ + etex,1);valPos(btex + $ -1 $ etex,0.5); + limGauche(btex $-\infty$ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0); +endTableau; + +beginTableau(16) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{10}\right))}{3}$ etex);val(btex $-1$ etex);val(btex $0$ etex);val(btex $1$ etex);val(btex $\frac{\sqrt{10}}{3}$ 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); +valPos(btex $\frac{100}{99}$ etex,0);valPos(btex $ 10 $ etex,0.5); 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 + $ 10 $ etex,0.5); + valPos(btex $1$ etex,0); +endTableau; + +beginTableau(17) newLigneVariables(btex $x$ etex);val(btex $-10$ etex);val(btex $-1$ etex);val(btex $\frac{(-\left(\sqrt{2}\right))}{2}$ etex);val(btex $0$ etex);val(btex $\frac{\sqrt{2}}{2}$ 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); +valPos(btex $\frac{100}{99}$ etex,0); limGauche(btex $+\infty $ etex,1);nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex + $ -1 $ etex,0.5); + valPos(btex $0$ + etex,1);valPos(btex + $ -1 $ etex,0.5); + limGauche(btex $-\infty$ etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $1$ etex,0); +endTableau; + +beginTableau(18) newLigneVariables(btex $x$ etex);val(btex $-\pi $ etex);val(btex $\frac{(-\pi )}{3}$ etex);val(btex $0$ etex);val(btex $\frac{\pi }{3}$ etex);val(btex $\pi $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @cos'(x)}$ etex);valBarre(btex 0 etex);plus;valBarre(btex$ + $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @cos}$ etex); +valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex $1$ + etex,1);valPos(btex + $ 1/2 $ etex,0.5);valPos(btex $-1$ etex,0); +endTableau; + +beginTableau(19) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +val(btex $ 0.156422$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(x)}$ etex);nonDefBarre;moins; valBarre(btex 0 etex);plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);nonDefBarre;limDroite(btex $-1$ etex,1); valPos(btex $ -1.145392$ + etex,0); +valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(20) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex); +val(btex $0$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle g'(t)}$ etex);moins; nonDefBarre;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle g}$ etex);valPos(btex $1$ etex,1); valPos(btex + $0$ + etex,0);valPos(btex $1$ etex,1); +endTableau; + +beginTableau(21) 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 $-3 \sin\left(\frac{3 \pi }{8}\right)$ 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 $\frac{(-\left(\sqrt{3}\right))}{2}$ + etex,0.5);valPos(btex $-1$ + etex,0); +valPos(btex $0$ etex,1); +endTableau; + +beginTableau(22) newLigneVariables(btex $t$ etex);val(btex $-\infty $ etex); +val(btex $-4$ etex); +val(btex $-1$ etex); +val(btex $0$ etex); +val(btex $2$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x'(t)}$ etex); moins;valBarre(btex $0$ etex);plus;nonDefBarre;plus;valBarre(btex $0$ etex);moins;nonDefBarre;moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle x}$ etex);valPos(btex $1$ etex,1);valPos(btex $\frac{8}{9}$ + 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); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex); moins;valBarre(btex $\frac{-64}{9}$ etex);moins;nonDefBarre;moins;valBarre(btex $0$ etex);plus;valBarre(btex $\frac{44}{9}$ etex);plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);valPos(btex $+\infty $ etex,1);valPos(btex $\frac{32}{3}$ + etex,0.5);limGauche(btex + $-\infty$ + etex,0);nonDefBarre;limDroite(btex $+\infty $ etex,1);valPos(btex $0$ + etex,0); +valPos(btex $\frac{16}{3}$ + etex,0.5);valPos(btex $+\infty $ etex,1); +endTableau; + + + beginTableau(23) + newLigneVariables(btex $ {x}$ etex); + val(btex $-\infty$ etex);val(btex $\frac{3}{2}$ etex); +val(btex $5$etex); +val(btex $+\infty$ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2x+3}$ etex);plus;valBarre(btex 0 etex);moins;barre;moins; +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(24) +newLigneVariables(btex $ {x}$ etex); + val(btex $-\infty $ etex);val(btex $-\left(\sqrt{2}\right)$ etex); +val(btex $-1$ etex); +val(btex $1$ etex); +val(btex $\sqrt{2}$ etex); +val(btex $\frac{3}{2}$ etex); +val(btex $+\infty $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2 x+3}$ etex); + plus;barre; + plus;barre; + plus;barre; + plus;barre; + plus;valBarre(btex 0 etex);moins; + + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}-1}$ etex); + plus;barre; + plus; + valBarre(btex 0 etex);moins; + valBarre(btex 0 etex);plus;barre; + plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+1}$ etex); + plus;barre; + plus;barre; + plus;barre; + plus;barre; + plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-1}$ etex); + moins;barre; + moins;barre; + moins; + valBarre(btex 0 etex);plus;barre; + plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}-2}$ etex); + plus; + valBarre(btex 0 etex);moins;barre; + moins;barre; + moins; + valBarre(btex 0 etex);plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle P(x)}$ etex); + moins;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins; + +endTableau; + + beginTableau(25) +newLigneVariables(btex $ {x}$ etex); + val(btex $-15$ 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 $\hbox{ Signe de }\atop{\displaystyle f(x)}$ etex); + plus;valBarre(btex 0 etex); moins; + valBarre(btex 0 etex); +endTableau; + + +beginTableau(26) +newLigneVariables(btex $ {x}$ etex); + val(btex $-\infty $ etex);val(btex $-4$ etex); +val(btex $\frac{5}{4}$ etex); +val(btex $\frac{3}{2}$ etex); +val(btex $2$ etex); +val(btex $4$ etex); +val(btex $+\infty $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -2 x+3}$ etex); plus;barre;plus;barre;plus; valBarre(btex 0 etex);moins;barre;moins;barre;moins; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -4 x+5}$ etex); plus;barre;plus; valBarre(btex 0 etex);moins;barre;moins;barre;moins;barre;moins; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}-16}$ etex); plus; valBarre(btex 0 etex);moins;barre;moins;barre;moins;barre;moins;valBarre(btex 0 etex);plus; +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-2}$ etex); moins;barre;moins;barre;moins;barre;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(27) +newLigneVariables(btex $ {x}$ etex); + val(btex $-10$ etex);val(btex $-3$ etex); +val(btex $5$ etex); +val(btex $10$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-10}$ etex); moins;barre;moins;barre;moins; + valBarre(btex 0 etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-5}$ etex); moins;barre;moins;valBarre(btex 0 etex);plus; +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+10}$ etex); valBarre(btex 0 etex);plus;barre;plus;barre;plus; +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+3}$ etex); moins; valBarre(btex 0 etex);plus;barre;plus; +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle Q(x)}$ etex);nonDefBarre;moins;nonDefBarre; plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex); +endTableau; + + + +beginTableau(28) +newLigneVariables(btex $\displaystyle {x}$ etex); + val(btex $-10$ etex);val(btex $-5$ etex); +val(btex $10$ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+5)}$ etex); + plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex); +endTableau; + + + +beginTableau(29) +newLigneVariables(btex $\displaystyle {x}$ etex); + val(btex $-10$ etex);val(btex $2$ etex); +val(btex $5$ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \frac{(x+10)}{(x-5) (x-2)}}$ etex); + valBarre(btex 0 etex); plus;nonDefBarre;moins;nonDefBarre; +endTableau; + + + +beginTableau(30) +newLigneVariables(btex $\displaystyle {x}$ etex); + val(btex $0$ etex);val(btex $\frac{\pi }{2}$ etex); +val(btex $\pi $ etex); +val(btex $\frac{3 \pi }{2}$ etex); +val(btex $2 \pi $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \tan\left(x\right)}$ etex); + valBarre(btex 0 etex); plus;nonDefBarre;moins;valBarre(btex 0 etex);plus;nonDefBarre;moins;valBarre(btex 0 etex); +endTableau; + + beginTableau(105) +newLigneVariables(btex $ {x}$ etex); + val(btex $-50$ etex);val(btex $-\frac{2}{3}$ etex); +val(btex $-\frac{\sqrt{5}}{5}$ etex); +val(btex $\frac{\sqrt{5}}{5}$ etex); +val(btex $50$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle 3 x+2}$ etex); + moins; + valBarre(btex 0 etex);plus;barre; + plus;barre;plus; + +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; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle F(x)}$ etex); + moins;valBarre(btex 0 etex); plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus; + +endTableau; + + beginTableau(31) 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 $-1$ + etex,0);valPos(btex + $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(32) 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 $0$ + etex,0);valPos(btex + $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(33) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $+\infty $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @ln'(x)}$ etex);nonDefBarre;plus;valBarre(btex$ + $ etex);plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @ln}$ etex); +nonDefBarre;limDroite(btex $-\infty$ etex,0);valPos(btex $ 2 $ etex,0.5);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(35) newLigneVariables(btex $x$ etex);val(btex $1$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle -@ln'(x)}$ etex); moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle -@ln}$ etex);valPos(btex $0$ etex,1);valPos(btex $-\infty$ etex,0); +endTableau; + +beginTableau(36) 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 $\hbox{ Signe de }\atop{\displaystyle @cos'(x)}$ etex);valBarre(btex 0 etex);plus;valBarre(btex$ + $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @cos}$ etex); +valPos(btex $-1$ etex,0);valPos(btex $ 1/2 $ etex,0.5); valPos(btex $1$ + etex,1);valPos(btex + $ 1/2 $ etex,0.5);valPos(btex $-1$ etex,0); +endTableau; + +beginTableau(37) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +val(btex $\pi $ etex); +val(btex $2 \pi $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @cos'(x)}$ etex);valBarre(btex 0 etex);moins; valBarre(btex 0 etex);plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @cos}$ etex);valPos(btex $1$ etex,1); valPos(btex $-1$ + etex,0); +valPos(btex $1$ etex,1); +endTableau; + +beginTableau(38) 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 $\hbox{ Signe de }\atop{\displaystyle @tan'(t)}$ etex); plus;valBarre(btex$ + $ etex);plus; nonDefBarre;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @tan}$ 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(39) newLigneVariables(btex $t$ etex);val(btex $0$ etex);val(btex $\mathrm{atan}\left(7\right)$ etex);val(btex $\frac{\pi }{2}$ etex);val(btex $\pi $ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle @tan'(t)}$ etex); plus;valBarre(btex$ + $ etex);plus; nonDefBarre;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle @tan}$ 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(40) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $\alpha_2$ etex);val(btex $1$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$ + $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); +valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex $\frac{3 \sqrt{3}}{4}$ + etex,1);valPos(btex + $ 1 $ etex,0.5);valPos(btex $0$ etex,0); +endTableau; + +beginTableau(41) newLigneVariables(btex $x$ etex);val(btex $-1$ etex);val(btex $ -0.839287$ etex);val(btex $\frac{-1}{2}$ etex);val(btex $0$ etex);val(btex $1$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus;valBarre(btex$ + $ etex);plus; valBarre(btex 0 etex);moins;valBarre(btex $ $ etex);moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex); +valPos(btex $0$ etex,0);valPos(btex $ 1 $ etex,0.5); valPos(btex $\frac{3 \sqrt{3}}{4}$ + etex,1);valPos(btex + $ 1 $ etex,0.5);valPos(btex $0$ etex,0); +endTableau; + +beginTableau(42) newLigneVariables(btex $x$ etex);val(btex $-1$ etex); +val(btex $0$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);nonDefBarre;plus; valBarre(btex 0 etex);moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);nonDefBarre;limDroite(btex $-\infty$ etex,0); valPos(btex $0$ + etex,1);valPos(btex $-\infty$ etex,0); +endTableau; + + beginTableau(43) +newLigneVariables(btex $ {x}$ etex); + val(btex $-10$ etex);val(btex $\frac{(-\left(\sqrt{5}\right)-3)}{2}$ etex); +val(btex $-1$ 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 $\hbox{ Signe de }\atop{\displaystyle -2 x+3}$ etex); + plus;barre; + plus;barre; + plus;barre; + plus;barre; + plus;valBarre(btex 0 etex);moins; + + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x-1}$ etex); + moins;barre; + moins;barre; + moins;barre; + moins; + valBarre(btex 0 etex);plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x+1}$ etex); + moins;barre; + moins; + valBarre(btex 0 etex);plus;barre; + plus;barre; + plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle x^{2}+3 x+1}$ etex); + plus; + valBarre(btex 0 etex);moins;barre; + moins; + valBarre(btex 0 etex);plus;barre; + plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle G(x)}$ etex); + plus;valBarre(btex 0 etex); moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins; + +endTableau; + + beginTableau(44) 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 $-\left(e^{-4}\right)-1$ + etex,0);valPos(btex + $ 0 $ etex,0.5);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(45) 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 $2$ + etex,1);valPos(btex + $ 0 $ etex,0.5);valPos(btex $-\infty$ etex,0); +endTableau; + +beginTableau(47) newLigneVariables(btex $x$ etex);val(btex $0$ etex); +val(btex $1$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex); plus; valBarre(btex 0 etex);moins; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $0$ etex,0); valPos(btex $\ln\left(\frac{(e^{1}+1)}{e^{1}}\right)$ + etex,1);valPos(btex $0$ etex,0); +endTableau; + +beginTableau(48) 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(49) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $\alpha_1$ etex);val(btex $\frac{1}{e^{\frac{-1}{2}}}$ 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 $\frac{1}{4}$ + etex,1);valPos(btex + $ -1 $ etex,0.5);valPos(btex $-\infty$ etex,0); +endTableau; + +beginTableau(50) newLigneVariables(btex $x$ etex);val(btex $0$ etex);val(btex $e^{\frac{(-\left(\sqrt{5}\right)+1)}{2}}$ etex);val(btex $\frac{1}{e^{\frac{-1}{2}}}$ etex);val(btex $e^{\frac{(\sqrt{5}+1)}{2}}$ 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 $\frac{1}{4}$ + etex,1);valPos(btex + $ -1 $ etex,0.5);valPos(btex $-\infty$ etex,0); +endTableau; + + + +beginTableau(51) +newLigneVariables(btex $\displaystyle {x}$ etex); + val(btex $-10$ etex);val(btex $10$ etex); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle (x-10) (x+10)}$ etex); + valBarre(btex 0 etex);moins; + valBarre(btex 0 etex); +endTableau; + +beginTableau(52) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +val(btex $-\left(\sqrt{2}\right)$ etex); +val(btex $-1$ etex); +val(btex $1$ etex); +val(btex $\sqrt{2}$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; valBarre(btex 0 etex);plus;debutNonDefStrict;finNonDefStrict;moins;valBarre(btex 0 etex);plus; +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(53) newLigneVariables(btex $x$ etex);val(btex $-\infty $ etex); +val(btex $-1$ etex); +val(btex $1$ etex); +val(btex $+\infty $ etex); + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle f'(x)}$ etex);moins; debutNonDefStrict;finNonDefStrict;plus; +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle f}$ etex);valPos(btex $+\infty $ etex,1); limGauche(btex $-\infty$ etex,0);debutNonDefStrict;finNonDefStrict;limDroite(btex $-\infty$ etex,0);valPos(btex $+\infty $ etex,1); +endTableau; + +beginTableau(54) 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 $-3 \sin\left(\frac{3 \pi }{8}\right)$ 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 $\frac{(-\left(\sqrt{3}\right))}{2}$ + etex,0.5);valPos(btex $-1$ + etex,0); +valPos(btex $0$ etex,1); +endTableau; + +beginTableau(55) newLigneVariables(btex $t$ etex);val(btex $0$ etex); +val(btex $\frac{\pi }{3}$ etex); +val(btex $\pi $ etex); +val(btex $\frac{5 \pi }{3}$ etex); +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 $\frac{(\pi -3 \sqrt{3})}{3}$ + etex,0); +valPos(btex $\pi $ + etex,0.5);valPos(btex $\frac{(5 \pi +3 \sqrt{3})}{3}$ + etex,1);valPos(btex $2 \pi $ etex,0); +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle y'(t)}$ etex);valBarre(btex $0$ etex);moins;valBarre(btex $-\left(\sqrt{3}\right)$ etex);moins;valBarre(btex $0$ etex);plus;valBarre(btex $\sqrt{3}$ etex);plus;valBarre(btex $0$ etex); +newLigneVariations(btex $\hbox{ Variations de }\atop{\displaystyle y}$ etex);valPos(btex $1$ etex,1);valPos(btex $0$ + etex,0.5);valPos(btex $-3$ + etex,0); +valPos(btex $0$ + etex,0.5);valPos(btex $1$ etex,1); +endTableau; + +beginTableau(56) 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); + +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 $-3 \cos\left(\frac{\pi }{8}\right)$ 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); +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 $0$ etex,1); +endTableau; + + beginTableau(57) +newLigneVariables(btex $ {x}$ etex); + val(btex $0$ 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);moins;barre; + moins; + valBarre(btex 0 etex);plus;barre;plus; + +newLigneSignes(btex $\hbox{ Signe de }\atop{\displaystyle \sin\left(x\right)+\frac{1}{2}}$ etex); + 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); moins;valBarre(btex 0 etex);plus;valBarre(btex 0 etex);moins;valBarre(btex 0 etex);plus; + +endTableau; + +
\ No newline at end of file diff --git a/macros/latex/contrib/tablor/README b/macros/latex/contrib/tablor/README new file mode 100644 index 0000000000..d6475d58bf --- /dev/null +++ b/macros/latex/contrib/tablor/README @@ -0,0 +1,27 @@ +The package allows the user to use the computer algebra system XCAS +to generate tables of signs and of variations (the actual plotting of +the tables uses the MetaPost macro package "tableauVariation.mp" : + +http://frederic.mazoit.free.fr/LaTeX_metapost/tableauVariations/ . + +The tablor package requires that shell escape be enabled. + + +For instance : + +\begin{TV} TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) \end{TV} + +draws table of variations of x->x^2/(x^2-1). + + +You can download XCAS here: + + +http://www-fourier.ujf-grenoble.fr/%7Eparisse/giac.html + + +The non-french users need to comment out every + +" \usepackage[upright]{fourier} " + +Just put tablor.sty and tablor.cfg into /texmf/tex/latex/tablor/ diff --git a/macros/latex/contrib/tablor/README-fr.txt b/macros/latex/contrib/tablor/README-fr.txt new file mode 100644 index 0000000000..df70726545 --- /dev/null +++ b/macros/latex/contrib/tablor/README-fr.txt @@ -0,0 +1,28 @@ +L'extension tablor.sty permet de crer des tableaux de signes et de +variations depuis latex en utilisant XCAS pour les calculs et MetaPOST +pour les tableaux. + +On rentre par exemple: + +\begin{TV} TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) \end{TV} + +et on obtient le tableau de variation de x->x^2/(x^2-1). + +Les tableaux sont construits partir du fichier tableauVariation.mp de +Frdric Mazoit disponible l'adresse + +http://frederic.mazoit.free.fr/LaTeX_metapost/tableauVariations/ + +XCAS est tlchargeable l'adresse : + +http://www-fourier.ujf-grenoble.fr/%7Eparisse/giac_fr.html + + +Les appels giac ont t amliors grce Yves Delhaye : + +http://www.yvesdelhaye.be/?Generateur-d-interrogations-le + + +Il faut activer le shell-escape. + + diff --git a/macros/latex/contrib/tablor/auto/tablor-xetex.el b/macros/latex/contrib/tablor/auto/tablor-xetex.el new file mode 100644 index 0000000000..2c7fbf4252 --- /dev/null +++ b/macros/latex/contrib/tablor/auto/tablor-xetex.el @@ -0,0 +1,51 @@ +(TeX-add-style-hook "tablor-xetex" + (lambda () + (LaTeX-add-environments + "TSa" + "TSq" + "TS" + "TSc" + "TV" + "TVP" + "TVZ" + "TVapp" + "TVI" + "TVIex" + "TVIapp" + "TVPC" + "TVS") + (TeX-add-symbols + '("initablor" ["argument"] 0) + '("nettoyer" ["argument"] 0) + '("dressetoile" 2) + '("dresse" 2) + '("coultab" 1) + '("ech" 1) + '("executGiacmp" 1) + "rem" + "cat" + "cp" + "echod" + "echof" + "nomtravail" + "tv" + "tvbis" + "echelle" + "couleurtab") + (TeX-run-style-hooks + "pst-eps" + "graphicx" + "babel" + "frenchb" + "fontenc" + "T1" + "latex2e" + "art10" + "article" + "ifxetex" + "ifpdf" + "fancyvrb" + "ifthen" + "filecontents" + "tablor"))) + diff --git a/macros/latex/contrib/tablor/auto/tablor.el b/macros/latex/contrib/tablor/auto/tablor.el new file mode 100644 index 0000000000..e9cbdd4143 --- /dev/null +++ b/macros/latex/contrib/tablor/auto/tablor.el @@ -0,0 +1,40 @@ +(TeX-add-style-hook "tablor" + (lambda () + (LaTeX-add-environments + "TSa" + "TSq" + "TS" + "TSc" + "TV" + "TVP" + "TVZ" + "TVapp" + "TVI" + "TVIex" + "TVIapp" + "TVPC" + "TVS") + (TeX-add-symbols + '("initablor" ["argument"] 0) + '("nettoyer" ["argument"] 0) + '("dressetoile" 2) + '("dresse" 2) + '("coultab" 1) + '("ech" 1) + '("executGiacmp" 1) + "rem" + "cat" + "cp" + "echod" + "echof" + "nomtravail" + "tv" + "tvbis" + "echelle" + "couleurtab") + (TeX-run-style-hooks + "ifpdf" + "fancyvrb" + "ifthen" + "filecontents"))) + diff --git a/macros/latex/contrib/tablor/tablor-xetex.sty b/macros/latex/contrib/tablor/tablor-xetex.sty new file mode 100644 index 0000000000..2ef9eba220 --- /dev/null +++ b/macros/latex/contrib/tablor/tablor-xetex.sty @@ -0,0 +1,3374 @@ +% Last modified: <tablor-xetex.sty modifié par Guillaume CONNAN le dimanche 6 octobre 2013 à 14h 46min 27s> + +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesPackage{tablor-xetex}[06/10/2013 v4.07-g la machine a creer des +tableaux de signes et variations compatible xetex] + +% \copyleft Connan le Barbare (aka Guillaume Connan) \copyright +% This work may be distributed and/or mofified under the conditions +% or the LaTeX Project Public Licence, either v1.3 or (at your option) +% any later version. The latest version is in +% http://www.latex-project.org/lppl/ +% This work consists of the files tablor.sty, tablor-xetex.sty, tablor.cfg, tablor.tex, +% tablor.pdf and tablor.html + + +%% Cree 16 environnements : +%% tableau de signes de 2 facteurs affines +% \begin{TSa} +% TSa(-2,3,-1,5,\tv); +% \end{TSa} +% %%%%%% Pour des tableaux de plus de 2 facteurs +% +% \begin{TS} +% TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[a,b],n,\tv); +% \end{TS} +% +% pour les tableaux de signes avec quotient +%\begin{TSq} +%TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],n,\tv) +%%\end{TSq} +% un tableau de variation : +% +% pour les tableaux de signes à une seule ligne +% \begin{TSc} +% TSc((x+10)/((x-5)*(x-2)),[-10,5],[2,5],n,0) +% \end{TSc} +% +% +% \begin{TV} +% TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,n,\tv) +% \end{TV} +% +% tableau de variation avec liste de valeurs +% \begin{TVS} +% TVS([1,2,3,4],[-1,-infinity,+infinity,2,9],[2],"f","x",\tv) +% \end{TVS} +% +% tableau de variation avec zones interdites +% +% \begin{TVZ} +% TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,\tv) +% \end{TVZ} +% +% +% tableau avec valeurs intermediares +%\begin{TVI} +%TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,\tv) +%\end{TVI} +%%% +%%% +% tableau avec valeurs intermediares et racines exactes +%\begin{TVIex} +%TVIex([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,\tv) +%\end{TVIex} +%%% +% +% +% tableau de variations avec f' sans zero formel +%\begin{TVapp} +% TVapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,\tv) +% \end{TVapp} +% +% +% tableau de variations avec f' sans zero formel +%\begin{TVIapp} +% TVIapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,0,\tv) +% \end{TVIapp} +% +% +%%% +% et leurs pendants etoiles qui permettent l'affichage intermediaire du +% fichier metapost pour le modifier +% +% +% Courbes parametrees +% \begin{TVP} +% TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,\tv) +% \end{TVP} +% +% +% \begin{TVP} +% TVP([0,pi/2],[[],[]],["x","y"],"t",[2*cos(t),sin(2*t)],1,t,\tv) +% \end{TVP} +% % +% % +% Fonctions prolongeables par continuité +% TVPC([intervalles d'étude],[valeurs prolongeables],[valeurs interdites pour f'],"g","t",e^(-1/x^2),1,n,\tv); +% \begin{TVPC} +% TVPC([-infinity,+infinity],[0],[0],"g","t",e^(-1/x^2),1,n,\tv); +% \end{TVPC} + + + + +%% extensions requises +%% Il faudra rajouter dans le preambule \usepackage{graphicx} si vous +%% ne l'avez pas de base + + +\RequirePackage{filecontents} +\RequirePackage{ifthen} +\RequirePackage{fancyvrb} +\RequirePackage{ifpdf} +\RequirePackage{ifxetex} +\fvset{gobble=0} + +% option xcas present + + +\newboolean{xcas}\setboolean{xcas}{false} +\DeclareOption{xcas}{\setboolean{xcas}{true}} + + +%% Initialisation du choix d'OS +\newboolean{windows}\setboolean{windows}{false} +\DeclareOption{windows}{\setboolean{windows}{true}} + +\ProcessOptions\relax + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% pour xelatex (ne marche que sur unix....) +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\ifxetex + +\begin{filecontents*}{convert-mp-pdf.sh} +#!/bin/sh +mpost -interaction=nonstopmode $1 ; + +cat>$1.tex<<EOF +\documentclass{article} +\usepackage[T1]{fontenc} +\usepackage[frenchb]{babel} +\usepackage{graphicx} +\usepackage{pst-eps} +\thispagestyle{empty} +\begin{document} +\begin{TeXtoEPS} +\includegraphics{$1.$2} +\end{TeXtoEPS} +\end{document} +EOF +latex $1 +dvips -o $1.eps -E $1.dvi +epstopdf $1.eps; +## Fin de convert-mp-pdf.sh +\end{filecontents*} + +%$>> + + +\immediate\write18{chmod 775 ./convert-mp-pdf.sh} + +\fi + + + +%% on configure tablor dans un fichier exterieur pour la plateforme +%% et l'editeur + +\IfFileExists{tablor.cfg}{\input{tablor.cfg}}%\typeout{pas de fichier tablor.cfg}} + + +%% Definit des commandes disque selon l'OS utilise +\ifthenelse{\boolean{windows}}% + {\newcommand{\rem}{DEL } \newcommand{\cat}{TYPE } + \newcommand{\cp}{COPY }\newcommand{\echod}{ECHO } + \newcommand{\echof}{}}% + {\newcommand{\rem}{rm }\newcommand{\cat}{cat } + \newcommand{\cp}{cp }\newcommand{\echod}{echo "} + \newcommand{\echof}{"}} + + + + + + + +%% pour ceux compilant via pdflatex + +\ifpdf +\DeclareGraphicsRule{*}{mps}{*}{} +\fi + +%% pour nettoyer les fichiers auxiliaires + +\AtEndDocument{\immediate\write18{\rem *.user XCas* Xcas* *.mpx} + } + + + + +%% Pour clore les fichiers metapost + + + \begin{VerbatimOut}{queue.mp} + + end + + \end{VerbatimOut} + + + +%% Nettoie les fichiers log dont le nom depend du choix de l'utilisateur +%% Par defaut, c'est le nom du fichier tex courant (\jobname) +%% Clôt le fichier metapost contenant le recapitulatif de tous les tableaux + + + +\newcommand{\nettoyer}[1][\jobname]% +{\immediate\write18{\rem #1_Tab.log queue.mp enteteMP.cfg session.tex config.cxx} +} + + + + +%% Donne comme prefixe aux tableaux le prefixe courant +%% Peut-être modifie par \initablor + +\newcommand{\nomtravail}{\jobname} + +%% initialise les compteurs + +\newcounter{TVn} +\newcommand{\tv}{\theTVn} + +\newcounter{TVnbis} +\newcommand{\tvbis}{\theTVnbis} + + + +%% permet de donner un prefixe aux tableaux produits (\jobname par defaut) +%% effectue quelques verifications : + + +\newcommand{\initablor}[1][\jobname]{% +\renewcommand{\nomtravail}{#1}% Arret du nom des tableaux +\setcounter{TVn}{0}% Initialisation du compteur de tableaux. +\ifthenelse{\boolean{xcas}}% Avec l'option XCas +{\IfFileExists{\nomtravail_Tab.mp}% Si Tableaux.mp est present... + {\immediate\write18{\rem \nomtravail_Tab.mp}}% le detruire + {}% + \immediate\write18{\cp enteteMP.cfg \nomtravail_Tab.mp}% Reconstituer l'entête de Tableaux.mp +} +{\IfFileExists{\nomtravail_Tab.mp}% Sans l'option XCas, si + % Tableaux.mp existe +{\immediate\write18{mpost -interaction=batchmode \nomtravail_Tab}}% l'executer pour reconstituer les figures +{\PackageWarning{tablor}{Pas de source metapost pour creer les tableaux.}}% sinon message d'erreur + % (mais pas d'arret car les tableaux + % peuvent être presents ) +}}% + + + +%% commande pour lancer giac selon l'OS + +\makeatletter +\newcommand{\executGiacmp}[1]{% +\ifthenelse{\boolean{windows}}% +{\immediate\write18{giac #1 }}% +{\immediate\write18{giac <#1 }}} +\makeatother + + + + +%%% +% +%%% LES SCRIPTS GIAC/XCAS +% +%%% + + + + +%% +%% Code giac/Xcas pour les Tableaux de Variations +%% + + +\begin{VerbatimOut}{XcasTV.cxx} +TV(L,F,nom,nomv,f,ftt,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + qq:=member(simplify(S[j]),Z)==0; + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}}; + fpour + fsi; +Z:=sort(Z); +nz:=size(Z); + + + tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); + ftantque; + + + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + +Z:=sort([op(set[op(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; + + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.1))>0; + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre; +"} +lm0:=limit(f(x),x,Z[0],1)==-infinity; + li:=lvic+nom+"}$ etex);"+ + if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)){ + "limGauche(btex + $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ + etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); +"}}} + }; } + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + +\end{VerbatimOut} + + + + + + +%%%% + + +% +% +% TVPC : pour les fonctions prolongeables par continuité. +%% +%% + + + + +\begin{VerbatimOut}{XcasTVPC.cxx} +TVPC(L,F,FP,nom,nomv,f,ftt,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +Z:=concat(Z,FP); +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + qq:=member(simplify(S[j]),Z)==0; + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}}; + fpour + fsi; +Z:=sort(Z); +nz:=size(Z); + + + tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); + ftantque; + + + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + +Z:=sort([op(set[op(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; + + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],FP)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.1))>0; + lsp:=lsp+if(member(Z[r],FP)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf:=if(member(Z[nz-1],FP)==0){""}else{"nonDefBarre; +"} +lm0:=limit(f(x),x,Z[0],1)==-infinity; + li:=lvic+nom+"}$ etex);"+ + if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)){ + "valPos(btex + $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ + etex,"+if(krm==1){"1);"}else{"0);"} } + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); +"}}} + }; } + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}}; + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + +\end{VerbatimOut} + + + + + + + + + + + + +%% +%% +%% TV avec une zone interdite : on rajoute comme argument la liste des intervalles interdits +%% par exemple, pour sqrt(x^2-1) : TVZ([-infinity,100],[],[[-1,1]],"f","x",sqrt(x^2-1),1,1) +%% + +\begin{VerbatimOut}{XcasTVZ.cxx} + + +TVZ(L,F,FF,nom,nomv,f,ftt,trigo,nmr):={ +nl:=size(L); +nf:=size(FF); + Ff:=NULL;IMIN:=NULL;IMAX:=NULL; +for(k:=0;k<nf;k++){ +if(FF[k][0]>L[0]){Imin[k]:=FF[k][0];LL:=L}else{Imin[k]:=L[0];LL:=[L[1]]}; +if(FF[k][1]<L[1]){Imax[k]:=FF[k][1];LL:=L}else{Imax[k]:=L[1];LL:=[L[0]]}; + Ff:=Ff,[Imin[k],Imax[k]]; + IMIN:=IMIN,Imin[k]; + IMAX:=IMAX,Imax[k]; + } + FF:=[Ff]; + IMIN:=[IMIN]; + IMAX:=[IMAX]; + f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(LL,F); + +for(k:=0;k<nf;k++){ +Z:=concat(Z,FF[k]); +} + +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + for(k:=0;k<nf;k++){ + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + kK:=(evalf(S[j])<evalf(Imin[k])) or (evalf(S[j])>evalf(Imax[k])); + Kk:=(kk) and kK; + if(Kk==1){Z:=append(Z,simplify(S[j]))}; + } + fpour + fsi; + + +Z:=sort([op(set[op(Z)])]); + +nz:=size(Z); + +for(j:=0;j<nf;j++){ + for(k:=1;k<nz;k++){ + if ((Z[k]>Imin[j])and(Z[k]<Imax[j])){Z:=augment(Z[0..k-1],Z[k+1..nz-1]);nz:=nz-1; + } + } +} +nz:=size(Z); + +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +";fpour; + + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ +if(member(Z[0],IMIN)!=0){if((member(Z[0],F)==0) and (fp(Z[0])!=undef)){"debutNonDef;"}else{"debutNonDefStrict;"}}else{if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }}} + + + + + + + + + +// modif 3 avril 2010 + +if(nz>2){ for(r:=1; r<=nz-2;r++){ + lsp:=lsp+ + if(member(Z[r],IMIN)!=0){ + if((member(Z[r],F)==0) and (fp(Z[r])!=undef)){"debutNonDef;"} + else{"debutNonDefStrict;"}} + else{if(member(Z[r],IMAX)!=0){if((member(Z[r],F)==0) and (fp(Z[r])!=undef)){"finNonDef;"} + else{"finNonDefStrict;"}+ + if(evalf(fp(Z[r]+0.01))>0){"plus;"} + else{"moins;"}} + else{if(member(Z[r],F)==0){"valBarre(btex 0 etex);"} + else{"nonDefBarre;"}+ + if(evalf(fp(Z[r]+0.01))>0){"plus;"} + else{"moins;"} + }} + }}; + +// fin modif + + + + + + + + +lsf:=if(member(Z[nz-1],IMAX)!=0){if((member(Z[nz-1],F)==0) and (fp(Z[nz-1])!=undef)){"finNonDef;"}else{"finNonDefStrict;"}}else{if(member(Z[nz-1],F)==0){""}else{"nonDefBarre; +"}} + + +lm0:=limit(f(x),x,Z[0],1)==-infinity; + li:=lvic +nom+"}$ etex);"+ + if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + +if(nz>2){ + for(r:=1; r<=nz-2;r++){ + krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + + lp:=lp+if(member(Z[r],IMIN)!=0){"limGauche(btex $"+if(lmrm==1){ + "-\\infty"}else{ + latex(simplify(limit(f(x),x,Z[r],-1)))} + +"$ etex,"+if(krm==1){ + "1);"}else{"0);"} + +if(member(Z[r],F)==0){"debutNonDef;"}else{"debutNonDefStrict;"} + }//fsi Zr=Imin + else{ + if (member(Z[r],IMAX)!=0){if(member(Z[r],F)==0){"finNonDef;"}else{"finNonDefStrict;"}+"limDroite(btex $"+if(lmrp==1){ + "-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))} + +"$ etex,"+if(krp==1){ + "1);"}else{"0);"} + }else{ + if(member(Z[r],F)){ + "limGauche(btex $"+if(lmrm==1){ + "-\\infty"}else{ + latex(simplify(limit(f(x),x,Z[r],-1)))} + +"$ etex,"+if(krm==1){ + "1);"}else{"0);"} + +"nonDefBarre;limDroite(btex $"+if(lmrp==1){ + "-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))} + +"$ etex,"+if(krp==1){ + "1);"}else{"0);"} + }//fsi (member Zr F) + else{"valPos(btex$"+latex(simplify(f(Z[r])))+"$etex,"+ + if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){ + "0.5);"}else{ + if(krp==1){ + "1);"}else{"0);"}//felse(krp) + }//felse(valpos) + }//felse(member Zr F) + } //felse(Zr=Imax) + }//felse(Zr=Imin) + };//ffor + }//fsi nz + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + } +:; + + +\end{VerbatimOut} + + +%% +%% +%% Quand les solutions formelles de f'(x)=0 ne sont pas calculables +%% + + + +\begin{VerbatimOut}{XcasTVapp.cxx} + + + + + + + +TVapp(L,F,nom,nomv,f,ftt,nmr):={ + + +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +z0:=concat(L,F);z:=sort(z0); +nz:=size(z); + + + + + + +S:=op(fsolve(fp(x),x)); + + + +if(L==[-infinity,+infinity]){j:=[seq(-50+2*k,k=0..50)]minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[0]==-infinity){j:=[seq(2*k,k=-25..0.5*floor(L[1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[1]==+infinity){ +j:=[seq(2*k,k=floor(0.5*L[0])..0.5*50)] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for +} +else{ j:=[seq(2*k,k=0.5*floor(z[0])..0.5*floor(z[nz-1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for } + }}; + + + + + + + +si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]); + if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}}; + fpour; +fsi; + + +S:=NULL; +S:=S,z[0]; +for(j:=1;j<size(z);j++){ + if(z[j]!=undef and (abs(z[j])>1e-15 or z[j]==0)){ + S:=S,z[j]}; +} +z:=[S]; + +Z:=sort(z); +nz:=size(Z); + +S:=NULL; +S:=S,Z[0]; +for(j:=1;j<nz;j++){ + if(Z[j]!=S[size(S)-1]){ + S:=S,Z[j]}; +} +Z:=[S]; + + +nz:=size(Z); +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +";fpour; + + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0; + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre; +"} +lm0:=limit(f(x),x,Z[0],1)==-infinity; + li:=lvic+nom+"}$ etex);"+ + if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); +"}}} + }; } + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + + + + + + +\end{VerbatimOut} + + + + + + + +%% +%% Code giac/Xcas pour les Tableaux de Variations avec +%% Valeurs intermediaires +%% + + + + + +\begin{VerbatimOut}{XcasTVI.cxx} + + +TVI(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + +Z:=sort([op(set[op(Z)])]); + + + +nz:=size(Z); +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" "; + + + +LI:=limit(f(x),x,Z[0],1); +LF:=limit(f(x),x,Z[nz-1],-1); +LP:=NULL; +PB:=1; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; +if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; + +NL:=size(LL); +A:=NULL;aa:=1; +kk:=0; + + + +if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); +if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}} +l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"}; +//chgmt NL->nz +if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); + +if(PB[k]==1){if(TestS==0){ + A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}}; +} + + l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);" + + }; + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp((Z[0]+10^(-3)))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp(10^(-3)+Z[0])))==1.0){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$ + $ etex);"+ +if(evalf(sign(fp(10^(-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; + + + + + +if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + ksp:=evalf(fp(Z[r]+0.01))>0; + TestL:=(abs(LL[r])==abs(LL[r+1])); + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $ $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; + }} +else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + + if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $ $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} + else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} +}}}}; + + + + + lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"} + + + +lm0:=limit(f(x),x,Z[0],1)==-infinity; + + + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + + li:=lvic+nom+"}$ etex); +"+ if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; + + + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)) { + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + $ "+ao+" $ etex,0.5);" + }else{" "}; +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[rr-1],1))< evalf(limit(f(x),x,Z[rr],-1)); + krp:=evalf(limit(f(x),x,Z[rr],1))> evalf(limit(f(x),x,Z[rr+1],-1)) ; + lmrm:=limit(f(x),x,Z[rr],-1)==-infinity;lmrp:=limit(f(x),x,Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + $ "+ao+" $ etex,0.5); + ";rr:=rr+1; +}// testS==0 +else{lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + "}}};rr:=rr+1; +}//else testS==0 +}//PB[r]==1 +}//for nz<NL +}// else nz<NL +//if nz=NL +};//if nz>2 + + + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + + +MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ +if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}}; + + + + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + + +\end{VerbatimOut} + + + +%% +% +% +% +% Pour avoir les racines sous forme exacte.... quand c'est possible ! +% +% +% +%%%%%%%%% + + +\begin{VerbatimOut}{XcasTVIex.cxx} + + + +TVIex(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +S:=[]; + +Sex:=NULL; +Zex:=solve(f(x)=ao); +Zex:=sort(Zex); +for(j:=0;j<size(Zex);j++){ +if((evalf(Zex[j])>=evalf(L[0])) and (evalf(Zex[j])<=evalf(L[nl-1]))){Sex:=Sex,Zex[j]}; +}; +Sex:=[Sex]; + + + + + + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + + + Z:=sort([op(set[op(Z)])]); + + +nz:=size(Z); +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" "; + + + +LI:=limit(f(x),x,Z[0],1); +LF:=limit(f(x),x,Z[nz-1],-1); +LP:=NULL; +PB:=1; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; +if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; + +NL:=size(LL); +A:=NULL;aa:=0; +kk:=0; + + + +if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); +if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $"+latex(simplify(Sex[aa]))+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}} +l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"}; +//chgmt NL->nz +if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); + +if(PB[k]==1){if(TestS==0){ + A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $"+latex(simplify(Sex[aa]))+"$ etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}}; +} + + l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);" + + }; + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(sign(fp((Z[0]+10^(-3))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$ + $ etex);"+ +if(evalf(sign(fp(10^(-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; + + + + +if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + ksp:=evalf(fp(Z[r]+0.01))>0; + TestL:=(abs(LL[r])==abs(LL[r+1])); + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $ $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; + }} +else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + + if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $ $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} + else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} +}}}}; + + + + + lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"} + + + +lm0:=limit(f(x),x,Z[0],1)==-infinity; + + + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + + li:=lvic+nom+"}$ etex); +"+ if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; + + + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)) { + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + $ "+ao+" $ etex,0.5);" + }else{" "}; +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[rr-1],1))< evalf(limit(f(x),x,Z[rr],-1)); + krp:=evalf(limit(f(x),x,Z[rr],1))> evalf(limit(f(x),x,Z[rr+1],-1)) ; + lmrm:=limit(f(x),x,Z[rr],-1)==-infinity;lmrp:=limit(f(x),x,Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + $ "+ao+" $ etex,0.5); + ";rr:=rr+1; +}// testS==0 +else{lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + "}}};rr:=rr+1; +}//else testS==0 +}//PB[r]==1 +}//for nz<NL +}// else nz<NL +//if nz=NL +};//if nz>2 + + + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + + +MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ +if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}}; + + + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + +\end{VerbatimOut} + + + + + + + +%% +%% +%% Quand les solutions de f'(x)=0 ne sont pas formellement calculables +%% + + + + +\begin{VerbatimOut}{XcasTVIapp.cxx} + +TVIapp(L,F,nom,nomv,f,ftt,ao,nmr):={ + + +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +z0:=concat(L,F);z:=sort(z0); +nz:=size(z); + + + + + + + +S:=op(fsolve(fp(x),x)); + + + + + +if(L==[-infinity,+infinity]){j:=[seq(-50+2*k,k=0..50)]minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[0]==-infinity){j:=[seq(2*k,k=-25..0.5*floor(L[1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[1]==+infinity){ +j:=[seq(2*k,k=floor(0.5*L[0])..0.5*50)] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for +} +else{ j:=[seq(2*k,k=0.5*floor(z[0])..0.5*floor(z[nz-1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for } + }}; + + + + + + + + +si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]); + if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}}; + fpour; +fsi; + + +S:=NULL; +S:=S,z[0]; +for(j:=1;j<size(z);j++){ + if(z[j]!=undef and (abs(z[j])>1e-15 or z[j]==0)){ + S:=S,z[j]}; +} +z:=[S]; + + + +Z:=sort(z); +nz:=size(Z); + +S:=NULL; +S:=S,Z[0]; +for(j:=1;j<nz;j++){ + if(Z[j]!=S[size(S)-1]){ + S:=S,Z[j]}; +} +Z:=[S]; + + +nz:=size(Z); +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" "; + + + +LI:=limit(f(x),x,Z[0],1); +LF:=limit(f(x),x,Z[nz-1],-1); +LP:=NULL; +PB:=1; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; +if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; + +NL:=size(LL); +A:=NULL;aa:=1; +kk:=0; + + +if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); +if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}} +l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"}; +//chgmt NL->nz +if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); + +if(PB[k]==1){if(TestS==0){ + A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}}; +} + + l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);" + + }; + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(sign(fp((Z[0]+10^(-3))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$ + $ etex);"+ + +if(evalf(sign(fp(10^(-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; + + + +if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + ksp:=evalf(fp(Z[r]+0.01))>0; + TestL:=(abs(LL[r])==abs(LL[r+1])); + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $ $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; + }} +else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + + if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $ $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} + else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} +}}}}; + + + + + lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"} + + + +lm0:=limit(f(x),x,Z[0],1)==-infinity; + + + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + + li:=lvic+nom+"}$ etex); +"+ if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; + + + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)) { + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + $ "+ao+" $ etex,0.5);" + }else{" "}; +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[rr-1],1))< evalf(limit(f(x),x,Z[rr],-1)); + krp:=evalf(limit(f(x),x,Z[rr],1))> evalf(limit(f(x),x,Z[rr+1],-1)) ; + lmrm:=limit(f(x),x,Z[rr],-1)==-infinity;lmrp:=limit(f(x),x,Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + $ "+ao+" $ etex,0.5); + ";rr:=rr+1; +}// testS==0 +else{lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + "}}};rr:=rr+1; +}//else testS==0 +}//PB[r]==1 +}//for nz<NL +}// else nz<NL +//if nz=NL +};//if nz>2 + + + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + + +MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ +if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}}; + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + + + +\end{VerbatimOut} + + + + + + + +%% +%% Code giac/Xcas pour les Tableaux de variations de courbes parametrees +%% + + + + + + + +\begin{VerbatimOut}{XcasTVP.cxx} +TVP(L,F,nom,nomv,ff,ftt,trigo,nmr):={ + +nl:=size(L); +fp:=[]; +S:=[]; +f:=[unapply(ff[0],t),unapply(ff[1],t)]; +fp:=[function_diff(f[0]),function_diff(f[1])]; +Z:=[]; +LLL:=[]; + + +all_trig_solutions:=1; +reset_solve_counter(-1,-1); + +for(d:=0;d<=1;d++){ +LLL:=concat(L,F[d]); +Z:=LLL union Z; +SS:=solve(factor(simplify(fp[d](t))),t); +ns:=size(SS); + + +for(k:=0;k<ns;k++){ +if(trigo==t){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ + +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; + +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ + +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; + +} +}else{ +S:=concat(S,SS); +} +} + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + qq:=member(simplify(S[j]),Z)==0; + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}}; + fpour + fsi; +Z:=sort(Z); +nz:=size(Z); + + + tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); + ftantque; + + + + +nz:=size(Z); +u:=1; + tantque (u<nz-2) and (nz>2) faire + tantque evalf(Z[u])==evalf(Z[u+1]) faire + Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=size(Z); + ftantque; + u:=u+1; + ftantque; + + + }; + +Z:=sort(Z); +nz:=size(Z); + + + + l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:="",""; lf:="","";lsp:="",""; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +";fpour; + + lsi:="",""; + +FFF:=[[],[]]; + +for(d:=0;d<=1;d++){ +FFF[d]:=concat(F[d],[-infinity,+infinity]); + k0:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1)); + kz:=evalf(limit(f[d](x),x=Z[nz-1],-1))> evalf(limit(f[d](x),x=Z[nz-2],1)); +//} +//$ + lsi[d]:=lsic+nom[d]+"'("+nomv+")}$ etex);"+if(member(Z[0],FFF[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[0])))+"$ etex);"}else{if(Z[0]==-infinity){" "}else{"nonDefBarre; +"}}+ + if(Z[0]==-infinity){if(sign(evalf(fp[d](if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F[d])==0){ + if(sign(fp[d](Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{ + if(sign(fp[d]((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp[d](Z[r]+0.01))>0; + lsp[d]:=lsp[d]+if(member(Z[r],F[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[r])))+"$ etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[nz-1])))+"$ etex);"}else{if(Z[nz-1]==+infinity){" "}else{"nonDefBarre;"}} + + + + + } + + + + + + + + + + + + lm0:=1,2; li:=1,2; krm:=1,2; krp:=1,2; lmrm:=1,2; lmrp:=1,2; lp:="",""; lnz:=1,2; lf:=1,2; Kz:=1,2;K0:=1,2; + + +for(d:=0;d<=1;d++){ + K0[d]:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1)); + Kz[d]:=evalf(limit(f[d](x),x,Z[nz-1],-1))> evalf(limit(f[d](x),x,Z[nz-2],1)); +//{ +//$ +lm0[d]:=limit(f[d](x),x,Z[0],1)==-infinity; + li[d]:=lvic+nom[d]+"}$ etex);"+ + if(member(Z[0],F[d])==0){"valPos(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$ etex,"}+ + if(K0[d]==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm[d]:=evalf(limit(f[d](x),x=Z[r-1],1))< evalf(limit(f[d](x),x=Z[r],-1)); + krp[d]:=evalf(limit(f[d](x),x=Z[r],1))> evalf(limit(f[d](x),x,Z[r+1],-1)) ; + lmrm[d]:=limit(f[d](x),x,Z[r],-1)==-infinity;lmrp[d]:=limit(f[d](x),x,Z[r],1)==-infinity; + lp[d]:=lp[d]+if(member(Z[r],F[d])){ + "limGauche(btex + $"+if(lmrm[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],-1)))}+"$ + etex,"+if(krm[d]==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],1)))}+"$ etex,"+if(krp[d]==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f[d](Z[r])))+"$ + etex,"+if(sign(evalf(fp[d](Z[r]-0.001)))==sign(evalf((fp[d](Z[r]+0.001))) )){"0.5);"}else{if(krp[d]==1){"1);"}else{"0); +"}}} + }; } + +lnz[d]:=limit(f[d](x),x=Z[nz-1],-1)==-infinity; + + +lf[d]:=if(member(Z[nz-1],F[d])==0){"valPos(btex $"+ + if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$ etex,"+ + if(Kz[d]==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$ etex,"+ + if(Kz[d]==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + +} + + + + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi[0]+lsp[0]+lsf[0]+lsi[1]+lsp[1]+lsf[1]+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi[0]+lsf[0]+lsi[1]+lsf[1]+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li[0]+ +lp[0]+ +lf[0]+ +li[1]+ +lp[1]+ +lf[1] ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li[0]+ +lf[0]+ +li[1]+ +lf[1] ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi[0]+lsp[0]+lsf[0]+ +li[0]+ +lp[0]+ +lf[0]+ +lsi[1]+lsp[1]+lsf[1]+ +li[1]+ +lp[1]+ +lf[1] ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi[0]+lsf[0]+ +li[0]+ +lf[0]+ +lsi[1]+lsf[1]+ +li[1]+ +lf[1] ++" +endTableau; + +";} +} +} + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + +}:; +\end{VerbatimOut} + + + + +%% +%% Code giac/Xcas pour les Tableaux de signes de produits +%% + + + + +\begin{VerbatimOut}{XcasTabSignL.cxx} + + +TS(nomf,L,D,trigo,nmr):={ +L:=apply(f->unapply(f,x),L) +n:=size(L); +Z:=NULL; +nl:=size(L); +S:=[]; +mini:=D[0]; maxi:=D[1]; + +pour k de 0 jusque n-1 faire + + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(L[k](x))),x); +ns:=size(SS); +for(j:=0;j<ns;j++){ +m:=0; +while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1; +} +} + +}else{ +S:=solve(L[k](x),x); +} + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j]);} + fpour; + fsi; +fpour; + + + + + +Z:=sort(Z); +nz:=size(Z); + + + Z:=sort([op(set[(Z)])]); + + +nz:=size(Z); + +if(nz==0){li:="";l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);"; + for(p:=0;p<=n-1;p++){li:=li+lsic+latex(L[p](x))+"}$ etex);"+ +if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}else{" + "}+ +if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){" + valBarre(btex 0 etex);"}else{" + "} + +} + lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"}; + + +MetaLfc:=" beginTableau("+nmr+") +newLigneVariables(btex $ {x}$ etex); + "+l0+li+ lsic+nomf+"(x)}$ etex);"+ + if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+ lf+ + if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+" +endTableau; +" +; + +}else{ + +l0:="val(btex $"+latex(D[0])+"$ etex);";li:=" ";lr:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +";fpour; +l0:=l0+"val(btex $"+latex(D[1])+"$ etex);"; + + +for(p:=0;p<=n-1;p++){lp:=""; + li:=li+lsic+latex(L[p](x))+"}$ etex);"+ + if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}else{" + "}+ + if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"}; + + for(r:=0; r<=nz-2;r++){ + lp:=lp+if(simplify(L[p](Z[r]))==0){" + valBarre(btex 0 etex);"}else{"barre; + "}+ + if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}}; + + li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins; + "}+if(maxi!=+infinity and L[p](maxi)==0){" + valBarre(btex 0 etex);"}else{" + "} + }; + + +pour t de 0 jusque nz-2 faire + lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);" + fpour + +MetaLfc:=" beginTableau("+nmr+") +newLigneVariables(btex $ {x}$ etex); + "+l0+ + li + + lsic+nomf+"(x)}$ etex);"+ + if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+ + if(product(L[s](Z[0]-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"+ + lr+ + if(product(L[s](Z[nz-1]+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+" +endTableau; + + "; +} +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + }:; + +\end{VerbatimOut} + + + + +%% +%% Code giac/Xcas pour les Tableaux de signes de quotients +%% + + + +\begin{VerbatimOut}{XcasTabSignQ.cxx} +TSq(nomf,L,Fo,D,trigo,nmr):={ +L:=apply(f->unapply(f,x),L); +Fo:=apply(f->unapply(f,x),Fo); +L:=concat(L,Fo); +n:=size(L); +Z:=NULL; +m:=size(Fo); +F:=NULL;FF:=NULL; +mini:=D[0]; maxi:=D[1]; +S:=[]; +SF:=[]; + +pour k de 0 jusque n-1 faire + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(L[k](x))),x); +ns:=size(SS); +for(j:=0;j<ns;j++){ +mm:=0; +while(evalf(simplify(subst(SS[j],n_1=mm)))<=evalf(maxi)){ +S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm+1; +};mm:=-1; +while(evalf(subst(SS[j],n_1=mm))>=evalf(mini)){ +S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm-1; +} +} + +}else{ +S:=concat(S,solve(L[k](x),x)); +} + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j]);} + fpour; + fsi; +fpour; + + +pour k de 0 jusque m-1 faire + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SSF:=solve(factor(simplify(Fo[k](x))),x); +nsf:=size(SSF); +for(j:=0;j<nsf;j++){ +mm:=0; +while(evalf(simplify(subst(SSF[j],n_1=mm)))<=evalf(maxi)){ +SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm+1; +};mm:=-1; +while(evalf(subst(SSF[j],n_1=mm))>=evalf(mini)){ +SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm-1; +} +} + +}else{ +SF:=concat(SF,solve(Fo[k](x),x)); +} + + si size(SF)>0 alors pour j de 0 jusque size(SF)-1 faire + FF:=FF,simplify(SF[j]); + if(SF[j]>mini and SF[j]<maxi){F:=F,simplify(SF[j]);} + fpour; + fsi; +fpour; + + + +Z:=[Z,F]; + + +Z:=sort([op(set[op(Z)])]); + +nz:=size(Z); + +if(nz==0){li:="";l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);"; + for(p:=0;p<=n-1;p++){li:=li+lsic+latex(L[p](x))+"}$ etex);"+ +if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}else{" + "}+ +if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){" + valBarre(btex 0 etex);"}else{" + "} + +} + lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"}; + + + + +MetaLfc:=" +beginTableau("+nmr+") +newLigneVariables(btex $ {x}$ etex); + "+l0+li+ + lsic+nomf+"(x)}$ etex);"+ + if(member(mini,FF)==0){if((mini!=-infinity) and (product(L[s](mini),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+ lf+ + if(member(maxi,FF)==0){if((maxi!=+infinity) and (product(L[s](maxi),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+" +endTableau; + +" +; + + + + +}else{ + + +l0:="val(btex $"+latex(D[0])+"$ etex);";li:=" ";lr:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +";fpour; +l0:=l0+"val(btex $"+latex(D[1])+"$ etex);"; + + +for(p:=0;p<=n-1;p++){lp:=""; + li:=li+lsic+latex(L[p](x))+"}$ etex);"+ + if(mini!=-infinity and L[p](mini)==0){" valBarre(btex 0 etex);"}else{" "}+ + if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"}; + + for(r:=0; r<=nz-2;r++){lp:=lp+if(simplify(L[p](Z[r]))==0){" valBarre(btex 0 etex);"}else{"barre;"}+ + if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}}; + + li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins; + "}+if(maxi!=+infinity and L[p](maxi)==0){"valBarre(btex 0 etex);"}else{" "} + + }; + + +pour t de 0 jusque nz-2 faire + lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(Z[t+1],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"} + fpour + + + + +MetaLfc:=" +beginTableau("+nmr+") +newLigneVariables(btex $ {x}$ etex); + "+l0+ + li + + + lsic+nomf+"(x)}$ etex);"+ + if(member(mini,FF)==0){if((mini!=-infinity) and (product(L[s](mini),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+ + if(product(L[s](Z[0]-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(Z[0],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"}+ + lr+ + if(product(L[s](Z[nz-1]+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(maxi,FF)==0){if((maxi!=+infinity) and (product(L[s](maxi),s,0,n-1)==0)){"valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+" +endTableau; + +" + + +} + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + + + + }:; + +\end{VerbatimOut} + + + + +%% Code giac/Xcas pour les Tableaux de signes du produit +%% de 2 facteurs affines +%% + + + + +\begin{VerbatimOut}{XcasTabSigna.cxx} +TSa(a,b,c,d,nmr):={ +zA:=solve(a*x+b=0,x)[0]; +zB:=solve(c*x+d=0,x)[0]; +zmin:=min(zA,zB); +zmax:=max(zA,zB); + Meta:= " + beginTableau("+nmr+") + newLigneVariables(btex $ {x}$ etex); + val(btex $-\\infty$ etex);val(btex $"+latex(zmin)+"$ etex); +val(btex $"+latex(zmax)+"$etex); +val(btex $+\\infty$ etex); + "+lsic+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+"}$ etex);" + + if(a>0){"moins;"}else{"plus;"}+ + if(zmin==zA){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(zmin==zA){si a>0 alors "plus;"; sinon "moins;";fsi} + else{si a>0 alors "moins;"; sinon "plus;"; fsi}+ + if(zmin==zA){"barre;"}else{"valBarre(btex 0 etex);"}+ + if(a>0){"plus;"}else{"moins;"} + +lsic+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+"}$ etex);" + + if(c>0){"moins"}else{"plus"}+";"+ + if(zmin==zB){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(zmin==zB){si c>0 alors "plus;"; sinon "moins;";fsi} + else{si c>0 alors "moins;"; sinon "plus;"; fsi}+ + if(zmin==zB){"barre;"}else{"valBarre(btex 0 etex);"}+ + if(c>0){"plus;"}else{"moins;"} + + +lsic+"{("+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+")("+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+")}}$ etex);" + + si a*c>0 alors plus; sinon moins;fsi+";"+ + "valBarre(btex 0 etex);"+ + si a*c>0 alors moins; sinon plus;fsi+";"+ + "valBarre(btex 0 etex);"+ + si a*c>0 alors plus; sinon moins;fsi+";"+" +endTableau; +" +; + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,Meta); +fclose(sortie); + + + }:; +\end{VerbatimOut} + + + + + + +%%$ +%% Code giac/Xcas pour les Tableaux de Signes d'expression ne contenant +%% qu'un seul terme + + + + +\begin{VerbatimOut}{XcasTSc.cxx} +TSc(g,D,F,trigo,nmr):={ +f:=unapply(g,x); +mini:=D[0]; maxi:=D[1];lm:=" "; +Z:=mini,maxi; +S:=[]; + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(f(x))),x); +ns:=size(SS); +for(j:=0;j<ns;j++){ +m:=0; +while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1; +} +} + +}else{ +S:=solve(f(x),x); +} + + + + + +if(size(S)==0 and size(F)==0){ +l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);"; +li:=if(member(mini,F)!=0){"nonDefBarre;"}else{if(mini!=-infinity and f(mini)==0){" + valBarre(btex 0 etex);"}else{" + "}}+ +if(mini!=-infinity or maxi!=+infinity){if(f((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}}else{if(f(0.3145274774464545777744)>0){"plus;"}else{"moins;"}}; +lf:=if(member(maxi,F)!=0){"nonDefBarre;"}else{if(maxi!=+infinity and f(maxi)==0){" + valBarre(btex 0 etex);"}else{" + "}}; +}else{ +if(size(S!=0)){pour j de 0 jusque size(S)-1 faire + if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j])}; + fpour} + +Z:=concat([Z],F); + + Z:=sort([op(set[op(Z)])]); + + +nz:=size(Z); +l0:=" ";li:=" ";lr:=" "; +if(nz==2){l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);"; +li:=if(mini!=-infinity and f(mini)==0){" + valBarre(btex 0 etex);"}else{if(member(mini,F)==0){" + "}else{"nonDefBarre;"}}+ +if(f((mini+maxi)*0.5)>0){"plus;"}else{"moins;"}; +lf:=if(maxi!=+infinity and f(maxi)==0){" + valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){" + "}else{"nonDefBarre;"} + }; + +}else{ +l0:="val(btex $"+latex(Z[0])+"$ etex);";li:=" "; +pour m de 1 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +"; +fpour; + + +li:= if(mini!=-infinity and f(mini)==0){" + valBarre(btex 0 etex);"}else{if(member(mini,F)==0){" + "}else{"nonDefBarre;"} + } + +lm:=if(nz>2){for(r:=0; r<nz-2;r++){lm:=lm+if(Z[r]==-infinity){ +if(f((Z[r+1]-1))>0){"plus;"}else{"moins;"} +}else{if(f((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}} ++ + if(member(Z[r+1],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"} + }}else{" "}; + +lf:=if(f(Z[nz-2]+0.1)>0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){" + "}else{"nonDefBarre;"} + }; +} +}; + + + + +MetaLfc:=" + +beginTableau("+nmr+") +newLigneVariables(btex $\\displaystyle {x}$ etex); + "+l0+lsic+latex(f(x))+"}$ etex);"+ + li+lm+lf + +" +endTableau; + +" +; + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + }:; + + +\end{VerbatimOut} + + + + + + + + + +%%$ + + + + + + + + +%%%% +%%% +%%% Pour des tableaux de variations simples sans fonctions +%%% +%%% + + + +\begin{VerbatimOut}{XcasTVS.cxx} +TVS(La,Lo,F,nomf,nomv,nmr):={ + +na:=size(La); +f:=F; +if(member(La[0],F)){f:=f[1..size(f)-1]}; +if(member(La[na-1],F)){f:=f[0..size(f)-2]}; +Z:=sort(concat(La,f)); +Zo:=sort([op(set[op(Z)])]); +nz:=size(Z); +nzo:=size(Zo); + + +k0:= evalf(Lo[0])> evalf(Lo[1]); +kz:=evalf(Lo[nz-1])> evalf(Lo[nz-2]); + + +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" "; + for(m:=0;m<=nzo-1;m++){l0:=l0+"val(btex $"+latex(Zo[m])+"$ etex);"} + +li:=lvic+nomf+"}$ etex);"+ + if(member(Z[0],F)==0){"valPos(btex $"+latex(Lo[0])+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+latex(Lo[0])+"$ etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ + krm:=evalf(Lo[r-1])< evalf(Lo[r]); + krp:=evalf(Lo[r])> evalf(Lo[r+1]) ; + + lp:=lp+if(Z[r]==Z[r+1]){ + "limGauche(btex$"+latex(Lo[r])+"$etex,"+ + if(krm==1){"1);"} + else{"0);"} + }// fin if zr=zr+1 + else{ + if(Z[r]==Z[r-1]){ + "nonDefBarre;limDroite(btex$"+latex(Lo[r])+"$etex,"+ + if(krp==1){"1);"} + else{"0);"} + }//fin if zr=zr-1 + else{ + "valPos(btex $"+latex(Lo[r])+"$etex,"+ + if(krp==1){"1);"}else{"0);"} +}//fin else zr=zr-1 +}//fin else zr=zr+1 +}//fin for +}//fin de if nz>2 + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+latex(Lo[nz-1])+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+latex(Lo[nz-1])+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + +MetaLfc:= + + if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";} + +//return(MetaLfc); + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + +}:; + +\end{VerbatimOut} + +%%$ + + + + + + + + + + + + + + + + + +%% +%% traitement des fichiers produits par giac/xcas +%% +%% + +% pour l'échelle des tableaux taper \ech{facteur de réduction} + +\newcommand\echelle{1} +\newcommand\ech[1]{\renewcommand\echelle{#1}} + + + +\newcommand\couleurtab{black} +\newcommand\coultab[1]{\renewcommand\couleurtab{#1}} + +\newcommand{\dresse}[2]{% + + + +\ifxetex + + + +\ifthenelse{\boolean{xcas}}{% Avec l'option "XCas present" + \executGiacmp{XCas#2.giac}% reconstituer le tableau + % exporter le source mp + % puis lancer metapost pour creer + % l'image du tableau + \immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab.mp} + \immediate\write18{\cat enteteMP.cfg >> \nomtravail_Tab#2.mp} +\immediate\write18{\echod def beginTableau(expr c) =\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod begingroup\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod charcode:=c;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod clearxy; clearit; clearpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod pickup defaultpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod drawoptions(withcolor(#1));\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod initTableau;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod enddef;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab#2.mp} + \immediate\write18{\cat queue.mp >> \nomtravail_Tab#2.mp} + \immediate\write18{./convert-mp-pdf.sh \nomtravail_Tab#2 \theTVn} + \immediate\write18{\cp \nomtravail_Tab#2.pdf \nomtravail_Tab\theTVn.pdf} + \immediate\write18{\rem \nomtravail_Tab#2.mp} + }% + {% sinon, si le tableau est absent, alerte. + \IfFileExists{\nomtravail_Tab.\theTVn}{}{% + \PackageError{tablor}{Tableau absent non + reconstituable.}{Pour compiler il faut, soit les fichiers de + tableaux, soit le fichier \nomtravail_Tab.mp, soit disposer de + XCas.}}} + +\begin{center} + \includegraphics[scale=\echelle]{\nomtravail_Tab\theTVn.pdf} +\end{center} +\stepcounter{TVn} + + + +\else +\ifthenelse{\boolean{xcas}}{% Avec l'option "XCas present" + \executGiacmp{XCas#2.giac}% reconstituer le tableau + % exporter le source mp + % puis lancer metapost pour creer + % l'image du tableau + \immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab.mp} + \immediate\write18{\cat enteteMP.cfg >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod def beginTableau(expr c) =\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod begingroup\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod charcode:=c;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod clearxy; clearit; clearpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod pickup defaultpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod drawoptions(withcolor(#1));\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod initTableau;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod enddef;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab#2.mp} + \immediate\write18{\cat queue.mp >> \nomtravail_Tab#2.mp} + \immediate\write18{mpost -jobname=\nomtravail_Tab \nomtravail_Tab#2.mp} + \immediate\write18{\rem \nomtravail_Tab#2.mp} + }% + {% sinon, si le tableau est absent, alerte. + \IfFileExists{\nomtravail_Tab.\theTVn}{}{% + \PackageError{tablor}{Tableau absent non + reconstituable.}{Pour compiler il faut, soit les fichiers de + tableaux, soit le fichier \nomtravail_Tab.mp, soit disposer de + XCas.}}} + +\begin{center} + \includegraphics[scale=\echelle]{\nomtravail_Tab.\theTVn} +\end{center} +\stepcounter{TVn} + +\fi + +} + + +%% +%% traitement des fichiers produits par giac/xcas avec possibilite +%% de modifier le fichier metapost (environnement etoile)) +%% + + + +\newcommand{\dressetoile}[2]{% + + + +\ifxetex + +\IfFileExists{\nomtravail_Tab.\theTVn}{% Test sur l'existence du tableau +% Si oui, inclusion du fichier source de sauvegarde mp dans Tableaux +\immediate\write18{\cat TSav-\theTVn.mp >> \nomtravail_Tab.mp}} +% Si non, lancement des operations de fabrication +{\executGiacmp{XCas#2.giac}% +\immediate\write18{\editeur XCasmpfc.mp } + + % Modification avec l'editeur choisi +\immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab.mp} +\immediate\write18{\cp XCasmpfc.mp TSav-\theTVn.mp} % Sauvegarde du + % source mp sur le disque pour une + % inclusion ulterieure dans Tableaux.mp. +\immediate\write18{\cat enteteMP.cfg >> \nomtravail_Tab#2.mp} +\immediate\write18{\echod def beginTableau(expr c) =\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod begingroup\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod charcode:=c;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod clearxy; clearit; clearpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod pickup defaultpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod drawoptions(withcolor(#1));\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod initTableau;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod enddef;\echof >> \nomtravail_Tab#2.mp} +\immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab#2.mp}} % Inclusion du + % source dans le + % fichier + % Tableaux +\immediate\write18{\cat queue.mp >> \nomtravail_Tab#2.mp} + \immediate\write18{./convert-mp-pdf.sh \nomtravail_Tab#1 \theTVn} + \immediate\write18{\cp \nomtravail_Tab#2.pdf \nomtravail_Tab\theTVn.pdf}% Reconstitution des tableaux + % et creation du dernier. L'option + % pallie l'absence de end en fin de + % fichier +\immediate\write18{\rem \nomtravail_Tab#2.mp} + +\begin{center} + \includegraphics[scale=\echelle]{\nomtravail_Tab\theTVn.pdf} +\end{center} +\ech{1} +\setcounter{TVn}{\theTVnbis} % Restauration du compteur TVn + + +\else + +\IfFileExists{\nomtravail_Tab.\theTVn}{% Test sur l'existence du tableau +% Si oui, inclusion du fichier source de sauvegarde mp dans Tableaux +\immediate\write18{\cat TSav-\theTVn.mp >> \nomtravail_Tab.mp}} +% Si non, lancement des operations de fabrication +{\executGiacmp{XCas#2.giac}% +\immediate\write18{\editeur XCasmpfc.mp } + + % Modification avec l'editeur choisi +\immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab.mp} +\immediate\write18{\cp XCasmpfc.mp TSav-\theTVn.mp} % Sauvegarde du + % source mp sur le disque pour une + % inclusion ulterieure dans Tableaux.mp. +\immediate\write18{\cat enteteMP.cfg >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod def beginTableau(expr c) =\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod begingroup\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod charcode:=c;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod clearxy; clearit; clearpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod pickup defaultpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod drawoptions(withcolor(#1));\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod initTableau;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod enddef;\echof >> \nomtravail_Tab#2.mp} +\immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab#2.mp}} % Inclusion du + % source dans le + % fichier + % Tableaux +\immediate\write18{\cat queue.mp >> \nomtravail_Tab#2.mp} +\immediate\write18{mpost -jobname=\nomtravail_Tab \nomtravail_Tab#2.mp}% Reconstitution des tableaux + % et creation du dernier. L'option + % pallie l'absence de end en fin de + % fichier +\immediate\write18{\rem \nomtravail_Tab#2.mp} + +\begin{center} + \includegraphics[scale=\echelle]{\nomtravail_Tab.\theTVn} +\end{center} +\ech{1} +\setcounter{TVn}{\theTVnbis} % Restauration du compteur TVn + + +\fi + +} + + + + + + + +%% +%% +%%% +%%% +%%% les "giac" qui permettent d'executer la commande rentree dans le fichier tex +%%% suivis des environnements qui permettront la saisie du code giac/xcas +%%% Les versions etoilees permettent de modifier le code metapost produit initialement +%%% + + + + +\begin{VerbatimOut}{XCasa.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTabSigna.cxx"); +read("XCasa.user"); +\end{VerbatimOut} + +\newenvironment{TSa} +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasa.user}} +{\end{VerbatimOut} + \dresse{\couleurtab}{a} +} + + + + + + + + + +\begin{VerbatimOut}{XCasQ.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTabSignQ.cxx"); +read("XCasQ.user"); +\end{VerbatimOut} + +\newenvironment{TSq}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasQ.user}} +{\end{VerbatimOut}\dresse{\couleurtab}{Q}} + + + +\newenvironment{TSq*}[1]% +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasQ.user}} +{\end{VerbatimOut}\dressetoile{\couleurtab}{Q}} + + +\begin{VerbatimOut}{XCasL.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTabSignL.cxx"); +read("XCasL.user"); +\end{VerbatimOut} + +\newenvironment{TS}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasL.user}} +{\end{VerbatimOut}\dresse{\couleurtab}{L}} + + +\newenvironment{TS*}[1] +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasL.user}} +{\end{VerbatimOut}\dressetoile{\couleurtab}{L}} + + +\begin{VerbatimOut}{XCasTSc.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTSc.cxx"); +read("XCasTSc.user"); +\end{VerbatimOut} + + + + +\newenvironment{TSc*}[1]% +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTSc.user}} +{\end{VerbatimOut}\dressetoile{\couleurtab}{TSc}} + + +\newenvironment{TSc}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTSc.user}} +{\end{VerbatimOut}\dresse{\couleurtab}{TSc}} + + +\begin{VerbatimOut}{XCasTV.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTV.cxx"); +read("XCasTV.user"); +\end{VerbatimOut} + +\newenvironment{TV}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTV.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TV}} + +\newenvironment{TV*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTV.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TV}} + + + + + + + +\begin{VerbatimOut}{XCasTVP.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVP.cxx"); +read("XCasTVP.user"); +\end{VerbatimOut} + +\newenvironment{TVP}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVP.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TVP}} + +\newenvironment{TVP*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVP.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVP}} + + + + + + + + + + +\begin{VerbatimOut}{XCasTVZ.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVZ.cxx"); +read("XCasTVZ.user"); +\end{VerbatimOut} + +\newenvironment{TVZ}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVZ.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TVZ}} + +\newenvironment{TVZ*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVZ.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVZ}} + + + + + + + + + + +\begin{VerbatimOut}{XCasTVapp.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVapp.cxx"); +read("XCasTVapp.user"); +\end{VerbatimOut} + +\newenvironment{TVapp}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVapp.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TVapp}} + +\newenvironment{TVapp*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVapp.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVapp}} + + + + + + + + + + + +\begin{VerbatimOut}{XCasTVI.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVI.cxx"); +read("XCasTVI.user"); +\end{VerbatimOut} + +\newenvironment{TVI}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVI.user}}% +{\end{VerbatimOut}\dresse{\couleurtab}{TVI}} + + +\newenvironment{TVI*}[1]% +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVI.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVI}} + + + + + +\begin{VerbatimOut}{XCasTVIex.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVIex.cxx"); +read("XCasTVIex.user"); +\end{VerbatimOut} + +\newenvironment{TVIex}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIex.user}}% +{\end{VerbatimOut}\dresse{\couleurtab}{TVIex}} + + +\newenvironment{TVIex*}[1]% +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIex.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVIex}} + + + + + +\begin{VerbatimOut}{XCasTVIapp.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVIapp.cxx"); +read("XCasTVIapp.user"); +\end{VerbatimOut} + +\newenvironment{TVIapp}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIapp.user}}% +{\end{VerbatimOut}\dresse{\couleurtab}{TVIapp}} + + +\newenvironment{TVIapp*}[1]% +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIapp.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVIapp}} + + + +\begin{VerbatimOut}{XCasTVPC.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVPC.cxx"); +read("XCasTVPC.user"); +\end{VerbatimOut} + +\newenvironment{TVPC}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVPC.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TVPC}} + +\newenvironment{TVPC*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVPC.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVPC}} + + + +\begin{VerbatimOut}{XCasTVS.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVS.cxx"); +read("XCasTVS.user"); +\end{VerbatimOut} + +\newenvironment{TVS}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVS.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TVS}} + +\newenvironment{TVS*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVS.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVS}} + + + + + +%% pour nettoyer les fichiers auxiliaires + +\AtEndDocument{\immediate\write18{\cat queue.mp >> \nomtravail_Tab.mp} + } + + + + +%% +%% Zi end -> enjoy :) diff --git a/macros/latex/contrib/tablor/tablor.cfg b/macros/latex/contrib/tablor/tablor.cfg new file mode 100644 index 0000000000..82048c7197 --- /dev/null +++ b/macros/latex/contrib/tablor/tablor.cfg @@ -0,0 +1,113 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Fichier de configuration de tablor.sty % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +% La mise jour de ce fichier permet d'adapter certains paramtres du package tablor.sty +% au poste de travail et aux habitudes des utilisateurs. + + +%======================================== +% I - Configuration du prambule MetaPOST +%======================================== + +\begin{filecontents*}{enteteMP.cfg} +input tableauVariation; +verbatimtex +%&latex +\documentclass{article} +\usepackage[upright]{kpfonts}% ou mathpazo, lmodern, etc. ou rien ! +%\usepackage{amsmath} +\renewcommand\mbox[1]{ #1 } % pour les mbox intempestifs de xcas +\renewcommand\cdot{ } % idem pour les cdot +\begin{document} +\catcode`\@=0 % pour utiliser le @ +etex +\end{filecontents*} + + + +%================================= +% II - Dclaration de l'diteur utilis +% ================================ +% +% Remplacez "gedit" par la commande qui lance un autre editeur que votre diteur favori pour pouvoir modifier certains tableaux. +% Laissez une espace avant de fermer l'accolade. + +\newcommand{\editeur}{emacsclient -c } + + + + + + + + + + + +%================================= +%III - 1re colonne +%================================= +% +%permet de configurer les termes dans la premire colonne des +%tableaux : "signe de" ou "sign of" ou "" etc. +% + + + +\begin{VerbatimOut}{config.cxx} + +//reglage de epsilon : seuil du zero de giac +epsilon:=1e-100; + +// POUR LES TV, TVI,TVZ,TVapp,TSq,TSa +// pour la ligne signe +lsic:=" +newLigneSignes(btex $\\hbox{ Signe de }\\atop{\\displaystyle "; + +// POUR LES TV, TVI,TVZ,TVapp +// pour la ligne variation +lvic:=" +newLigneVariations(btex $\\hbox{ Variations de }\\atop{\\displaystyle "; + +\end{VerbatimOut} + + + +%% you may prefer + +% \begin{VerbatimOut}{config.cxx} + +% // FOR TV, TVI,TVZ,TVapp,TSq,TSa +% // for the signs +% lsic:=" +% newLigneSignes(btex $\\hbox{ Sign of }\\atop{\\displaystyle "; + +% // POUR LES TV, TVI,TVZ,TVapp +% // for the variations +% lvic:=" +% newLigneVariations(btex $\\hbox{ Variations of }\\atop{\\displaystyle "; + +%\end{VerbatimOut} + + + +%% ou si vous prfrez que ni signe ni variation n'apparaissent + + + +% \begin{VerbatimOut}{config.cxx} + +% // POUR LES TV, TVI,TVZ,TVapp,TSq,TSa +% // pour la ligne signe +% lsic:=" +% newLigneSignes(btex ${\\displaystyle "; + +% // POUR LES TV, TVI,TVZ,TVapp +% // pour la ligne variation +% lvic:=" +% newLigneVariations(btex ${\\displaystyle "; + +% \end{VerbatimOut} + diff --git a/macros/latex/contrib/tablor/tablor.html b/macros/latex/contrib/tablor/tablor.html new file mode 100644 index 0000000000..1d5c91754d --- /dev/null +++ b/macros/latex/contrib/tablor/tablor.html @@ -0,0 +1,3321 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN"> +<!-- Created by htmlize-1.34 in css mode. --> +<html> + <head> + <title>tablor.sty</title> + <style type="text/css"> + <!-- + body { + color: #cdba96; + background-color: #0d0d0d; + font-weight: bold; + } + .comment { + /* font-lock-comment-face */ + color: #ffd700; + background-color: #525252; + } + .comment-delimiter { + /* font-lock-comment-delimiter-face */ + color: #ffd700; + background-color: #525252; + } + .constant { + /* font-lock-constant-face */ + color: #9932cc; + font-weight: bold; + } + .font-latex-math { + /* font-latex-math-face */ + color: #436eee; + } + .font-latex-sedate { + /* font-latex-sedate-face */ + color: #d3d3d3; + } + .font-latex-subscript { + /* font-latex-subscript-face */ + font-size: 80%; + } + .font-latex-superscript { + /* font-latex-superscript-face */ + font-size: 80%; + } + .font-latex-warning { + /* font-latex-warning-face */ + color: #8b0000; + font-weight: bold; + } + .function-name { + /* font-lock-function-name-face */ + color: #87ceeb; + } + .keyword { + /* font-lock-keyword-face */ + color: #6495ed; + font-weight: bold; + } + .variable-name { + /* font-lock-variable-name-face */ + color: #98fb98; + } + + a { + color: inherit; + background-color: inherit; + font: inherit; + text-decoration: inherit; + } + a:hover { + text-decoration: underline; + } + --> + </style> + </head> + <body> + <pre> +<span class="font-latex-sedate">\NeedsTeXFormat</span>{LaTeX2e}[1995/12/01] +<span class="font-latex-sedate">\ProvidesPackage</span>{tablor}[09/05/2010 v4.07 la machine a creer des tableaux de signes et variations] + +<span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\copyleft</span></span><span class="comment"> Connan le Barbare (aka Guillaume Connan) </span><span class="font-latex-sedate"><span class="comment">\copyright</span></span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">This work may be distributed and/or mofified under the conditions +</span><span class="comment-delimiter">% </span><span class="comment">or the LaTeX Project Public Licence, either v1.3 or (at your option) +</span><span class="comment-delimiter">% </span><span class="comment">any later version. The latest version is in +</span><span class="comment-delimiter">% </span><span class="comment">http://www.latex-project.org/lppl/ +</span><span class="comment-delimiter">% </span><span class="comment">This work consists of the files tablor.sty, tablor-xetex.sty, tablor.cfg, tablor.tex, +</span><span class="comment-delimiter">% </span><span class="comment">tablor.pdf and tablor.html +</span> + +<span class="comment-delimiter">%% </span><span class="comment">Cree 16 environnements : +</span><span class="comment-delimiter">%% </span><span class="comment">tableau de signes de 2 facteurs affines +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TSa} +</span><span class="comment-delimiter">% </span><span class="comment">TSa(-2,3,-1,5,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">); +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TSa} +</span><span class="comment-delimiter">% </span><span class="comment">%%%%%% Pour des tableaux de plus de 2 facteurs +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TS} +</span><span class="comment-delimiter">% </span><span class="comment">TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[a,b],n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">); +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TS} +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">pour les tableaux de signes avec quotient +</span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TSq} +</span><span class="comment-delimiter">%</span><span class="comment">TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) +</span><span class="comment-delimiter">%%</span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TSq} +</span><span class="comment-delimiter">% </span><span class="comment">un tableau de variation : +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">pour les tableaux de signes à une seule ligne +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TSc} +</span><span class="comment-delimiter">% </span><span class="comment">TSc((x+10)/((x-5)*(x-2)),[-10,5],[2,5],n,0) +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TSc} +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TV} +</span><span class="comment-delimiter">% </span><span class="comment">TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TV} +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">tableau de variation avec liste de valeurs +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVS} +</span><span class="comment-delimiter">% </span><span class="comment">TVS([1,2,3,4],[-1,-infinity,+infinity,2,9],[2],"f","x",</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVS} +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">tableau de variation avec zones interdites +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVZ} +</span><span class="comment-delimiter">% </span><span class="comment">TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVZ} +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">tableau avec valeurs intermediares +</span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVI} +</span><span class="comment-delimiter">%</span><span class="comment">TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) +</span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVI} +</span><span class="comment-delimiter">%%%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">tableau avec valeurs intermediares et racines exactes +</span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVIex} +</span><span class="comment-delimiter">%</span><span class="comment">TVIex([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) +</span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVIex} +</span><span class="comment-delimiter">%%%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">tableau de variations avec f' sans zero formel +</span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVapp} +</span><span class="comment-delimiter">% </span><span class="comment">TVapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVapp} +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">tableau de variations avec f' sans zero formel +</span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVIapp} +</span><span class="comment-delimiter">% </span><span class="comment">TVIapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,0,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVIapp} +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%%%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">et leurs pendants etoiles qui permettent l'affichage intermediaire du +</span><span class="comment-delimiter">% </span><span class="comment">fichier metapost pour le modifier +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">Courbes parametrees +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVP} +</span><span class="comment-delimiter">% </span><span class="comment">TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVP} +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVP} +</span><span class="comment-delimiter">% </span><span class="comment">TVP([0,pi/2],[[],[]],["x","y"],"t",[2*cos(t),sin(2*t)],1,t,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVP} +</span><span class="comment-delimiter">% </span><span class="comment">% +</span> +<span class="comment-delimiter">% </span><span class="comment">Fonctions prolongeables par continuité +</span><span class="comment-delimiter">% </span><span class="comment">TVP([intervalles d'étude],[valeurs prolongeables],[valeurs interdites pour f'],"g","t",e^(-1/x^2),1,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">); +</span> + +<span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TVPC} +</span><span class="comment-delimiter">% </span><span class="comment">TVPC([-infinity,+infinity],[0],[0],"g","t",e^(-1/x^2),1,n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">); +</span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVPC} +</span> + + + + +<span class="comment-delimiter">%% </span><span class="comment">extensions requises +</span><span class="comment-delimiter">%% </span><span class="comment">Il faudra rajouter dans le preambule </span><span class="font-latex-sedate"><span class="comment">\usepackage</span></span><span class="comment">{graphicx} si vous +</span><span class="comment-delimiter">%% </span><span class="comment">ne l'avez pas de base +</span> + +<span class="font-latex-sedate">\RequirePackage</span>{filecontents} +<span class="font-latex-sedate">\RequirePackage</span>{ifthen} +<span class="font-latex-sedate">\RequirePackage</span>{fancyvrb} +<span class="font-latex-sedate">\RequirePackage</span>{ifpdf} + +<span class="font-latex-sedate">\fvset</span>{gobble=0} + +<span class="comment-delimiter">% </span><span class="comment">option xcas present +</span> + +<span class="font-latex-sedate">\newboolean</span>{xcas}<span class="font-latex-sedate">\setboolean</span>{xcas}{false} +<span class="font-latex-sedate">\DeclareOption</span>{xcas}{<span class="font-latex-sedate">\setboolean</span>{xcas}{true}} + +<span class="comment-delimiter">%% </span><span class="comment">Initialisation du choix d'OS +</span><span class="font-latex-sedate">\newboolean</span>{windows}<span class="font-latex-sedate">\setboolean</span>{windows}{false} +<span class="font-latex-sedate">\DeclareOption</span>{windows}{<span class="font-latex-sedate">\setboolean</span>{windows}{true}} + +<span class="font-latex-sedate">\ProcessOptions</span><span class="font-latex-sedate">\relax</span> + + + +<span class="comment-delimiter">%% </span><span class="comment">on configure tablor dans un fichier exterieur pour la plateforme +</span><span class="comment-delimiter">%% </span><span class="comment">et l'editeur +</span> +<span class="font-latex-sedate">\IfFileExists</span>{tablor.cfg}{<span class="font-latex-sedate"><span class="keyword">\input</span></span><span class="constant">{tablor.cfg}</span>}<span class="comment">%</span><span class="font-latex-sedate"><span class="comment">\typeout</span></span><span class="comment">{pas de fichier tablor.cfg}} +</span> + +<span class="comment-delimiter">%% </span><span class="comment">Definit des commandes disque selon l'OS utilise +</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{windows}}<span class="comment">% +</span> {<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\rem</span></span><span class="function-name">}</span>{DEL } <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cat</span></span><span class="function-name">}</span>{TYPE } + <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{COPY } <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\echod</span></span><span class="function-name">}</span>{ECHO } + <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\echof</span></span><span class="function-name">}</span>{ }}<span class="comment">% +</span> {<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\rem</span></span><span class="function-name">}</span>{rm }<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cat</span></span><span class="function-name">}</span>{cat } + <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{cp } <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\echod</span></span><span class="function-name">}</span>{echo "} + <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\echof</span></span><span class="function-name">}</span>{"}} + + + + + + + +<span class="comment-delimiter">%% </span><span class="comment">pour ceux compilant via pdflatex +</span> +<span class="font-latex-sedate">\ifpdf</span> +<span class="font-latex-sedate">\DeclareGraphicsRule</span>{*}{mps}{*}{} +<span class="font-latex-sedate">\fi</span> + +<span class="comment-delimiter">%% </span><span class="comment">pour nettoyer les fichiers auxiliaires +</span> +<span class="font-latex-sedate">\AtEndDocument</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> *.user XCas* Xcas* *.mpx} + } + + + + +<span class="comment-delimiter">%% </span><span class="comment">Pour clore les fichiers metapost +</span> + + <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{queue.mp} + + end + + <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + +<span class="comment-delimiter">%% </span><span class="comment">Nettoie les fichiers log dont le nom depend du choix de l'utilisateur +</span><span class="comment-delimiter">%% </span><span class="comment">Par defaut, c'est le nom du fichier tex courant (</span><span class="font-latex-sedate"><span class="comment">\jobname</span></span><span class="comment">) +</span><span class="comment-delimiter">%% </span><span class="comment">Clôt le fichier metapost contenant le recapitulatif de tous les tableaux +</span> + + +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\nettoyer</span></span><span class="function-name">}</span>[1][<span class="font-latex-sedate">\jobname</span>]<span class="comment">% +</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> #1.Tab.log queue.mp enteteMP.cfg session.tex config.cxx} +} + + + + +<span class="comment-delimiter">%% </span><span class="comment">Donne comme prefixe aux tableaux le prefixe courant +</span><span class="comment-delimiter">%% </span><span class="comment">Peut-être modifie par </span><span class="font-latex-sedate"><span class="comment">\initablor</span></span><span class="comment"> +</span> +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\nomtravail</span></span><span class="function-name">}</span>{<span class="font-latex-sedate">\jobname</span>} + +<span class="comment-delimiter">%% </span><span class="comment">initialise les compteurs +</span> +<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{TVn}</span> +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\tv</span></span><span class="function-name">}</span>{<span class="font-latex-sedate">\theTVn</span>} + +<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{TVnbis}</span> +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\tvbis</span></span><span class="function-name">}</span>{<span class="font-latex-sedate">\theTVnbis</span>} + + + +<span class="comment-delimiter">%% </span><span class="comment">permet de donner un prefixe aux tableaux produits (</span><span class="font-latex-sedate"><span class="comment">\jobname</span></span><span class="comment"> par defaut) +</span><span class="comment-delimiter">%% </span><span class="comment">effectue quelques verifications : +</span> + +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\initablor</span></span><span class="function-name">}</span>[1][<span class="font-latex-sedate">\jobname</span>]{<span class="comment">% +</span><span class="font-latex-sedate"><span class="keyword">\renewcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\nomtravail</span></span><span class="function-name">}</span>{#1}<span class="comment">% Arret du nom des tableaux +</span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{0}</span><span class="comment">% Initialisation du compteur de tableaux. +</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{xcas}}<span class="comment">% Avec l'option XCas +</span>{<span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\nomtravail</span>_Tab.mp}<span class="comment">% Si Tableaux.mp est present... +</span> {<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> <span class="font-latex-sedate">\nomtravail</span>_Tab.mp}}<span class="comment">% le detruire +</span> {}<span class="comment">% +</span> <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cp</span> enteteMP.cfg <span class="font-latex-sedate">\nomtravail</span>_Tab.mp}<span class="comment">% Reconstituer l'entête de Tableaux.mp +</span>} +{<span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\nomtravail</span>_Tab.mp}<span class="comment">% Sans l'option XCas, si +</span> <span class="comment">% Tableaux.mp existe +</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost -interaction=batchmode <span class="font-latex-sedate">\nomtravail</span>_Tab}}<span class="comment">% l'executer pour reconstituer les figures +</span>{<span class="font-latex-sedate">\PackageWarning</span>{tablor}{Pas de source metapost pour creer les tableaux.}}<span class="comment">% sinon message d'erreur +</span> <span class="comment">% (mais pas d'arret car les tableaux +</span> <span class="comment">% peuvent être presents ) +</span>}}<span class="comment">% +</span> + + +<span class="comment-delimiter">%% </span><span class="comment">commande pour lancer giac selon l'OS +</span> +<span class="font-latex-sedate">\makeatletter</span> +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\executGiacmp</span></span><span class="function-name">}</span>[1]{<span class="comment">% +</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{windows}}<span class="comment">% +</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{giac #1 }}<span class="comment">% +</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{giac <#1 }}} +<span class="font-latex-sedate">\makeatother</span> + + + + +<span class="comment-delimiter">%%%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%%% </span><span class="comment">LES SCRIPTS GIAC/XCAS +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%%%</span><span class="comment"> +</span> + + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">Code giac/Xcas pour les Tableaux de Variations +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTV.cxx} +TV(L,F,nom,nomv,f,ftt,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + qq:=member(simplify(S[j]),Z)==0; + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}}; + fpour + fsi; +Z:=sort(Z); +nz:=size(Z); + + + tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); + ftantque; + + + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + +Z:=sort([op(set[op(Z)])]); + +nz:=size(Z); +l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex); +";fpour; + + k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); + kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ + if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)))))==1.0){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.1))>0; + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre; +"} +lm0:=limit(f(x),x=Z[0],1)==-infinity; + li:=lvic+nom+"}$</span> etex);"+ + if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"} + else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1)); + krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ; + lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)){ + "limGauche(btex + <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> + etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span> + etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); +"}}} + }; } + +lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + + + + +<span class="comment-delimiter">%%%%</span><span class="comment"> +</span> + +<span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">TVPC : pour les fonctions prolongeables par continuité. +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVPC.cxx} +TVPC(L,F,FP,nom,nomv,f,ftt,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +Z:=concat(Z,FP); +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + qq:=member(simplify(S[j]),Z)==0; + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}}; + fpour + fsi; +Z:=sort(Z); +nz:=size(Z); + + + tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); + ftantque; + + + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + +Z:=sort([op(set[op(Z)])]); + +nz:=size(Z); +l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex); +";fpour; + + k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); + kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ + if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],FP)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)))))==1.0){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.1))>0; + lsp:=lsp+if(member(Z[r],FP)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf:=if(member(Z[nz-1],FP)==0){""}else{"nonDefBarre; +"} +lm0:=limit(f(x),x=Z[0],1)==-infinity; + li:=lvic+nom+"}$</span> etex);"+ + if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"} + else{"limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1)); + krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ; + lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)){ + "valPos(btex + <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> + etex,"+if(krm==1){"1);"}else{"0);"} } + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span> + etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); +"}}} + }; } + +lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);"}else{"0);"}}; + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + + + + + + + + + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">TV avec une zone interdite : on rajoute comme argument la liste des intervalles interdits +</span><span class="comment-delimiter">%% </span><span class="comment">par exemple, pour sqrt(x^2-1) : TVZ([-infinity,100],[],[[-1,1]],"f","x",sqrt(x^2-1),1,1) +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVZ.cxx} + + +TVZ(L,F,FF,nom,nomv,f,ftt,trigo,nmr):={ +nl:=size(L); +nf:=size(FF); + Ff:=NULL;IMIN:=NULL;IMAX:=NULL; +for(k:=0;k<nf;k++){ +if(FF[k][0]>L[0]){Imin[k]:=FF[k][0];LL:=L}else{Imin[k]:=L[0];LL:=[L[1]]}; +if(FF[k][1]<L[1]){Imax[k]:=FF[k][1];LL:=L}else{Imax[k]:=L[1];LL:=[L[0]]}; + Ff:=Ff,[Imin[k],Imax[k]]; + IMIN:=IMIN,Imin[k]; + IMAX:=IMAX,Imax[k]; + } + FF:=[Ff]; + IMIN:=[IMIN]; + IMAX:=[IMAX]; + f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(LL,F); + +for(k:=0;k<nf;k++){ +Z:=concat(Z,FF[k]); +} + +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + for(k:=0;k<nf;k++){ + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + kK:=(evalf(S[j])<evalf(Imin[k])) or (evalf(S[j])>evalf(Imax[k])); + Kk:=(kk) and kK; + if(Kk==1){Z:=append(Z,simplify(S[j]))}; + } + fpour + fsi; + + +Z:=sort([op(set[op(Z)])]); + +nz:=size(Z); + +for(j:=0;j<nf;j++){ + for(k:=1;k<nz;k++){ + if ((Z[k]>Imin[j])and(Z[k]<Imax[j])){Z:=augment(Z[0..k-1],Z[k+1..nz-1]);nz:=nz-1; + } + } +} +nz:=size(Z); + +l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex); +";fpour; + + k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); + kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ +if(member(Z[0],IMIN)!=0){if((member(Z[0],F)==0) and (fp(Z[0])!=undef)){"debutNonDef;"}else{"debutNonDefStrict;"}}else{if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)))))==1.0){"plus;"}else{"moins;"} }}} + + + +// modif 3 avril 2010 + +if(nz>2){ for(r:=1; r<=nz-2;r++){ + lsp:=lsp+ + if(member(Z[r],IMIN)!=0){ + if((member(Z[r],F)==0) and (fp(Z[r])!=undef)){"debutNonDef;"} + else{"debutNonDefStrict;"}} + else{if(member(Z[r],IMAX)!=0){if((member(Z[r],F)==0) and (fp(Z[r])!=undef)){"finNonDef;"} + else{"finNonDefStrict;"}+ + if(evalf(fp(Z[r]+0.01))>0){"plus;"} + else{"moins;"}} + else{if(member(Z[r],F)==0){"valBarre(btex 0 etex);"} + else{"nonDefBarre;"}+ + if(evalf(fp(Z[r]+0.01))>0){"plus;"} + else{"moins;"} + }} + }}; + +// fin modif + + + + + +lsf:=if(member(Z[nz-1],IMAX)!=0){if((member(Z[nz-1],F)==0) and (fp(Z[nz-1])!=undef)){"finNonDef;"}else{"finNonDefStrict;"}}else{if(member(Z[nz-1],F)==0){""}else{"nonDefBarre; +"}} + + +lm0:=limit(f(x),x=Z[0],1)==-infinity; + li:=lvic +nom+"}$</span> etex);"+ + if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"} + else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + +if(nz>2){ + for(r:=1; r<=nz-2;r++){ + krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1)); + krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ; + lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity; + + lp:=lp+if(member(Z[r],IMIN)!=0){"limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){ + "-\\infty"}else{ + latex(simplify(limit(f(x),x=Z[r],-1)))} + +"$</span> etex,"+if(krm==1){ + "1);"}else{"0);"} + +if(member(Z[r],F)==0){"debutNonDef;"}else{"debutNonDefStrict;"} + }//fsi Zr=Imin + else{ + if (member(Z[r],IMAX)!=0){if(member(Z[r],F)==0){"finNonDef;"}else{"finNonDefStrict;"}+"limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){ + "-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))} + +"$</span> etex,"+if(krp==1){ + "1);"}else{"0);"} + }else{ + if(member(Z[r],F)){ + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){ + "-\\infty"}else{ + latex(simplify(limit(f(x),x=Z[r],-1)))} + +"$</span> etex,"+if(krm==1){ + "1);"}else{"0);"} + +"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){ + "-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))} + +"$</span> etex,"+if(krp==1){ + "1);"}else{"0);"} + }//fsi (member Zr F) + else{"valPos(btex<span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span>etex,"+ + if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){ + "0.5);"}else{ + if(krp==1){ + "1);"}else{"0);"}//felse(krp) + }//felse(valpos) + }//felse(member Zr F) + } //felse(Zr=Imax) + }//felse(Zr=Imin) + };//ffor + }//fsi nz + +lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + } +:; + + +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">Quand les solutions formelles de f'(x)=0 ne sont pas calculables +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVapp.cxx} + + +TVapp(L,F,nom,nomv,f,ftt,nmr):={ +local nl,fp,z0,z,nz,S,k,j,m,kk,kok,Z,l0,lp,lf,lsp,k0,kz,lsi,r,ksp,lsf,lm0,li,krm,krp,lmrm,lmrp,lnz; + +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +z0:=concat(L,F);z:=sort(z0); +nz:=size(z); + + + +S:=NULL; + + + +if(L==[-infinity,+infinity]){j:=[seq(-50+2*k,k=0..50)]minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[0]==-infinity){j:=[seq(2*k,k=-25..0.5*floor(L[1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[1]==+infinity){ +j:=[seq(2*k,k=floor(0.5*L[0])..0.5*50)] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for +} +else{ j:=[seq(2*k,k=0.5*floor(z[0])..0.5*floor(z[nz-1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for } + }}; + + + + +si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]); + if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}}; + fpour; +fsi; + + +S:=NULL; +S:=S,z[0]; +for(j:=1;j<size(z);j++){ + if(z[j]!=undef and (abs(z[j])>1e-15 or z[j]==0)){ + S:=S,z[j]}; +} +z:=[S]; + +Z:=sort(z); +nz:=size(Z); + +S:=NULL; +S:=S,Z[0]; +for(j:=1;j<nz;j++){ + if(Z[j]!=S[size(S)-1]){ + S:=S,Z[j]}; +} +Z:=[S]; + + +nz:=size(Z); +l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex); +";fpour; + + k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); + kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ + if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)))))==1.0){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0; + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre; +"} +lm0:=limit(f(x),x=Z[0],1)==-infinity; + li:=lvic+nom+"}$</span> etex);"+ + if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"} + else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1)); + krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ; + lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)){ + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span> + etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); +"}}} + }; } + +lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + + + + + + +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + + + + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">Code giac/Xcas pour les Tableaux de Variations avec +</span><span class="comment-delimiter">%% </span><span class="comment">Valeurs intermediaires +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVI.cxx} + + +TVI(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + +Z:=sort([op(set[op(Z)])]); + + + +nz:=size(Z); +l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" "; + + + +LI:=limit(f(x),x,Z[0],1); +LF:=limit(f(x),x,Z[nz-1],-1); +LP:=NULL; +PB:=1; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; +if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; + +NL:=size(LL); +A:=NULL;aa:=1; +kk:=0; + + + +if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); +if(TestS==0){A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"}} +l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);"}; +//chgmt NL->nz +if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); + +if(PB[k]==1){if(TestS==0){ + A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=kk+1}}; +} + + l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);" + + }; + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); + kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ + if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3)))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp(10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3)+Z[0])))==1.0){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$</span> + <span class="font-latex-math">$ etex);"+ +if(evalf(sign(fp(10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; + + + + + +if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + ksp:=evalf(fp(Z[r]+0.01))>0; + TestL:=(abs(LL[r])==abs(LL[r+1])); + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $</span> <span class="font-latex-math">$ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; + }} +else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + + if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $</span> <span class="font-latex-math">$ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} + else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} +}}}}; + + + + + lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"} + + + +lm0:=limit(f(x),x=Z[0],1)==-infinity; + + + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + + li:=lvic+nom+"}$</span> etex); +"+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"} + else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+ + if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}else{" "}; + + + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1)); + krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ; + lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)) { + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span> + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);" + }else{" "}; +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1)); + krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ; + lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span> + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + <span class="font-latex-math">$ "+ao+" $</span> etex,0.5); + ";rr:=rr+1; +}// testS==0 +else{lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span> + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + "}}};rr:=rr+1; +}//else testS==0 +}//PB[r]==1 +}//for nz<NL +}// else nz<NL +//if nz=NL +};//if nz>2 + + + +lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + + +MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ +if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}}; + + + + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + + +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">% </span><span class="comment">Pour avoir les racines sous forme exacte.... quand c'est possible ! +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%</span><span class="comment"> +</span><span class="comment-delimiter">%%%%%%%%%</span><span class="comment"> +</span> + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVIex.cxx} + + + +TVIex(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +S:=[]; + +Sex:=NULL; +Zex:=solve(f(x)=ao); +Zex:=sort(Zex); +for(j:=0;j<size(Zex);j++){ +if((evalf(Zex[j])>=evalf(L[0])) and (evalf(Zex[j])<=evalf(L[nl-1]))){Sex:=Sex,Zex[j]}; +}; +Sex:=[Sex]; + + + + + + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + + + Z:=sort([op(set[op(Z)])]); + + +nz:=size(Z); +l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" "; + + + +LI:=limit(f(x),x,Z[0],1); +LF:=limit(f(x),x,Z[nz-1],-1); +LP:=NULL; +PB:=1; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; +if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; + +NL:=size(LL); +A:=NULL;aa:=0; +kk:=0; + + + +if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); +if(TestS==0){A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"+"val(btex <span class="font-latex-math">$"+latex(simplify(Sex[aa]))+"$</span> etex);";aa:=aa+1;}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"}} +l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);"}; +//chgmt NL->nz +if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); + +if(PB[k]==1){if(TestS==0){ + A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);"+"val(btex <span class="font-latex-math">$"+latex(simplify(Sex[aa]))+"$</span> etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=kk+1}}; +} + + l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);" + + }; + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); + kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ + if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(sign(fp((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(sign(fp(10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$</span> + <span class="font-latex-math">$ etex);"+ +if(evalf(sign(fp(10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; + + + + +if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + ksp:=evalf(fp(Z[r]+0.01))>0; + TestL:=(abs(LL[r])==abs(LL[r+1])); + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $</span> <span class="font-latex-math">$ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; + }} +else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + + if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $</span> <span class="font-latex-math">$ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} + else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} +}}}}; + + + + + lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"} + + + +lm0:=limit(f(x),x=Z[0],1)==-infinity; + + + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + + li:=lvic+nom+"}$</span> etex); +"+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"} + else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+ + if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}else{" "}; + + + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1)); + krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ; + lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)) { + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span> + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);" + }else{" "}; +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1)); + krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ; + lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span> + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + <span class="font-latex-math">$ "+ao+" $</span> etex,0.5); + ";rr:=rr+1; +}// testS==0 +else{lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span> + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + "}}};rr:=rr+1; +}//else testS==0 +}//PB[r]==1 +}//for nz<NL +}// else nz<NL +//if nz=NL +};//if nz>2 + + + +lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + + +MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ +if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}}; + + + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + + + + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">Quand les solutions de f'(x)=0 ne sont pas formellement calculables +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVIapp.cxx} + +TVIapp(L,F,nom,nomv,f,ftt,ao,nmr):={ + + +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +z0:=concat(L,F);z:=sort(z0); +nz:=size(z); + + + + + + + +S:=op(fsolve(fp(x),x)); + + + + +if(L==[-infinity,+infinity]){j:=[seq(-50+2*k,k=0..50)]minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[0]==-infinity){j:=[seq(2*k,k=-25..0.5*floor(L[1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[1]==+infinity){ +j:=[seq(2*k,k=floor(0.5*L[0])..0.5*50)] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for +} +else{ j:=[seq(2*k,k=0.5*floor(z[0])..0.5*floor(z[nz-1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for } + }}; + + + + + + + + + + + + + +si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]); + if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}}; + fpour; +fsi; + + +S:=NULL; +S:=S,z[0]; +for(j:=1;j<size(z);j++){ + if(z[j]!=undef and (abs(z[j])>1e-15 or z[j]==0)){ + S:=S,z[j]}; +} +z:=[S]; + + + +Z:=sort(z); +nz:=size(Z); + +S:=NULL; +S:=S,Z[0]; +for(j:=1;j<nz;j++){ + if(Z[j]!=S[size(S)-1]){ + S:=S,Z[j]}; +} +Z:=[S]; + + +nz:=size(Z); +l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" "; + + + +LI:=limit(f(x),x,Z[0],1); +LF:=limit(f(x),x,Z[nz-1],-1); +LP:=NULL; +PB:=1; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; +if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; + +NL:=size(LL); +A:=NULL;aa:=1; +kk:=0; + + +if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); +if(TestS==0){A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"}} +l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);"}; +//chgmt NL->nz +if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); + +if(PB[k]==1){if(TestS==0){ + A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=kk+1}}; +} + + l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);" + + }; + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); + kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ + if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(sign(fp((Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(sign(fp(10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$</span> + <span class="font-latex-math">$ etex);"+ + +if(evalf(sign(fp(10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; + + + +if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + ksp:=evalf(fp(Z[r]+0.01))>0; + TestL:=(abs(LL[r])==abs(LL[r+1])); + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $</span> <span class="font-latex-math">$ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; + }} +else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + + if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $</span> <span class="font-latex-math">$ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} + else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} +}}}}; + + + + + lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"} + + + +lm0:=limit(f(x),x=Z[0],1)==-infinity; + + + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + + li:=lvic+nom+"}$</span> etex); +"+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"} + else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"}+ + if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}else{" "}; + + + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1)); + krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ; + lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)) { + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span> + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);" + }else{" "}; +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1)); + krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ; + lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span> + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + <span class="font-latex-math">$ "+ao+" $</span> etex,0.5); + ";rr:=rr+1; +}// testS==0 +else{lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span> + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + "}}};rr:=rr+1; +}//else testS==0 +}//PB[r]==1 +}//for nz<NL +}// else nz<NL +//if nz=NL +};//if nz>2 + + + +lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex <span class="font-latex-math">$"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + + +MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ +if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}}; + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + + + +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + + + + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">Code giac/Xcas pour les Tableaux de variations de courbes parametrees +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> + + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVP.cxx} +TVP(L,F,nom,nomv,ff,ftt,trigo,nmr):={ + +nl:=size(L); +fp:=[]; +S:=[]; +f:=[unapply(ff[0],t),unapply(ff[1],t)]; +fp:=[function_diff(f[0]),function_diff(f[1])]; +Z:=[]; +LLL:=[]; + + +all_trig_solutions:=1; +reset_solve_counter(-1,-1); + +for(d:=0;d<=1;d++){ +LLL:=concat(L,F[d]); +Z:=LLL union Z; +SS:=solve(factor(simplify(fp[d](t))),t); +ns:=size(SS); + + +for(k:=0;k<ns;k++){ +if(trigo==t){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ + +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; + +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ + +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; + +} +}else{ +S:=concat(S,SS); +} +} + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + qq:=member(simplify(S[j]),Z)==0; + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}}; + fpour + fsi; +Z:=sort(Z); +nz:=size(Z); + + + tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); + ftantque; + + + + +nz:=size(Z); +u:=1; + tantque (u<nz-2) and (nz>2) faire + tantque evalf(Z[u])==evalf(Z[u+1]) faire + Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=size(Z); + ftantque; + u:=u+1; + ftantque; + + + }; + +Z:=sort(Z); +nz:=size(Z); + + + + l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:="",""; lf:="","";lsp:="",""; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex); +";fpour; + + lsi:="",""; + +FFF:=[[],[]]; + +for(d:=0;d<=1;d++){ +FFF[d]:=concat(F[d],[-infinity,+infinity]); + k0:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1)); + kz:=evalf(limit(f[d](x),x=Z[nz-1],-1))> evalf(limit(f[d](x),x=Z[nz-2],1)); +//} +//<span class="font-latex-math">$ + lsi[d]:=lsic+nom[d]+"'("+nomv+")}$</span> etex);"+if(member(Z[0],FFF[d])==0){"valBarre(btex <span class="font-latex-math">$"+latex(simplify(fp[d](Z[0])))+"$</span> etex);"}else{if(Z[0]==-infinity){" "}else{"nonDefBarre; +"}}+ + if(Z[0]==-infinity){if(sign(evalf(fp[d](if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F[d])==0){ + if(sign(fp[d](Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{ + if(sign(fp[d]((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp[d](Z[r]+0.01))>0; + lsp[d]:=lsp[d]+if(member(Z[r],F[d])==0){"valBarre(btex <span class="font-latex-math">$"+latex(simplify(fp[d](Z[r])))+"$</span> etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex <span class="font-latex-math">$"+latex(simplify(fp[d](Z[nz-1])))+"$</span> etex);"}else{if(Z[nz-1]==+infinity){" "}else{"nonDefBarre;"}} + + + + + } + + + + + + + + + + + + lm0:=1,2; li:=1,2; krm:=1,2; krp:=1,2; lmrm:=1,2; lmrp:=1,2; lp:="",""; lnz:=1,2; lf:=1,2; Kz:=1,2;K0:=1,2; + + +for(d:=0;d<=1;d++){ + K0[d]:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1)); + Kz[d]:=evalf(limit(f[d](x),x,Z[nz-1],-1))> evalf(limit(f[d](x),x,Z[nz-2],1)); +//{ +//<span class="font-latex-math">$ +lm0[d]:=limit(f[d](x),x,Z[0],1)==-infinity; + li[d]:=lvic+nom[d]+"}$</span> etex);"+ + if(member(Z[0],F[d])==0){"valPos(btex <span class="font-latex-math">$"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$</span> etex,"} + else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$</span> etex,"}+ + if(K0[d]==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm[d]:=evalf(limit(f[d](x),x=Z[r-1],1))< evalf(limit(f[d](x),x=Z[r],-1)); + krp[d]:=evalf(limit(f[d](x),x=Z[r],1))> evalf(limit(f[d](x),x,Z[r+1],-1)) ; + lmrm[d]:=limit(f[d](x),x,Z[r],-1)==-infinity;lmrp[d]:=limit(f[d](x),x,Z[r],1)==-infinity; + lp[d]:=lp[d]+if(member(Z[r],F[d])){ + "limGauche(btex + <span class="font-latex-math">$"+if(lmrm[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],-1)))}+"$</span> + etex,"+if(krm[d]==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],1)))}+"$</span> etex,"+if(krp[d]==1){"1);"}else{"0);"}} + else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f[d](Z[r])))+"$</span> + etex,"+if(sign(evalf(fp[d](Z[r]-0.001)))==sign(evalf((fp[d](Z[r]+0.001))) )){"0.5);"}else{if(krp[d]==1){"1);"}else{"0); +"}}} + }; } + +lnz[d]:=limit(f[d](x),x=Z[nz-1],-1)==-infinity; + + +lf[d]:=if(member(Z[nz-1],F[d])==0){"valPos(btex <span class="font-latex-math">$"+ + if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(Kz[d]==1){"1);"}else{"0);"}} + else{"limGauche(btex <span class="font-latex-math">$"+ + if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(Kz[d]==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + +} + + + + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi[0]+lsp[0]+lsf[0]+lsi[1]+lsp[1]+lsf[1]+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi[0]+lsf[0]+lsi[1]+lsf[1]+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li[0]+ +lp[0]+ +lf[0]+ +li[1]+ +lp[1]+ +lf[1] ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li[0]+ +lf[0]+ +li[1]+ +lf[1] ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi[0]+lsp[0]+lsf[0]+ +li[0]+ +lp[0]+ +lf[0]+ +lsi[1]+lsp[1]+lsf[1]+ +li[1]+ +lp[1]+ +lf[1] ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi[0]+lsf[0]+ +li[0]+ +lf[0]+ +lsi[1]+lsf[1]+ +li[1]+ +lf[1] ++" +endTableau; + +";} +} +} + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + +}:; +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">Code giac/Xcas pour les Tableaux de signes de produits +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignL.cxx} + + +TS(nomf,L,D,trigo,nmr):={ +L:=apply(f->unapply(f,x),L) +n:=size(L); +Z:=NULL; +nl:=size(L); +S:=[]; +mini:=D[0]; maxi:=D[1]; + +pour k de 0 jusque n-1 faire + + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(L[k](x))),x); +ns:=size(SS); +for(j:=0;j<ns;j++){ +m:=0; +while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1; +} +} + +}else{ +S:=solve(L[k](x),x); +} + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j]);} + fpour; + fsi; +fpour; + + + + + +Z:=sort(Z); +nz:=size(Z); + + + Z:=sort([op(set[(Z)])]); + + +nz:=size(Z); + +if(nz==0){li:="";l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);"; + for(p:=0;p<=n-1;p++){li:=li+lsic+latex(L[p](x))+"}<span class="font-latex-math">$ etex);"+ +if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}else{" + "}+ +if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){" + valBarre(btex 0 etex);"}else{" + "} + +} + lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"}; + + +MetaLfc:=" beginTableau("+nmr+") +newLigneVariables(btex $</span> {x}<span class="font-latex-math">$ etex); + "+l0+li+ lsic+nomf+"(x)}$</span> etex);"+ + if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+ lf+ + if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+" +endTableau; +" +; + +}else{ + +l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);";li:=" ";lr:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex); +";fpour; +l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);"; + + +for(p:=0;p<=n-1;p++){lp:=""; + li:=li+lsic+latex(L[p](x))+"}<span class="font-latex-math">$ etex);"+ + if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}else{" + "}+ + if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"}; + + for(r:=0; r<=nz-2;r++){ + lp:=lp+if(simplify(L[p](Z[r]))==0){" + valBarre(btex 0 etex);"}else{"barre; + "}+ + if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}}; + + li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins; + "}+if(maxi!=+infinity and L[p](maxi)==0){" + valBarre(btex 0 etex);"}else{" + "} + }; + + +pour t de 0 jusque nz-2 faire + lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);" + fpour + +MetaLfc:=" beginTableau("+nmr+") +newLigneVariables(btex $</span> {x}<span class="font-latex-math">$ etex); + "+l0+ + li + + lsic+nomf+"(x)}$</span> etex);"+ + if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+ + if(product(L[s](Z[0]-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"+ + lr+ + if(product(L[s](Z[nz-1]+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+" +endTableau; + + "; +} +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + }:; + +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">Code giac/Xcas pour les Tableaux de signes de quotients +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignQ.cxx} +TSq(nomf,L,Fo,D,trigo,nmr):={ +L:=apply(f->unapply(f,x),L); +Fo:=apply(f->unapply(f,x),Fo); +L:=concat(L,Fo); +n:=size(L); +Z:=NULL; +m:=size(Fo); +F:=NULL;FF:=NULL; +mini:=D[0]; maxi:=D[1]; +S:=[]; +SF:=[]; + +pour k de 0 jusque n-1 faire + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(L[k](x))),x); +ns:=size(SS); +for(j:=0;j<ns;j++){ +mm:=0; +while(evalf(simplify(subst(SS[j],n_1=mm)))<=evalf(maxi)){ +S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm+1; +};mm:=-1; +while(evalf(subst(SS[j],n_1=mm))>=evalf(mini)){ +S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm-1; +} +} + +}else{ +S:=concat(S,solve(L[k](x),x)); +} + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j]);} + fpour; + fsi; +fpour; + + +pour k de 0 jusque m-1 faire + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SSF:=solve(factor(simplify(Fo[k](x))),x); +nsf:=size(SSF); +for(j:=0;j<nsf;j++){ +mm:=0; +while(evalf(simplify(subst(SSF[j],n_1=mm)))<=evalf(maxi)){ +SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm+1; +};mm:=-1; +while(evalf(subst(SSF[j],n_1=mm))>=evalf(mini)){ +SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm-1; +} +} + +}else{ +SF:=concat(SF,solve(Fo[k](x),x)); +} + + si size(SF)>0 alors pour j de 0 jusque size(SF)-1 faire + FF:=FF,simplify(SF[j]); + if(SF[j]>mini and SF[j]<maxi){F:=F,simplify(SF[j]);} + fpour; + fsi; +fpour; + + + +Z:=[Z,F]; + + +Z:=sort([op(set[op(Z)])]); + +nz:=size(Z); + +if(nz==0){li:="";l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);"; + for(p:=0;p<=n-1;p++){li:=li+lsic+latex(L[p](x))+"}<span class="font-latex-math">$ etex);"+ +if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}else{" + "}+ +if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){" + valBarre(btex 0 etex);"}else{" + "} + +} + lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"}; + + + + +MetaLfc:=" +beginTableau("+nmr+") +newLigneVariables(btex $</span> {x}<span class="font-latex-math">$ etex); + "+l0+li+ + lsic+nomf+"(x)}$</span> etex);"+ + if(member(mini,FF)==0){if((mini!=-infinity) and (product(L[s](mini),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+ lf+ + if(member(maxi,FF)==0){if((maxi!=+infinity) and (product(L[s](maxi),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+" +endTableau; + +" +; + + + + +}else{ + + +l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);";li:=" ";lr:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex); +";fpour; +l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);"; + + +for(p:=0;p<=n-1;p++){lp:=""; + li:=li+lsic+latex(L[p](x))+"}<span class="font-latex-math">$ etex);"+ + if(mini!=-infinity and L[p](mini)==0){" valBarre(btex 0 etex);"}else{" "}+ + if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"}; + + for(r:=0; r<=nz-2;r++){lp:=lp+if(simplify(L[p](Z[r]))==0){" valBarre(btex 0 etex);"}else{"barre;"}+ + if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}}; + + li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins; + "}+if(maxi!=+infinity and L[p](maxi)==0){"valBarre(btex 0 etex);"}else{" "} + + }; + + +pour t de 0 jusque nz-2 faire + lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(Z[t+1],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"} + fpour + + + + +MetaLfc:=" +beginTableau("+nmr+") +newLigneVariables(btex $</span> {x}<span class="font-latex-math">$ etex); + "+l0+ + li + + + lsic+nomf+"(x)}$</span> etex);"+ + if(member(mini,FF)==0){if((mini!=-infinity) and (product(L[s](mini),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+ + if(product(L[s](Z[0]-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(Z[0],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"}+ + lr+ + if(product(L[s](Z[nz-1]+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(maxi,FF)==0){if((maxi!=+infinity) and (product(L[s](maxi),s,0,n-1)==0)){"valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+" +endTableau; + +" + + +} + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + + + + }:; + +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + + +<span class="comment-delimiter">%% </span><span class="comment">Code giac/Xcas pour les Tableaux de signes du produit +</span><span class="comment-delimiter">%% </span><span class="comment">de 2 facteurs affines +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSigna.cxx} +TSa(a,b,c,d,nmr):={ +zA:=solve(a*x+b=0,x)[0]; +zB:=solve(c*x+d=0,x)[0]; +zmin:=min(zA,zB); +zmax:=max(zA,zB); + Meta:= " + beginTableau("+nmr+") + newLigneVariables(btex <span class="font-latex-math">$ {x}$</span> etex); + val(btex <span class="font-latex-math">$-\\infty$</span> etex);val(btex <span class="font-latex-math">$"+latex(zmin)+"$</span> etex); +val(btex <span class="font-latex-math">$"+latex(zmax)+"$</span>etex); +val(btex <span class="font-latex-math">$+\\infty$</span> etex); + "+lsic+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+"}<span class="font-latex-math">$ etex);" + + if(a>0){"moins;"}else{"plus;"}+ + if(zmin==zA){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(zmin==zA){si a>0 alors "plus;"; sinon "moins;";fsi} + else{si a>0 alors "moins;"; sinon "plus;"; fsi}+ + if(zmin==zA){"barre;"}else{"valBarre(btex 0 etex);"}+ + if(a>0){"plus;"}else{"moins;"} + +lsic+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+"}$</span> etex);" + + if(c>0){"moins"}else{"plus"}+";"+ + if(zmin==zB){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(zmin==zB){si c>0 alors "plus;"; sinon "moins;";fsi} + else{si c>0 alors "moins;"; sinon "plus;"; fsi}+ + if(zmin==zB){"barre;"}else{"valBarre(btex 0 etex);"}+ + if(c>0){"plus;"}else{"moins;"} + + +lsic+"{("+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+")("+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+")}}<span class="font-latex-math">$ etex);" + + si a*c>0 alors plus; sinon moins;fsi+";"+ + "valBarre(btex 0 etex);"+ + si a*c>0 alors moins; sinon plus;fsi+";"+ + "valBarre(btex 0 etex);"+ + si a*c>0 alors plus; sinon moins;fsi+";"+" +endTableau; +" +; + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,Meta); +fclose(sortie); + + + }:; +</span><span class="font-latex-sedate"><span class="keyword"><span class="font-latex-math">\end</span></span></span><span class="function-name"><span class="font-latex-math">{VerbatimOut}</span></span><span class="font-latex-math"> + + + + + + +%%$</span> +<span class="comment-delimiter">%% </span><span class="comment">Code giac/Xcas pour les Tableaux de Signes d'expression ne contenant +</span><span class="comment-delimiter">%% </span><span class="comment">qu'un seul terme +</span> + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTSc.cxx} + +TSc(g,D,F,trigo,nmr):={ +f:=unapply(g,x); +mini:=D[0]; maxi:=D[1];lm:=" "; +Z:=mini,maxi; +S:=[]; + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(f(x))),x); +ns:=size(SS); +for(j:=0;j<ns;j++){ +m:=0; +while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1; +} +} + +}else{ +S:=solve(f(x),x); +} + + + + + +if(size(S)==0 and size(F)==0){ +l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);"; +li:=if(member(mini,F)!=0){"nonDefBarre;"}else{if(mini!=-infinity and f(mini)==0){" + valBarre(btex 0 etex);"}else{" + "}}+ +if(mini!=-infinity or maxi!=+infinity){if(f((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}}else{if(f(0.3145274774464545777744)>0){"plus;"}else{"moins;"}}; +lf:=if(member(maxi,F)!=0){"nonDefBarre;"}else{if(maxi!=+infinity and f(maxi)==0){" + valBarre(btex 0 etex);"}else{" + "}}; +}else{ +if(size(S!=0)){pour j de 0 jusque size(S)-1 faire + if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j])}; + fpour} + +Z:=concat([Z],F); + + Z:=sort([op(set[op(Z)])]); + + +nz:=size(Z); +l0:=" ";li:=" ";lr:=" "; +if(nz==2){l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);"; +li:=if(mini!=-infinity and f(mini)==0){" + valBarre(btex 0 etex);"}else{if(member(mini,F)==0){" + "}else{"nonDefBarre;"}}+ +if(f((mini+maxi)*0.5)>0){"plus;"}else{"moins;"}; +lf:=if(maxi!=+infinity and f(maxi)==0){" + valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){" + "}else{"nonDefBarre;"} + }; + +}else{ +l0:="val(btex <span class="font-latex-math">$"+latex(Z[0])+"$</span> etex);";li:=" "; +pour m de 1 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex); +"; +fpour; + + +li:= if(mini!=-infinity and f(mini)==0){" + valBarre(btex 0 etex);"}else{if(member(mini,F)==0){" + "}else{"nonDefBarre;"} + } + +lm:=if(nz>2){for(r:=0; r<nz-2;r++){lm:=lm+if(Z[r]==-infinity){ +if(f((Z[r+1]-1))>0){"plus;"}else{"moins;"} +}else{if(f((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}} ++ + if(member(Z[r+1],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"} + }}else{" "}; + +lf:=if(f(Z[nz-2]+0.1)>0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){" + "}else{"nonDefBarre;"} + }; +} +}; + + + + +MetaLfc:=" + +beginTableau("+nmr+") +newLigneVariables(btex <span class="font-latex-math">$\\displaystyle {x}$</span> etex); + "+l0+lsic+latex(f(x))+"}<span class="font-latex-math">$ etex);"+ + li+lm+lf + +" +endTableau; + +" +; + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + }:; + +</span><span class="font-latex-sedate"><span class="keyword"><span class="font-latex-math">\end</span></span></span><span class="function-name"><span class="font-latex-math">{VerbatimOut}</span></span><span class="font-latex-math"> + + + + + + + +%%$</span> + + + + + + +<span class="comment-delimiter">%%%%</span><span class="comment"> +</span><span class="comment-delimiter">%%%</span><span class="comment"> +</span><span class="comment-delimiter">%%% </span><span class="comment">Pour des tableaux de variations simples sans fonctions +</span><span class="comment-delimiter">%%%</span><span class="comment"> +</span><span class="comment-delimiter">%%%</span><span class="comment"> +</span> + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVS.cxx} +TVS(La,Lo,F,nomf,nomv,nmr):={ + +na:=size(La); +f:=F; +if(member(La[0],F)){f:=f[1..size(f)-1]}; +if(member(La[na-1],F)){f:=f[0..size(f)-2]}; +Z:=sort(concat(La,f)); +Zo:=sort([op(set[op(Z)])]); +nz:=size(Z); +nzo:=size(Zo); + + +k0:= evalf(Lo[0])> evalf(Lo[1]); +kz:=evalf(Lo[nz-1])> evalf(Lo[nz-2]); + + +l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" "; + for(m:=0;m<=nzo-1;m++){l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Zo[m])+"$</span> etex);"} + +li:=lvic+nomf+"}<span class="font-latex-math">$ etex);"+ + if(member(Z[0],F)==0){"valPos(btex $</span>"+latex(Lo[0])+"<span class="font-latex-math">$ etex,"} + else{"nonDefBarre;limDroite(btex $</span>"+latex(Lo[0])+"<span class="font-latex-math">$ etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ + krm:=evalf(Lo[r-1])< evalf(Lo[r]); + krp:=evalf(Lo[r])> evalf(Lo[r+1]) ; + + lp:=lp+if(Z[r]==Z[r+1]){ + "limGauche(btex$</span>"+latex(Lo[r])+"<span class="font-latex-math">$etex,"+ + if(krm==1){"1);"} + else{"0);"} + }// fin if zr=zr+1 + else{ + if(Z[r]==Z[r-1]){ + "nonDefBarre;limDroite(btex$</span>"+latex(Lo[r])+"<span class="font-latex-math">$etex,"+ + if(krp==1){"1);"} + else{"0);"} + }//fin if zr=zr-1 + else{ + "valPos(btex $</span>"+latex(Lo[r])+"<span class="font-latex-math">$etex,"+ + if(krp==1){"1);"}else{"0);"} +}//fin else zr=zr-1 +}//fin else zr=zr+1 +}//fin for +}//fin de if nz>2 + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $</span>"+latex(Lo[nz-1])+"<span class="font-latex-math">$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $</span>"+latex(Lo[nz-1])+"<span class="font-latex-math">$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + +MetaLfc:= + + if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";} + +//return(MetaLfc); + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + +}:; + +</span><span class="font-latex-sedate"><span class="keyword"><span class="font-latex-math">\end</span></span></span><span class="function-name"><span class="font-latex-math">{VerbatimOut}</span></span><span class="font-latex-math"> + +%%$</span> + + + + + + + + + + + + + + + + + + + + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">traitement des fichiers produits par giac/xcas +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> +<span class="comment-delimiter">% </span><span class="comment">pour l'échelle des tableaux taper </span><span class="font-latex-sedate"><span class="comment">\ech</span></span><span class="comment">{facteur de réduction} +</span> +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="font-latex-sedate">\echelle</span>{1} +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="font-latex-sedate">\ech</span>[1]{<span class="font-latex-sedate"><span class="keyword">\renewcommand</span></span><span class="font-latex-sedate">\echelle</span>{#1}} + + +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="font-latex-sedate">\couleurtab</span>{black} +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="font-latex-sedate">\coultab</span>[1]{<span class="font-latex-sedate"><span class="keyword">\renewcommand</span></span><span class="font-latex-sedate">\couleurtab</span>{#1}} + + +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\dresse</span></span><span class="function-name">}</span>[2]{<span class="comment">% +</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{xcas}}{<span class="comment">% Avec l'option "XCas present" +</span> <span class="font-latex-sedate">\executGiacmp</span>{XCas#2.giac}<span class="comment">% reconstituer le tableau +</span> <span class="comment">% exporter le source mp +</span> <span class="comment">% puis lancer metapost pour creer +</span> <span class="comment">% l'image du tableau +</span> <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp >> <span class="font-latex-sedate">\nomtravail</span>_Tab.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> enteteMP.cfg >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> def beginTableau(expr c) =<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> begingroup<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> charcode:=c;<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> clearxy; clearit; clearpen;<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> pickup defaultpen;<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> drawoptions(withcolor(#1));<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> initTableau;<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> enddef;<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> queue.mp >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost -jobname=<span class="font-latex-sedate">\nomtravail</span>_Tab <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + }<span class="comment">% +</span> {<span class="comment">% sinon, si le tableau est absent, alerte. +</span> <span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\nomtravail</span>_Tab.<span class="font-latex-sedate">\theTVn</span>}{}{<span class="comment">% +</span> <span class="font-latex-sedate">\PackageError</span>{tablor}{Tableau absent non + reconstituable.}{Pour compiler il faut, soit les fichiers de + tableaux, soit le fichier <span class="font-latex-sedate">\nomtravail</span>_Tab.mp, soit disposer de + XCas.}}} + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span> + <span class="font-latex-sedate">\includegraphics</span>[scale=<span class="font-latex-sedate">\echelle</span>]{<span class="font-latex-sedate">\nomtravail</span>_Tab.<span class="font-latex-sedate">\theTVn</span>} +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span> +<span class="font-latex-sedate">\stepcounter</span>{TVn} +} + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">traitement des fichiers produits par giac/xcas avec possibilite +</span><span class="comment-delimiter">%% </span><span class="comment">de modifier le fichier metapost (environnement etoile)) +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span> + + +<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\dressetoile</span></span><span class="function-name">}</span>[2]{<span class="comment">% +</span><span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\nomtravail</span>_Tab.<span class="font-latex-sedate">\theTVn</span>}{<span class="comment">% Test sur l'existence du tableau +</span><span class="comment-delimiter">% </span><span class="comment">Si oui, inclusion du fichier source de sauvegarde mp dans Tableaux +</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> TSav-<span class="font-latex-sedate">\theTVn</span>.mp >> <span class="font-latex-sedate">\nomtravail</span>_Tab.mp}} +<span class="comment-delimiter">% </span><span class="comment">Si non, lancement des operations de fabrication +</span>{<span class="font-latex-sedate">\executGiacmp</span>{XCas#2.giac}<span class="comment">% +</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\editeur</span> XCasmpfc.mp } + + <span class="comment">% Modification avec l'editeur choisi +</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp >> <span class="font-latex-sedate">\nomtravail</span>_Tab.mp} +<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cp</span> XCasmpfc.mp TSav-<span class="font-latex-sedate">\theTVn</span>.mp} <span class="comment">% Sauvegarde du +</span> <span class="comment">% source mp sur le disque pour une +</span> <span class="comment">% inclusion ulterieure dans Tableaux.mp. +</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> enteteMP.cfg >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> def beginTableau(expr c) =<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> begingroup<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> charcode:=c;<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> clearxy; clearit; clearpen;<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> pickup defaultpen;<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> drawoptions(withcolor(#1));<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> initTableau;<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\echod</span> enddef;<span class="font-latex-sedate">\echof</span> >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} +<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp}} <span class="comment">% Inclusion du +</span> <span class="comment">% source dans le +</span> <span class="comment">% fichier +</span> <span class="comment">% Tableaux +</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> queue.mp >> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} +<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost -jobname=<span class="font-latex-sedate">\nomtravail</span>_Tab <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp}<span class="comment">% Reconstitution des tableaux +</span> <span class="comment">% et creation du dernier. L'option +</span> <span class="comment">% pallie l'absence de end en fin de +</span> <span class="comment">% fichier +</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> <span class="font-latex-sedate">\nomtravail</span>_Tab#2.mp} + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span> + <span class="font-latex-sedate">\includegraphics</span>[scale=<span class="font-latex-sedate">\echelle</span>]{<span class="font-latex-sedate">\nomtravail</span>_Tab.<span class="font-latex-sedate">\theTVn</span>} +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span> +<span class="font-latex-sedate">\ech</span>{1} +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVnbis</span></span><span class="variable-name">}</span> <span class="comment">% Restauration du compteur TVn +</span>} + + + + + + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%%%</span><span class="comment"> +</span><span class="comment-delimiter">%%%</span><span class="comment"> +</span><span class="comment-delimiter">%%% </span><span class="comment">les "giac" qui permettent d'executer la commande rentree dans le fichier tex +</span><span class="comment-delimiter">%%% </span><span class="comment">suivis des environnements qui permettront la saisie du code giac/xcas +</span><span class="comment-delimiter">%%% </span><span class="comment">Les versions etoilees permettent de modifier le code metapost produit initialement +</span><span class="comment-delimiter">%%%</span><span class="comment"> +</span> + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasa.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTabSigna.cxx"); +read("XCasa.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSa}</span> +{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasa.user}} +{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + <span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{a} +} + + + + + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasQ.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTabSignQ.cxx"); +read("XCasQ.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSq}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasQ.user}} +{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{Q}} + + + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSq*}</span>[1]<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasQ.user}} +{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{Q}} + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasL.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTabSignL.cxx"); +read("XCasL.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TS}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasL.user}} +{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{L}} + + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TS*}</span>[1] +{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasL.user}} +{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{L}} + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTSc.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTSc.cxx"); +read("XCasTSc.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSc*}</span>[1]<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTSc.user}} +{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{TSc}} + + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSc}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTSc.user}} +{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{TSc}} + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTV.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTV.cxx"); +read("XCasTV.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TV}</span>{<span class="comment">% +</span><span class="font-latex-sedate">\VerbatimEnvironment</span> +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTV.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> +<span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{TV}} + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TV*}</span>[1]{<span class="comment">% +</span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTV.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{TV}} + + + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVP.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVP.cxx"); +read("XCasTVP.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVP}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVP.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> +<span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVP}} + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVP*}</span>[1]{<span class="comment">% +</span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVP.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVP}} + + + + + + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVZ.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVZ.cxx"); +read("XCasTVZ.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVZ}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVZ.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> +<span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVZ}} + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVZ*}</span>[1]{<span class="comment">% +</span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVZ.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVZ}} + + + + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVapp.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVapp.cxx"); +read("XCasTVapp.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVapp}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVapp.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> +<span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVapp}} + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVapp*}</span>[1]{<span class="comment">% +</span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVapp.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVapp}} + + + + + + + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVI.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVI.cxx"); +read("XCasTVI.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVI}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVI.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVI}} + + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVI*}</span>[1]<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVI.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVI}} + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVIex.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVIex.cxx"); +read("XCasTVIex.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVIex}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVIex.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVIex}} + + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVIex*}</span>[1]<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVIex.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVIex}} + + + + + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVIapp.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVIapp.cxx"); +read("XCasTVIapp.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVIapp}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVIapp.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVIapp}} + + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVIapp*}</span>[1]<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVIapp.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVIapp}} + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVPC.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVPC.cxx"); +read("XCasTVPC.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVPC}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVPC.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> +<span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVPC}} + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVPC*}</span>[1]{<span class="comment">% +</span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVPC.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVPC}} + + + + + + + + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVS.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVS.cxx"); +read("XCasTVS.user"); +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVS}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVS.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> +<span class="font-latex-sedate">\dresse</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVS}} + +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVS*}</span>[1]{<span class="comment">% +</span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span> +<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span> +<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>??]{XCasTVS.user}}<span class="comment">% +</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="font-latex-sedate">\couleurtab</span>}{TVS}} + + + + + + + + + + +<span class="comment-delimiter">%% </span><span class="comment">pour nettoyer les fichiers auxiliaires +</span> +<span class="font-latex-sedate">\AtEndDocument</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> queue.mp >> <span class="font-latex-sedate">\nomtravail</span>_Tab.mp} + } + + + + +<span class="comment-delimiter">%%</span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">Zi end -> enjoy :) +</span></pre> + </body> +</html> diff --git a/macros/latex/contrib/tablor/tablor.pdf b/macros/latex/contrib/tablor/tablor.pdf Binary files differnew file mode 100644 index 0000000000..4577546d55 --- /dev/null +++ b/macros/latex/contrib/tablor/tablor.pdf diff --git a/macros/latex/contrib/tablor/tablor.sty b/macros/latex/contrib/tablor/tablor.sty new file mode 100644 index 0000000000..7a1dc82fe4 --- /dev/null +++ b/macros/latex/contrib/tablor/tablor.sty @@ -0,0 +1,3245 @@ +% Last modified: <tablor.sty modifi par Guillaume CONNAN le dimanche 6 octobre 2013 14h 46min 18s> + + +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesPackage{tablor}[06/10/2013 v4.07g la machine a creer des tableaux de signes et variations] + +% \copyleft Connan le Barbare (aka Guillaume Connan) \copyright +% This work may be distributed and/or mofified under the conditions +% or the LaTeX Project Public Licence, either v1.3 or (at your option) +% any later version. The latest version is in +% http://www.latex-project.org/lppl/ +% This work consists of the files tablor.sty, tablor-xetex.sty, tablor.cfg, tablor.tex, +% tablor.pdf and tablor.html + + +%% Cree 16 environnements : +%% tableau de signes de 2 facteurs affines +% \begin{TSa} +% TSa(-2,3,-1,5,\tv); +% \end{TSa} +% %%%%%% Pour des tableaux de plus de 2 facteurs +% +% \begin{TS} +% TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[a,b],n,\tv); +% \end{TS} +% +% pour les tableaux de signes avec quotient +%\begin{TSq} +%TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],n,\tv) +%%\end{TSq} +% un tableau de variation : +% +% pour les tableaux de signes une seule ligne +% \begin{TSc} +% TSc((x+10)/((x-5)*(x-2)),[-10,5],[2,5],n,0) +% \end{TSc} +% +% +% \begin{TV} +% TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,n,\tv) +% \end{TV} +% +% tableau de variation avec liste de valeurs +% \begin{TVS} +% TVS([1,2,3,4],[-1,-infinity,+infinity,2,9],[2],"f","x",\tv) +% \end{TVS} +% +% +% tableau de variation avec zones interdites +% +% \begin{TVZ} +% TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,\tv) +% \end{TVZ} +% +% +% tableau avec valeurs intermediares +%\begin{TVI} +%TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,\tv) +%\end{TVI} +%%% +% tableau avec valeurs intermediares et racines exactes +%\begin{TVIex} +%TVIex([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,\tv) +%\end{TVIex} +%%% +% +% +% tableau de variations avec f' sans zero formel +%\begin{TVapp} +% TVapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,\tv) +% \end{TVapp} +% +% +% tableau de variations avec f' sans zero formel +%\begin{TVIapp} +% TVIapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,0,\tv) +% \end{TVIapp} +% +% +%%% +% et leurs pendants etoiles qui permettent l'affichage intermediaire du +% fichier metapost pour le modifier +% +% +% Courbes parametrees +% \begin{TVP} +% TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,\tv) +% \end{TVP} +% +% +% \begin{TVP} +% TVP([0,pi/2],[[],[]],["x","y"],"t",[2*cos(t),sin(2*t)],1,t,\tv) +% \end{TVP} +% % + +% Fonctions prolongeables par continuit +% TVP([intervalles d'tude],[valeurs prolongeables],[valeurs interdites pour f'],"g","t",e^(-1/x^2),1,n,\tv); + + +% \begin{TVPC} +% TVPC([-infinity,+infinity],[0],[0],"g","t",e^(-1/x^2),1,n,\tv); +% \end{TVPC} + + + + + +%% extensions requises +%% Il faudra rajouter dans le preambule \usepackage{graphicx} si vous +%% ne l'avez pas de base + + +\RequirePackage{filecontents} +\RequirePackage{ifthen} +\RequirePackage{fancyvrb} +\RequirePackage{ifpdf} + +\fvset{gobble=0} + +% option xcas present + + +\newboolean{xcas}\setboolean{xcas}{false} +\DeclareOption{xcas}{\setboolean{xcas}{true}} + +%% Initialisation du choix d'OS +\newboolean{windows}\setboolean{windows}{false} +\DeclareOption{windows}{\setboolean{windows}{true}} + +\ProcessOptions\relax + + + +%% on configure tablor dans un fichier exterieur pour la plateforme +%% et l'editeur + +\IfFileExists{tablor.cfg}{\input{tablor.cfg}}%\typeout{pas de fichier tablor.cfg}} + + +%% Definit des commandes disque selon l'OS utilise +\ifthenelse{\boolean{windows}}% + {\newcommand{\rem}{DEL } \newcommand{\cat}{TYPE } + \newcommand{\cp}{COPY } \newcommand{\echod}{ECHO } + \newcommand{\echof}{ }}% + {\newcommand{\rem}{rm }\newcommand{\cat}{cat } + \newcommand{\cp}{cp } \newcommand{\echod}{echo "} + \newcommand{\echof}{"}} + + + + + + + +%% pour ceux compilant via pdflatex + +\ifpdf +\DeclareGraphicsRule{*}{mps}{*}{} +\fi + +%% pour nettoyer les fichiers auxiliaires + +\AtEndDocument{\immediate\write18{\rem *.user XCas* Xcas* *.mpx} + } + + + + +%% Pour clore les fichiers metapost + + + \begin{VerbatimOut}{queue.mp} + + end + + \end{VerbatimOut} + + + +%% Nettoie les fichiers log dont le nom depend du choix de l'utilisateur +%% Par defaut, c'est le nom du fichier tex courant (\jobname) +%% Clt le fichier metapost contenant le recapitulatif de tous les tableaux + + + +\newcommand{\nettoyer}[1][\jobname]% +{\immediate\write18{\rem #1.Tab.log queue.mp enteteMP.cfg session.tex config.cxx} +} + + + + +%% Donne comme prefixe aux tableaux le prefixe courant +%% Peut-tre modifie par \initablor + +\newcommand{\nomtravail}{\jobname} + +%% initialise les compteurs + +\newcounter{TVn} +\newcommand{\tv}{\theTVn} + +\newcounter{TVnbis} +\newcommand{\tvbis}{\theTVnbis} + + + +%% permet de donner un prefixe aux tableaux produits (\jobname par defaut) +%% effectue quelques verifications : + + +\newcommand{\initablor}[1][\jobname]{% +\renewcommand{\nomtravail}{#1}% Arret du nom des tableaux +\setcounter{TVn}{0}% Initialisation du compteur de tableaux. +\ifthenelse{\boolean{xcas}}% Avec l'option XCas +{\IfFileExists{\nomtravail_Tab.mp}% Si Tableaux.mp est present... + {\immediate\write18{\rem \nomtravail_Tab.mp}}% le detruire + {}% + \immediate\write18{\cp enteteMP.cfg \nomtravail_Tab.mp}% Reconstituer l'entte de Tableaux.mp +} +{\IfFileExists{\nomtravail_Tab.mp}% Sans l'option XCas, si + % Tableaux.mp existe +{\immediate\write18{mpost -interaction=batchmode \nomtravail_Tab}}% l'executer pour reconstituer les figures +{\PackageWarning{tablor}{Pas de source metapost pour creer les tableaux.}}% sinon message d'erreur + % (mais pas d'arret car les tableaux + % peuvent tre presents ) +}}% + + + +%% commande pour lancer giac selon l'OS + +\makeatletter +\newcommand{\executGiacmp}[1]{% +\ifthenelse{\boolean{windows}}% +{\immediate\write18{giac #1 }}% +{\immediate\write18{giac <#1 }}} +\makeatother + + + + +%%% +% +%%% LES SCRIPTS GIAC/XCAS +% +%%% + + + + +%% +%% Code giac/Xcas pour les Tableaux de Variations +%% + + +\begin{VerbatimOut}{XcasTV.cxx} +TV(L,F,nom,nomv,f,ftt,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + qq:=member(simplify(S[j]),Z)==0; + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}}; + fpour + fsi; +Z:=sort(Z); +nz:=size(Z); + + + tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); + ftantque; + + + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + +Z:=sort([op(set[op(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; + + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.1))>0; + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre; +"} +lm0:=limit(f(x),x,Z[0],1)==-infinity; + li:=lvic+nom+"}$ etex);"+ + if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)){ + "limGauche(btex + $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ + etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); +"}}} + }; } + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + +\end{VerbatimOut} + + + + + + +%%%% + + +% +% +% TVPC : pour les fonctions prolongeables par continuit. +%% +%% + + + + +\begin{VerbatimOut}{XcasTVPC.cxx} +TVPC(L,F,FP,nom,nomv,f,ftt,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +Z:=concat(Z,FP); +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + qq:=member(simplify(S[j]),Z)==0; + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}}; + fpour + fsi; +Z:=sort(Z); +nz:=size(Z); + + + tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); + ftantque; + + + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + +Z:=sort([op(set[op(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; + + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],FP)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.1))>0; + lsp:=lsp+if(member(Z[r],FP)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf:=if(member(Z[nz-1],FP)==0){""}else{"nonDefBarre; +"} +lm0:=limit(f(x),x,Z[0],1)==-infinity; + li:=lvic+nom+"}$ etex);"+ + if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)){ + "valPos(btex + $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ + etex,"+if(krm==1){"1);"}else{"0);"} } + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); +"}}} + }; } + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}}; + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + +\end{VerbatimOut} + + + + + + + + + + + + +%% +%% +%% TV avec une zone interdite : on rajoute comme argument la liste des intervalles interdits +%% par exemple, pour sqrt(x^2-1) : TVZ([-infinity,100],[],[[-1,1]],"f","x",sqrt(x^2-1),1,1) +%% + +\begin{VerbatimOut}{XcasTVZ.cxx} + + +TVZ(L,F,FF,nom,nomv,f,ftt,trigo,nmr):={ +nl:=size(L); +nf:=size(FF); + Ff:=NULL;IMIN:=NULL;IMAX:=NULL; +for(k:=0;k<nf;k++){ +if(FF[k][0]>L[0]){Imin[k]:=FF[k][0];LL:=L}else{Imin[k]:=L[0];LL:=[L[1]]}; +if(FF[k][1]<L[1]){Imax[k]:=FF[k][1];LL:=L}else{Imax[k]:=L[1];LL:=[L[0]]}; + Ff:=Ff,[Imin[k],Imax[k]]; + IMIN:=IMIN,Imin[k]; + IMAX:=IMAX,Imax[k]; + } + FF:=[Ff]; + IMIN:=[IMIN]; + IMAX:=[IMAX]; + f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(LL,F); + +for(k:=0;k<nf;k++){ +Z:=concat(Z,FF[k]); +} + +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + for(k:=0;k<nf;k++){ + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + kK:=(evalf(S[j])<evalf(Imin[k])) or (evalf(S[j])>evalf(Imax[k])); + Kk:=(kk) and kK; + if(Kk==1){Z:=append(Z,simplify(S[j]))}; + } + fpour + fsi; + + +Z:=sort([op(set[op(Z)])]); + +nz:=size(Z); + +for(j:=0;j<nf;j++){ + for(k:=1;k<nz;k++){ + if ((Z[k]>Imin[j])and(Z[k]<Imax[j])){Z:=augment(Z[0..k-1],Z[k+1..nz-1]);nz:=nz-1; + } + } +} +nz:=size(Z); + +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +";fpour; + + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ +if(member(Z[0],IMIN)!=0){if((member(Z[0],F)==0) and (fp(Z[0])!=undef)){"debutNonDef;"}else{"debutNonDefStrict;"}}else{if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }}} + + + +// modif 3 avril 2010 + +if(nz>2){ for(r:=1; r<=nz-2;r++){ + lsp:=lsp+ + if(member(Z[r],IMIN)!=0){ + if((member(Z[r],F)==0) and (fp(Z[r])!=undef)){"debutNonDef;"} + else{"debutNonDefStrict;"}} + else{if(member(Z[r],IMAX)!=0){if((member(Z[r],F)==0) and (fp(Z[r])!=undef)){"finNonDef;"} + else{"finNonDefStrict;"}+ + if(evalf(fp(Z[r]+0.01))>0){"plus;"} + else{"moins;"}} + else{if(member(Z[r],F)==0){"valBarre(btex 0 etex);"} + else{"nonDefBarre;"}+ + if(evalf(fp(Z[r]+0.01))>0){"plus;"} + else{"moins;"} + }} + }}; + +// fin modif + + + + + +lsf:=if(member(Z[nz-1],IMAX)!=0){if((member(Z[nz-1],F)==0) and (fp(Z[nz-1])!=undef)){"finNonDef;"}else{"finNonDefStrict;"}}else{if(member(Z[nz-1],F)==0){""}else{"nonDefBarre; +"}} + + +lm0:=limit(f(x),x,Z[0],1)==-infinity; + li:=lvic +nom+"}$ etex);"+ + if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + +if(nz>2){ + for(r:=1; r<=nz-2;r++){ + krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + + lp:=lp+if(member(Z[r],IMIN)!=0){"limGauche(btex $"+if(lmrm==1){ + "-\\infty"}else{ + latex(simplify(limit(f(x),x,Z[r],-1)))} + +"$ etex,"+if(krm==1){ + "1);"}else{"0);"} + +if(member(Z[r],F)==0){"debutNonDef;"}else{"debutNonDefStrict;"} + }//fsi Zr=Imin + else{ + if (member(Z[r],IMAX)!=0){if(member(Z[r],F)==0){"finNonDef;"}else{"finNonDefStrict;"}+"limDroite(btex $"+if(lmrp==1){ + "-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))} + +"$ etex,"+if(krp==1){ + "1);"}else{"0);"} + }else{ + if(member(Z[r],F)){ + "limGauche(btex $"+if(lmrm==1){ + "-\\infty"}else{ + latex(simplify(limit(f(x),x,Z[r],-1)))} + +"$ etex,"+if(krm==1){ + "1);"}else{"0);"} + +"nonDefBarre;limDroite(btex $"+if(lmrp==1){ + "-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))} + +"$ etex,"+if(krp==1){ + "1);"}else{"0);"} + }//fsi (member Zr F) + else{"valPos(btex$"+latex(simplify(f(Z[r])))+"$etex,"+ + if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){ + "0.5);"}else{ + if(krp==1){ + "1);"}else{"0);"}//felse(krp) + }//felse(valpos) + }//felse(member Zr F) + } //felse(Zr=Imax) + }//felse(Zr=Imin) + };//ffor + }//fsi nz + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + } +:; + + +\end{VerbatimOut} + + +%% +%% +%% Quand les solutions formelles de f'(x)=0 ne sont pas calculables +%% + + + +\begin{VerbatimOut}{XcasTVapp.cxx} + + +TVapp(L,F,nom,nomv,f,ftt,nmr):={ +local nl,fp,z0,z,nz,S,k,j,m,kk,kok,Z,l0,lp,lf,lsp,k0,kz,lsi,r,ksp,lsf,lm0,li,krm,krp,lmrm,lmrp,lnz; + +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +z0:=concat(L,F);z:=sort(z0); +nz:=size(z); + + + +S:=NULL; + + + +if(L==[-infinity,+infinity]){j:=[seq(-50+2*k,k=0..50)]minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[0]==-infinity){j:=[seq(2*k,k=-25..0.5*floor(L[1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[1]==+infinity){ +j:=[seq(2*k,k=floor(0.5*L[0])..0.5*50)] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for +} +else{ j:=[seq(2*k,k=0.5*floor(z[0])..0.5*floor(z[nz-1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for } + }}; + + + + +si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]); + if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}}; + fpour; +fsi; + + +S:=NULL; +S:=S,z[0]; +for(j:=1;j<size(z);j++){ + if(z[j]!=undef and (abs(z[j])>1e-15 or z[j]==0)){ + S:=S,z[j]}; +} +z:=[S]; + +Z:=sort(z); +nz:=size(Z); + +S:=NULL; +S:=S,Z[0]; +for(j:=1;j<nz;j++){ + if(Z[j]!=S[size(S)-1]){ + S:=S,Z[j]}; +} +Z:=[S]; + + +nz:=size(Z); +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +";fpour; + + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0; + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre; +"} +lm0:=limit(f(x),x,Z[0],1)==-infinity; + li:=lvic+nom+"}$ etex);"+ + if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); +"}}} + }; } + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}} + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + + + + + + +\end{VerbatimOut} + + + + + + + +%% +%% Code giac/Xcas pour les Tableaux de Variations avec +%% Valeurs intermediaires +%% + + + + + +\begin{VerbatimOut}{XcasTVI.cxx} + + +TVI(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +S:=[]; + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + +Z:=sort([op(set[op(Z)])]); + + + +nz:=size(Z); +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" "; + + + +LI:=limit(f(x),x,Z[0],1); +LF:=limit(f(x),x,Z[nz-1],-1); +LP:=NULL; +PB:=1; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; +if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; + +NL:=size(LL); +A:=NULL;aa:=1; +kk:=0; + + + +if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); +if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}} +l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"}; +//chgmt NL->nz +if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); + +if(PB[k]==1){if(TestS==0){ + A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}}; +} + + l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);" + + }; + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(evalf(sign(fp((Z[0]+10^(-3)))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(evalf(sign(fp(10^(-3)+Z[0])))==1.0){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$ + $ etex);"+ +if(evalf(sign(fp(10^(-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; + + + + + +if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + ksp:=evalf(fp(Z[r]+0.01))>0; + TestL:=(abs(LL[r])==abs(LL[r+1])); + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $ $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; + }} +else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + + if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $ $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} + else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} +}}}}; + + + + + lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"} + + + +lm0:=limit(f(x),x,Z[0],1)==-infinity; + + + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + + li:=lvic+nom+"}$ etex); +"+ if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; + + + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)) { + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + $ "+ao+" $ etex,0.5);" + }else{" "}; +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[rr-1],1))< evalf(limit(f(x),x,Z[rr],-1)); + krp:=evalf(limit(f(x),x,Z[rr],1))> evalf(limit(f(x),x,Z[rr+1],-1)) ; + lmrm:=limit(f(x),x,Z[rr],-1)==-infinity;lmrp:=limit(f(x),x,Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + $ "+ao+" $ etex,0.5); + ";rr:=rr+1; +}// testS==0 +else{lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + "}}};rr:=rr+1; +}//else testS==0 +}//PB[r]==1 +}//for nz<NL +}// else nz<NL +//if nz=NL +};//if nz>2 + + + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + + +MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ +if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}}; + + + + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + + +\end{VerbatimOut} + + + +%% +% +% +% +% Pour avoir les racines sous forme exacte.... quand c'est possible ! +% +% +% +%%%%%%%%% + + +\begin{VerbatimOut}{XcasTVIex.cxx} + + + +TVIex(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +S:=[]; + +Sex:=NULL; +Zex:=solve(f(x)=ao); +Zex:=sort(Zex); +for(j:=0;j<size(Zex);j++){ +if((evalf(Zex[j])>=evalf(L[0])) and (evalf(Zex[j])<=evalf(L[nl-1]))){Sex:=Sex,Zex[j]}; +}; +Sex:=[Sex]; + + + + + + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(factor(simplify(fp(x))),x); +} + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + + + + Z:=sort([op(set[op(Z)])]); + + +nz:=size(Z); +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" "; + + + +LI:=limit(f(x),x,Z[0],1); +LF:=limit(f(x),x,Z[nz-1],-1); +LP:=NULL; +PB:=1; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; +if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; + +NL:=size(LL); +A:=NULL;aa:=0; +kk:=0; + + + +if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); +if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $"+latex(simplify(Sex[aa]))+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}} +l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"}; +//chgmt NL->nz +if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); + +if(PB[k]==1){if(TestS==0){ + A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $"+latex(simplify(Sex[aa]))+"$ etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}}; +} + + l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);" + + }; + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(sign(fp((Z[0]+10^(-3))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$ + $ etex);"+ +if(evalf(sign(fp(10^(-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; + + + + +if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + ksp:=evalf(fp(Z[r]+0.01))>0; + TestL:=(abs(LL[r])==abs(LL[r+1])); + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $ $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; + }} +else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + + if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $ $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} + else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} +}}}}; + + + + + lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"} + + + +lm0:=limit(f(x),x,Z[0],1)==-infinity; + + + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + + li:=lvic+nom+"}$ etex); +"+ if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; + + + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)) { + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + $ "+ao+" $ etex,0.5);" + }else{" "}; +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[rr-1],1))< evalf(limit(f(x),x,Z[rr],-1)); + krp:=evalf(limit(f(x),x,Z[rr],1))> evalf(limit(f(x),x,Z[rr+1],-1)) ; + lmrm:=limit(f(x),x,Z[rr],-1)==-infinity;lmrp:=limit(f(x),x,Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + $ "+ao+" $ etex,0.5); + ";rr:=rr+1; +}// testS==0 +else{lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + "}}};rr:=rr+1; +}//else testS==0 +}//PB[r]==1 +}//for nz<NL +}// else nz<NL +//if nz=NL +};//if nz>2 + + + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + + +MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ +if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}}; + + + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + +\end{VerbatimOut} + + + + + + + +%% +%% +%% Quand les solutions de f'(x)=0 ne sont pas formellement calculables +%% + + + + +\begin{VerbatimOut}{XcasTVIapp.cxx} + +TVIapp(L,F,nom,nomv,f,ftt,ao,nmr):={ + + +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +z0:=concat(L,F);z:=sort(z0); +nz:=size(z); + + + + + + + +S:=op(fsolve(fp(x),x)); + + + + +if(L==[-infinity,+infinity]){j:=[seq(-50+2*k,k=0..50)]minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[0]==-infinity){j:=[seq(2*k,k=-25..0.5*floor(L[1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for} +else{if(L[1]==+infinity){ +j:=[seq(2*k,k=floor(0.5*L[0])..0.5*50)] minus F; + for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for +} +else{ j:=[seq(2*k,k=0.5*floor(z[0])..0.5*floor(z[nz-1]))] minus F; + for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for } + }}; + + + + + + + + + + + + + +si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]); + if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}}; + fpour; +fsi; + + +S:=NULL; +S:=S,z[0]; +for(j:=1;j<size(z);j++){ + if(z[j]!=undef and (abs(z[j])>1e-15 or z[j]==0)){ + S:=S,z[j]}; +} +z:=[S]; + + + +Z:=sort(z); +nz:=size(Z); + +S:=NULL; +S:=S,Z[0]; +for(j:=1;j<nz;j++){ + if(Z[j]!=S[size(S)-1]){ + S:=S,Z[j]}; +} +Z:=[S]; + + +nz:=size(Z); +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" "; + + + +LI:=limit(f(x),x,Z[0],1); +LF:=limit(f(x),x,Z[nz-1],-1); +LP:=NULL; +PB:=1; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; +if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; + +NL:=size(LL); +A:=NULL;aa:=1; +kk:=0; + + +if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); +if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}} +l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"}; +//chgmt NL->nz +if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); + +if(PB[k]==1){if(TestS==0){ + A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}}; +} + + l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);" + + }; + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + k0:= evalf(limit(f(x),x,Z[0],1))> evalf(limit(f(x),x,Z[1],-1)); + kz:=evalf(limit(f(x),x,Z[nz-1],-1))> evalf(limit(f(x),x,Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(sign(fp((Z[0]+10^(-3))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$ + $ etex);"+ + +if(evalf(sign(fp(10^(-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; + + + +if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + ksp:=evalf(fp(Z[r]+0.01))>0; + TestL:=(abs(LL[r])==abs(LL[r+1])); + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $ $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; + }} +else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + + if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $ $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} + else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} +}}}}; + + + + + lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"} + + + +lm0:=limit(f(x),x,Z[0],1)==-infinity; + + + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + + li:=lvic+nom+"}$ etex); +"+ if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; + + + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[r-1],1))< evalf(limit(f(x),x,Z[r],-1)); + krp:=evalf(limit(f(x),x,Z[r],1))> evalf(limit(f(x),x,Z[r+1],-1)) ; + lmrm:=limit(f(x),x,Z[r],-1)==-infinity;lmrp:=limit(f(x),x,Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)) { + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + $ "+ao+" $ etex,0.5);" + }else{" "}; +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x,Z[rr-1],1))< evalf(limit(f(x),x,Z[rr],-1)); + krp:=evalf(limit(f(x),x,Z[rr],1))> evalf(limit(f(x),x,Z[rr+1],-1)) ; + lmrm:=limit(f(x),x,Z[rr],-1)==-infinity;lmrp:=limit(f(x),x,Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + $ "+ao+" $ etex,0.5); + ";rr:=rr+1; +}// testS==0 +else{lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + "}}};rr:=rr+1; +}//else testS==0 +}//PB[r]==1 +}//for nz<NL +}// else nz<NL +//if nz=NL +};//if nz>2 + + + +lnz:=limit(f(x),x,Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x,Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + + +MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ +if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}}; + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + + + +\end{VerbatimOut} + + + + + + + +%% +%% Code giac/Xcas pour les Tableaux de variations de courbes parametrees +%% + + + + + + + +\begin{VerbatimOut}{XcasTVP.cxx} +TVP(L,F,nom,nomv,ff,ftt,trigo,nmr):={ + +nl:=size(L); +fp:=[]; +S:=[]; +f:=[unapply(ff[0],t),unapply(ff[1],t)]; +fp:=[function_diff(f[0]),function_diff(f[1])]; +Z:=[]; +LLL:=[]; + + +all_trig_solutions:=1; +reset_solve_counter(-1,-1); + +for(d:=0;d<=1;d++){ +LLL:=concat(L,F[d]); +Z:=LLL union Z; +SS:=solve(factor(simplify(fp[d](t))),t); +ns:=size(SS); + + +for(k:=0;k<ns;k++){ +if(trigo==t){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ + +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; + +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ + +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; + +} +}else{ +S:=concat(S,SS); +} +} + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + qq:=member(simplify(S[j]),Z)==0; + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}}; + fpour + fsi; +Z:=sort(Z); +nz:=size(Z); + + + tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); + ftantque; + + + + +nz:=size(Z); +u:=1; + tantque (u<nz-2) and (nz>2) faire + tantque evalf(Z[u])==evalf(Z[u+1]) faire + Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=size(Z); + ftantque; + u:=u+1; + ftantque; + + + }; + +Z:=sort(Z); +nz:=size(Z); + + + + l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:="",""; lf:="","";lsp:="",""; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +";fpour; + + lsi:="",""; + +FFF:=[[],[]]; + +for(d:=0;d<=1;d++){ +FFF[d]:=concat(F[d],[-infinity,+infinity]); + k0:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1)); + kz:=evalf(limit(f[d](x),x=Z[nz-1],-1))> evalf(limit(f[d](x),x=Z[nz-2],1)); +//} +//$ + lsi[d]:=lsic+nom[d]+"'("+nomv+")}$ etex);"+if(member(Z[0],FFF[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[0])))+"$ etex);"}else{if(Z[0]==-infinity){" "}else{"nonDefBarre; +"}}+ + if(Z[0]==-infinity){if(sign(evalf(fp[d](if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F[d])==0){ + if(sign(fp[d](Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{ + if(sign(fp[d]((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }} + +if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp[d](Z[r]+0.01))>0; + lsp[d]:=lsp[d]+if(member(Z[r],F[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[r])))+"$ etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"} + }; } + +lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[nz-1])))+"$ etex);"}else{if(Z[nz-1]==+infinity){" "}else{"nonDefBarre;"}} + + + + + } + + + + + + + + + + + + lm0:=1,2; li:=1,2; krm:=1,2; krp:=1,2; lmrm:=1,2; lmrp:=1,2; lp:="",""; lnz:=1,2; lf:=1,2; Kz:=1,2;K0:=1,2; + + +for(d:=0;d<=1;d++){ + K0[d]:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1)); + Kz[d]:=evalf(limit(f[d](x),x,Z[nz-1],-1))> evalf(limit(f[d](x),x,Z[nz-2],1)); +//{ +//$ +lm0[d]:=limit(f[d](x),x,Z[0],1)==-infinity; + li[d]:=lvic+nom[d]+"}$ etex);"+ + if(member(Z[0],F[d])==0){"valPos(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$ etex,"}+ + if(K0[d]==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ krm[d]:=evalf(limit(f[d](x),x=Z[r-1],1))< evalf(limit(f[d](x),x=Z[r],-1)); + krp[d]:=evalf(limit(f[d](x),x=Z[r],1))> evalf(limit(f[d](x),x,Z[r+1],-1)) ; + lmrm[d]:=limit(f[d](x),x,Z[r],-1)==-infinity;lmrp[d]:=limit(f[d](x),x,Z[r],1)==-infinity; + lp[d]:=lp[d]+if(member(Z[r],F[d])){ + "limGauche(btex + $"+if(lmrm[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],-1)))}+"$ + etex,"+if(krm[d]==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],1)))}+"$ etex,"+if(krp[d]==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f[d](Z[r])))+"$ + etex,"+if(sign(evalf(fp[d](Z[r]-0.001)))==sign(evalf((fp[d](Z[r]+0.001))) )){"0.5);"}else{if(krp[d]==1){"1);"}else{"0); +"}}} + }; } + +lnz[d]:=limit(f[d](x),x=Z[nz-1],-1)==-infinity; + + +lf[d]:=if(member(Z[nz-1],F[d])==0){"valPos(btex $"+ + if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$ etex,"+ + if(Kz[d]==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$ etex,"+ + if(Kz[d]==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + +} + + + + + + + + +MetaLfc:=if(ftt==2){if(nz>2){" + +beginTableau("+nmr+")"+ + l0+lsi[0]+lsp[0]+lsf[0]+lsi[1]+lsp[1]+lsf[1]+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi[0]+lsf[0]+lsi[1]+lsf[1]+" +endTableau; + +"; +} +}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li[0]+ +lp[0]+ +lf[0]+ +li[1]+ +lp[1]+ +lf[1] ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li[0]+ +lf[0]+ +li[1]+ +lf[1] ++" +endTableau; + +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi[0]+lsp[0]+lsf[0]+ +li[0]+ +lp[0]+ +lf[0]+ +lsi[1]+lsp[1]+lsf[1]+ +li[1]+ +lp[1]+ +lf[1] ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi[0]+lsf[0]+ +li[0]+ +lf[0]+ +lsi[1]+lsf[1]+ +li[1]+ +lf[1] ++" +endTableau; + +";} +} +} + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + +}:; +\end{VerbatimOut} + + + + +%% +%% Code giac/Xcas pour les Tableaux de signes de produits +%% + + + + +\begin{VerbatimOut}{XcasTabSignL.cxx} + + +TS(nomf,L,D,trigo,nmr):={ +L:=apply(f->unapply(f,x),L) +n:=size(L); +Z:=NULL; +nl:=size(L); +S:=[]; +mini:=D[0]; maxi:=D[1]; + +pour k de 0 jusque n-1 faire + + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(L[k](x))),x); +ns:=size(SS); +for(j:=0;j<ns;j++){ +m:=0; +while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1; +} +} + +}else{ +S:=solve(L[k](x),x); +} + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j]);} + fpour; + fsi; +fpour; + + + + + +Z:=sort(Z); +nz:=size(Z); + + + Z:=sort([op(set[(Z)])]); + + +nz:=size(Z); + +if(nz==0){li:="";l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);"; + for(p:=0;p<=n-1;p++){li:=li+lsic+latex(L[p](x))+"}$ etex);"+ +if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}else{" + "}+ +if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){" + valBarre(btex 0 etex);"}else{" + "} + +} + lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"}; + + +MetaLfc:=" beginTableau("+nmr+") +newLigneVariables(btex $ {x}$ etex); + "+l0+li+ lsic+nomf+"(x)}$ etex);"+ + if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+ lf+ + if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+" +endTableau; +" +; + +}else{ + +l0:="val(btex $"+latex(D[0])+"$ etex);";li:=" ";lr:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +";fpour; +l0:=l0+"val(btex $"+latex(D[1])+"$ etex);"; + + +for(p:=0;p<=n-1;p++){lp:=""; + li:=li+lsic+latex(L[p](x))+"}$ etex);"+ + if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}else{" + "}+ + if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"}; + + for(r:=0; r<=nz-2;r++){ + lp:=lp+if(simplify(L[p](Z[r]))==0){" + valBarre(btex 0 etex);"}else{"barre; + "}+ + if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}}; + + li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins; + "}+if(maxi!=+infinity and L[p](maxi)==0){" + valBarre(btex 0 etex);"}else{" + "} + }; + + +pour t de 0 jusque nz-2 faire + lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);" + fpour + +MetaLfc:=" beginTableau("+nmr+") +newLigneVariables(btex $ {x}$ etex); + "+l0+ + li + + lsic+nomf+"(x)}$ etex);"+ + if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+ + if(product(L[s](evalf(Z[0])-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"+ + lr+ + if(product(L[s](evalf(Z[nz-1])+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){" + valBarre(btex 0 etex);"}else{" + "}+" +endTableau; + + "; +} +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + }:; + +\end{VerbatimOut} + + + + +%% +%% Code giac/Xcas pour les Tableaux de signes de quotients +%% + + + +\begin{VerbatimOut}{XcasTabSignQ.cxx} +TSq(nomf,L,Fo,D,trigo,nmr):={ +L:=apply(f->unapply(f,x),L); +Fo:=apply(f->unapply(f,x),Fo); +L:=concat(L,Fo); +n:=size(L); +Z:=NULL; +m:=size(Fo); +F:=NULL;FF:=NULL; +mini:=D[0]; maxi:=D[1]; +S:=[]; +SF:=[]; + +pour k de 0 jusque n-1 faire + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(L[k](x))),x); +ns:=size(SS); +for(j:=0;j<ns;j++){ +mm:=0; +while(evalf(simplify(subst(SS[j],n_1=mm)))<=evalf(maxi)){ +S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm+1; +};mm:=-1; +while(evalf(subst(SS[j],n_1=mm))>=evalf(mini)){ +S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm-1; +} +} + +}else{ +S:=concat(S,solve(L[k](x),x)); +} + + + + + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j]);} + fpour; + fsi; +fpour; + + +pour k de 0 jusque m-1 faire + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SSF:=solve(factor(simplify(Fo[k](x))),x); +nsf:=size(SSF); +for(j:=0;j<nsf;j++){ +mm:=0; +while(evalf(simplify(subst(SSF[j],n_1=mm)))<=evalf(maxi)){ +SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm+1; +};mm:=-1; +while(evalf(subst(SSF[j],n_1=mm))>=evalf(mini)){ +SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm-1; +} +} + +}else{ +SF:=concat(SF,solve(Fo[k](x),x)); +} + + si size(SF)>0 alors pour j de 0 jusque size(SF)-1 faire + FF:=FF,simplify(SF[j]); + if(SF[j]>mini and SF[j]<maxi){F:=F,simplify(SF[j]);} + fpour; + fsi; +fpour; + + + +Z:=[Z,F]; + + +Z:=sort([op(set[op(Z)])]); + +nz:=size(Z); + +if(nz==0){li:="";l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);"; + for(p:=0;p<=n-1;p++){li:=li+lsic+latex(L[p](x))+"}$ etex);"+ +if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}else{" + "}+ +if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){" + valBarre(btex 0 etex);"}else{" + "} + +} + lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"}; + + + + +MetaLfc:=" +beginTableau("+nmr+") +newLigneVariables(btex $ {x}$ etex); + "+l0+li+ + lsic+nomf+"(x)}$ etex);"+ + if(member(mini,FF)==0){if((mini!=-infinity) and (product(L[s](mini),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+ lf+ + if(member(maxi,FF)==0){if((maxi!=+infinity) and (product(L[s](maxi),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+" +endTableau; + +" +; + + + + +}else{ + + +l0:="val(btex $"+latex(D[0])+"$ etex);";li:=" ";lr:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +";fpour; +l0:=l0+"val(btex $"+latex(D[1])+"$ etex);"; + + +for(p:=0;p<=n-1;p++){lp:=""; + li:=li+lsic+latex(L[p](x))+"}$ etex);"+ + if(mini!=-infinity and L[p](mini)==0){" valBarre(btex 0 etex);"}else{" "}+ + if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"}; + + for(r:=0; r<=nz-2;r++){lp:=lp+if(simplify(L[p](Z[r]))==0){" valBarre(btex 0 etex);"}else{"barre;"}+ + if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}}; + + li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(L[p](evalf(Z[nz-1])+1.0)>0){"plus;"}else{"moins; + "}+if(maxi!=+infinity and L[p](maxi)==0){"valBarre(btex 0 etex);"}else{" "} + + }; + + +pour t de 0 jusque nz-2 faire + lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(Z[t+1],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"} + fpour + + + + +MetaLfc:=" +beginTableau("+nmr+") +newLigneVariables(btex $ {x}$ etex); + "+l0+ + li + + + lsic+nomf+"(x)}$ etex);"+ + if(member(mini,FF)==0){if((mini!=-infinity) and (product(L[s](mini),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+ + if(product(L[s](evalf(Z[0])-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(Z[0],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"}+ + lr+ + if(product(L[s](evalf(Z[nz-1])+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(maxi,FF)==0){if((maxi!=+infinity) and (product(L[s](maxi),s,0,n-1)==0)){"valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+" +endTableau; + +" + + +} + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + + + + }:; + +\end{VerbatimOut} + + + + +%% Code giac/Xcas pour les Tableaux de signes du produit +%% de 2 facteurs affines +%% + + + + +\begin{VerbatimOut}{XcasTabSigna.cxx} +TSa(a,b,c,d,nmr):={ +zA:=solve(a*x+b=0,x)[0]; +zB:=solve(c*x+d=0,x)[0]; +zmin:=min(zA,zB); +zmax:=max(zA,zB); + Meta:= " + beginTableau("+nmr+") + newLigneVariables(btex $ {x}$ etex); + val(btex $-\\infty$ etex);val(btex $"+latex(zmin)+"$ etex); +val(btex $"+latex(zmax)+"$etex); +val(btex $+\\infty$ etex); + "+lsic+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+"}$ etex);" + + if(a>0){"moins;"}else{"plus;"}+ + if(zmin==zA){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(zmin==zA){si a>0 alors "plus;"; sinon "moins;";fsi} + else{si a>0 alors "moins;"; sinon "plus;"; fsi}+ + if(zmin==zA){"barre;"}else{"valBarre(btex 0 etex);"}+ + if(a>0){"plus;"}else{"moins;"} + +lsic+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+"}$ etex);" + + if(c>0){"moins"}else{"plus"}+";"+ + if(zmin==zB){"valBarre(btex 0 etex);"}else{"barre;"}+ + if(zmin==zB){si c>0 alors "plus;"; sinon "moins;";fsi} + else{si c>0 alors "moins;"; sinon "plus;"; fsi}+ + if(zmin==zB){"barre;"}else{"valBarre(btex 0 etex);"}+ + if(c>0){"plus;"}else{"moins;"} + + +lsic+"{("+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+")("+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+")}}$ etex);" + + si a*c>0 alors plus; sinon moins;fsi+";"+ + "valBarre(btex 0 etex);"+ + si a*c>0 alors moins; sinon plus;fsi+";"+ + "valBarre(btex 0 etex);"+ + si a*c>0 alors plus; sinon moins;fsi+";"+" +endTableau; +" +; + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,Meta); +fclose(sortie); + + + }:; +\end{VerbatimOut} + + + + + + +%%$ +%% Code giac/Xcas pour les Tableaux de Signes d'expression ne contenant +%% qu'un seul terme + + + + +\begin{VerbatimOut}{XcasTSc.cxx} + +TSc(g,D,F,trigo,nmr):={ +f:=unapply(g,x); +mini:=D[0]; maxi:=D[1];lm:=" "; +Z:=mini,maxi; +S:=[]; + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(f(x))),x); +ns:=size(SS); +for(j:=0;j<ns;j++){ +m:=0; +while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){ +S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1; +} +} + +}else{ +S:=solve(f(x),x); +} + + + + + +if(size(S)==0 and size(F)==0){ +l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);"; +li:=if(member(mini,F)!=0){"nonDefBarre;"}else{if(mini!=-infinity and f(mini)==0){" + valBarre(btex 0 etex);"}else{" + "}}+ +if(mini!=-infinity or maxi!=+infinity){if(f((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}}else{if(f(0.3145274774464545777744)>0){"plus;"}else{"moins;"}}; +lf:=if(member(maxi,F)!=0){"nonDefBarre;"}else{if(maxi!=+infinity and f(maxi)==0){" + valBarre(btex 0 etex);"}else{" + "}}; +}else{ +if(size(S!=0)){pour j de 0 jusque size(S)-1 faire + if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j])}; + fpour} + +Z:=concat([Z],F); + + Z:=sort([op(set[op(Z)])]); + + +nz:=size(Z); +l0:=" ";li:=" ";lr:=" "; +if(nz==2){l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);"; +li:=if(mini!=-infinity and f(mini)==0){" + valBarre(btex 0 etex);"}else{if(member(mini,F)==0){" + "}else{"nonDefBarre;"}}+ +if(f((mini+maxi)*0.5)>0){"plus;"}else{"moins;"}; +lf:=if(maxi!=+infinity and f(maxi)==0){" + valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){" + "}else{"nonDefBarre;"} + }; + +}else{ +l0:="val(btex $"+latex(Z[0])+"$ etex);";li:=" "; +pour m de 1 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex); +"; +fpour; + + +li:= if(mini!=-infinity and f(mini)==0){" + valBarre(btex 0 etex);"}else{if(member(mini,F)==0){" + "}else{"nonDefBarre;"} + } + +lm:=if(nz>2){for(r:=0; r<nz-2;r++){lm:=lm+if(Z[r]==-infinity){ +if(f((Z[r+1]-1))>0){"plus;"}else{"moins;"} +}else{if(f((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}} ++ + if(member(Z[r+1],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"} + }}else{" "}; + +lf:=if(f(Z[nz-2]+0.1)>0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){" + "}else{"nonDefBarre;"} + }; +} +}; + + + + +MetaLfc:=" + +beginTableau("+nmr+") +newLigneVariables(btex $\\displaystyle {x}$ etex); + "+l0+lsic+latex(f(x))+"}$ etex);"+ + li+lm+lf + +" +endTableau; + +" +; + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + }:; + +\end{VerbatimOut} + + + + + + + +%%$ + + + + + + +%%%% +%%% +%%% Pour des tableaux de variations simples sans fonctions +%%% +%%% + + + +\begin{VerbatimOut}{XcasTVS.cxx} +TVS(La,Lo,F,nomf,nomv,nmr):={ + +na:=size(La); +f:=F; +if(member(La[0],F)){f:=f[1..size(f)-1]}; +if(member(La[na-1],F)){f:=f[0..size(f)-2]}; +Z:=sort(concat(La,f)); +Zo:=sort([op(set[op(Z)])]); +nz:=size(Z); +nzo:=size(Zo); + + +k0:= evalf(Lo[0])> evalf(Lo[1]); +kz:=evalf(Lo[nz-1])> evalf(Lo[nz-2]); + + +l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" "; + for(m:=0;m<=nzo-1;m++){l0:=l0+"val(btex $"+latex(Zo[m])+"$ etex);"} + +li:=lvic+nomf+"}$ etex);"+ + if(member(Z[0],F)==0){"valPos(btex $"+latex(Lo[0])+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+latex(Lo[0])+"$ etex,"}+ + if(k0==1){"1"}else{"0"}+ + ");"; + + if(nz>2){ for(r:=1; r<=nz-2;r++){ + krm:=evalf(Lo[r-1])< evalf(Lo[r]); + krp:=evalf(Lo[r])> evalf(Lo[r+1]) ; + + lp:=lp+if(Z[r]==Z[r+1]){ + "limGauche(btex$"+latex(Lo[r])+"$etex,"+ + if(krm==1){"1);"} + else{"0);"} + }// fin if zr=zr+1 + else{ + if(Z[r]==Z[r-1]){ + "nonDefBarre;limDroite(btex$"+latex(Lo[r])+"$etex,"+ + if(krp==1){"1);"} + else{"0);"} + }//fin if zr=zr-1 + else{ + "valPos(btex $"+latex(Lo[r])+"$etex,"+ + if(krp==1){"1);"}else{"0);"} +}//fin else zr=zr-1 +}//fin else zr=zr+1 +}//fin for +}//fin de if nz>2 + + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+latex(Lo[nz-1])+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+latex(Lo[nz-1])+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + +MetaLfc:= + + if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; + +";} + +//return(MetaLfc); + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + +}:; + +\end{VerbatimOut} + +%%$ + + + + + + + + + + + + + + + + + + + + + +%% +%% traitement des fichiers produits par giac/xcas +%% +%% + +% pour l'chelle des tableaux taper \ech{facteur de rduction} + +\newcommand\echelle{1} +\newcommand\ech[1]{\renewcommand\echelle{#1}} + + +\newcommand\couleurtab{black} +\newcommand\coultab[1]{\renewcommand\couleurtab{#1}} + + +\newcommand{\dresse}[2]{% +\ifthenelse{\boolean{xcas}}{% Avec l'option "XCas present" + \executGiacmp{XCas#2.giac}% reconstituer le tableau + % exporter le source mp + % puis lancer metapost pour creer + % l'image du tableau + \immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab.mp} + \immediate\write18{\cat enteteMP.cfg >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod def beginTableau(expr c) =\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod begingroup\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod charcode:=c;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod clearxy; clearit; clearpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod pickup defaultpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod drawoptions(withcolor(#1));\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod initTableau;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod enddef;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab#2.mp} + \immediate\write18{\cat queue.mp >> \nomtravail_Tab#2.mp} + \immediate\write18{mpost -jobname=\nomtravail_Tab \nomtravail_Tab#2.mp} + \immediate\write18{\rem \nomtravail_Tab#2.mp} + }% + {% sinon, si le tableau est absent, alerte. + \IfFileExists{\nomtravail_Tab.\theTVn}{}{% + \PackageError{tablor}{Tableau absent non + reconstituable.}{Pour compiler il faut, soit les fichiers de + tableaux, soit le fichier \nomtravail_Tab.mp, soit disposer de + XCas.}}} + +\begin{center} + \includegraphics[scale=\echelle]{\nomtravail_Tab.\theTVn} +\end{center} +\stepcounter{TVn} +} + + +%% +%% traitement des fichiers produits par giac/xcas avec possibilite +%% de modifier le fichier metapost (environnement etoile)) +%% + + + +\newcommand{\dressetoile}[2]{% +\IfFileExists{\nomtravail_Tab.\theTVn}{% Test sur l'existence du tableau +% Si oui, inclusion du fichier source de sauvegarde mp dans Tableaux +\immediate\write18{\cat TSav-\theTVn.mp >> \nomtravail_Tab.mp}} +% Si non, lancement des operations de fabrication +{\executGiacmp{XCas#2.giac}% +\immediate\write18{\editeur XCasmpfc.mp } + + % Modification avec l'editeur choisi +\immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab.mp} +\immediate\write18{\cp XCasmpfc.mp TSav-\theTVn.mp} % Sauvegarde du + % source mp sur le disque pour une + % inclusion ulterieure dans Tableaux.mp. +\immediate\write18{\cat enteteMP.cfg >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod def beginTableau(expr c) =\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod begingroup\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod charcode:=c;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod clearxy; clearit; clearpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod pickup defaultpen;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod drawoptions(withcolor(#1));\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod initTableau;\echof >> \nomtravail_Tab#2.mp} + \immediate\write18{\echod enddef;\echof >> \nomtravail_Tab#2.mp} +\immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab#2.mp}} % Inclusion du + % source dans le + % fichier + % Tableaux +\immediate\write18{\cat queue.mp >> \nomtravail_Tab#2.mp} +\immediate\write18{mpost -jobname=\nomtravail_Tab \nomtravail_Tab#2.mp}% Reconstitution des tableaux + % et creation du dernier. L'option + % pallie l'absence de end en fin de + % fichier +\immediate\write18{\rem \nomtravail_Tab#2.mp} + +\begin{center} + \includegraphics[scale=\echelle]{\nomtravail_Tab.\theTVn} +\end{center} +\ech{1} +\setcounter{TVn}{\theTVnbis} % Restauration du compteur TVn +} + + + + + + + +%% +%% +%%% +%%% +%%% les "giac" qui permettent d'executer la commande rentree dans le fichier tex +%%% suivis des environnements qui permettront la saisie du code giac/xcas +%%% Les versions etoilees permettent de modifier le code metapost produit initialement +%%% + + + + +\begin{VerbatimOut}{XCasa.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTabSigna.cxx"); +read("XCasa.user"); +\end{VerbatimOut} + +\newenvironment{TSa} +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasa.user}} +{\end{VerbatimOut} + \dresse{\couleurtab}{a} +} + + + + + + + + + +\begin{VerbatimOut}{XCasQ.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTabSignQ.cxx"); +read("XCasQ.user"); +\end{VerbatimOut} + +\newenvironment{TSq}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasQ.user}} +{\end{VerbatimOut}\dresse{\couleurtab}{Q}} + + + +\newenvironment{TSq*}[1]% +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasQ.user}} +{\end{VerbatimOut}\dressetoile{\couleurtab}{Q}} + + +\begin{VerbatimOut}{XCasL.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTabSignL.cxx"); +read("XCasL.user"); +\end{VerbatimOut} + +\newenvironment{TS}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasL.user}} +{\end{VerbatimOut}\dresse{\couleurtab}{L}} + + +\newenvironment{TS*}[1] +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasL.user}} +{\end{VerbatimOut}\dressetoile{\couleurtab}{L}} + + +\begin{VerbatimOut}{XCasTSc.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTSc.cxx"); +read("XCasTSc.user"); +\end{VerbatimOut} + + + + +\newenvironment{TSc*}[1]% +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTSc.user}} +{\end{VerbatimOut}\dressetoile{\couleurtab}{TSc}} + + +\newenvironment{TSc}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTSc.user}} +{\end{VerbatimOut}\dresse{\couleurtab}{TSc}} + + +\begin{VerbatimOut}{XCasTV.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTV.cxx"); +read("XCasTV.user"); +\end{VerbatimOut} + + + +\newenvironment{TV}{% +\VerbatimEnvironment +\begin{VerbatimOut}[commandchars=\\??]{XCasTV.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TV}} + +\newenvironment{TV*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTV.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TV}} + + + + + + + +\begin{VerbatimOut}{XCasTVP.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVP.cxx"); +read("XCasTVP.user"); +\end{VerbatimOut} + +\newenvironment{TVP}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVP.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TVP}} + +\newenvironment{TVP*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVP.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVP}} + + + + + + + + + + +\begin{VerbatimOut}{XCasTVZ.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVZ.cxx"); +read("XCasTVZ.user"); +\end{VerbatimOut} + +\newenvironment{TVZ}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVZ.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TVZ}} + +\newenvironment{TVZ*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVZ.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVZ}} + + + + + + + + +\begin{VerbatimOut}{XCasTVapp.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVapp.cxx"); +read("XCasTVapp.user"); +\end{VerbatimOut} + +\newenvironment{TVapp}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVapp.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TVapp}} + +\newenvironment{TVapp*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVapp.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVapp}} + + + + + + + + + + + +\begin{VerbatimOut}{XCasTVI.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVI.cxx"); +read("XCasTVI.user"); +\end{VerbatimOut} + +\newenvironment{TVI}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVI.user}}% +{\end{VerbatimOut}\dresse{\couleurtab}{TVI}} + + +\newenvironment{TVI*}[1]% +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVI.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVI}} + + + + + +\begin{VerbatimOut}{XCasTVIex.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVIex.cxx"); +read("XCasTVIex.user"); +\end{VerbatimOut} + +\newenvironment{TVIex}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIex.user}}% +{\end{VerbatimOut}\dresse{\couleurtab}{TVIex}} + + +\newenvironment{TVIex*}[1]% +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIex.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVIex}} + + + + + + + + + +\begin{VerbatimOut}{XCasTVIapp.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVIapp.cxx"); +read("XCasTVIapp.user"); +\end{VerbatimOut} + +\newenvironment{TVIapp}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIapp.user}}% +{\end{VerbatimOut}\dresse{\couleurtab}{TVIapp}} + + +\newenvironment{TVIapp*}[1]% +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIapp.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVIapp}} + + + + + +\begin{VerbatimOut}{XCasTVPC.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVPC.cxx"); +read("XCasTVPC.user"); +\end{VerbatimOut} + +\newenvironment{TVPC}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVPC.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TVPC}} + +\newenvironment{TVPC*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVPC.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVPC}} + + + + + + + + + + + + +\begin{VerbatimOut}{XCasTVS.giac} +maple_mode(0); +approx_mode:=0; +read("config.cxx"); +read("XcasTVS.cxx"); +read("XCasTVS.user"); +\end{VerbatimOut} + +\newenvironment{TVS}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVS.user}}% +{\end{VerbatimOut} +\dresse{\couleurtab}{TVS}} + +\newenvironment{TVS*}[1]{% +\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVS.user}}% +{\end{VerbatimOut}\dressetoile{\couleurtab}{TVS}} + + + + + + + + + + +%% pour nettoyer les fichiers auxiliaires + +\AtEndDocument{\immediate\write18{\cat queue.mp >> \nomtravail_Tab.mp} + } + + + + +%% +%% Zi end -> enjoy :) diff --git a/macros/latex/contrib/tablor/tablor.tex b/macros/latex/contrib/tablor/tablor.tex new file mode 100644 index 0000000000..70afb09205 --- /dev/null +++ b/macros/latex/contrib/tablor/tablor.tex @@ -0,0 +1,2404 @@ +% \copyleft Connan le Barbare (aka Guillaume Connan) \copyright +% This work may be distributed and/or mofified under the conditions +% or the LaTeX Project Public Licence, either v1.3 or (at your option) +% any later version. The latest version is in +% http://www.latex-project.org/lppl/ +% This work consists of the files tablor.sty, tablor-xetex.sty, tablor.cfg, tablor.tex, +% tablor.pdf and tablor.html + + + + +\documentclass[11pt]{article} +\usepackage{etex} +\usepackage[height=250mm,width=183mm]{geometry} +\usepackage[latin1]{inputenc} +\usepackage[T1]{fontenc} +\usepackage[french]{babel} +\usepackage[upright]{kpfonts} +\usepackage{bold-extra} +\usepackage[scaled=0.85]{luximono} +\usepackage[xcas]{tablor} +\usepackage{listings,keystroke} +\usepackage{graphicx,bclogo,amssymb,amsbsy,amsfonts,amstext,amscd,amsopn,amsxtra} +% bclogo est tlchargeable ici : http://melusine.eu.org/syracuse/wiki/doku.php/mc/bclogo + + +\usepackage{tocloft} +%ajoute de l'espace entre le +%numero de chapitre (chap) et le titre +%dans la table des matieres + +\addtolength{\cftsecnumwidth}{2em} +\addtolength{\cftsubsecnumwidth}{1em} + +% pour une TdM hyperactive... +\usepackage[dvips,colorlinks=true,linkcolor=blue]{hyperref} + +% quelques gris + +\usepackage{color} +\definecolor{0.9white}{rgb}{.9,.9,.9} +\definecolor{0.8white}{rgb}{.8,.8,.8} +\definecolor{0.2white}{rgb}{.2,.2,.2} +\definecolor{0.4white}{rgb}{.4,.4,.4} +\definecolor{0.6white}{rgb}{.6,.6,.6} +\definecolor{0.1white}{rgb}{.1,.1,.1} +\definecolor{bleu}{rgb}{0.4,0.2,1} \newrgbcolor{bleu}{0.4 0.2 1} +\definecolor{orange}{rgb}{0.589999,0.269997,0.080004} +\definecolor{rouge}{rgb}{1,0,0} \newrgbcolor{rouge}{1 0 0} +% style des listings + + +\newcommand\lat{\lstset{numbers=none,language=[LaTeX]{TeX},xleftmargin=10pt,% +keywordstyle =\color{bleu}\bfseries,basicstyle=\ttfamily\color{0.1white},commentstyle=\normalfont\scriptsize\slshape,breaklines=true,backgroundcolor=\color{green!20},frame=trBL,framerule=1pt,framesep=4pt,rulesep=1pt,showstringspaces=false,stringstyle=\slshape,captionpos=b} +} + + +\newcommand\xcas{\lstset{numbers=none,language=XCAS,xleftmargin=10pt,% +keywordstyle =\color{rouge!70!black}\bfseries,basicstyle=\ttfamily\color{0.1white},commentstyle=\normalfont\scriptsize\slshape,breaklines=true,backgroundcolor=\color{orange!20},frame=trBL,framerule=1pt,framesep=4pt,rulesep=1pt,showstringspaces=false,stringstyle=\slshape,captionpos=b} +} + + + +% petits environnements bclogo + + + +\newenvironment{DANGER}[1]{% +\begin{bclogo}[logo=\bctakecare,arrondi=0.1,couleur=0.9white]{#1}} +{\end{bclogo}} + +\newenvironment{Idee}[1]{% +\begin{bclogo}[logo=\bclampe,arrondi=0.1,couleur=0.9white]{#1}} +{\end{bclogo}} + + + +% style des sections +\usepackage{sectsty} + + +\sectionfont{\LARGE \color{0.2white}} +\subsectionfont{\color{0.4white}} +\renewcommand\thesection{\Roman{section} -} +\renewcommand\thesubsection{\alph{subsection}. } +\subsubsectionfont{\color{0.6white}} +\renewcommand\thesubsubsection{\roman{subsection}. } + +\graphicspath{{./figures/}} + + + +% titre + +\title{\texttt{tablor.sty} \\La machine crer des tableaux de signes et de variations } + +\author{Guillaume \textsc{Connan} \\ \href{http://tehessin.tuxfamily.org/}{http://tehessin.tuxfamily.org/}\\ +avec l'efficace participation de Jean-Michel \textsc{Boucart}\\ +Forum d'aide ~:~\href{http://gconnan.free.fr/punbb/upload/index.php}{http://gconnan.free.fr/punbb/upload/index.php}} + +\date{9 mai 2010 - Version 4.07} + + + + + + + + +%% +% +% Dbut du document +% +%% + + + + +\begin{document} + +\setlength{\parindent}{0mm} + +\maketitle + + +\vspace{1cm} + +\initablor + +\section{a sert quoi~?} + +Il s'agit d'obtenir rapidement un tableau de signe ou un tableau de variation en entrant un +minimum de commandes. + +\section{Nouveauts} + +\subsection{Changements depuis la version 3.00} + + +\begin{figure}[!h] + \begin{DANGER}{Attention~!} + partir de la version 4.03 de \texttt{tablor}, il est + ncessaire d'avoir la nouvelle version de + tableauVariation.mp (la 2.1 datant de dcembre 2008) mais + pour l'instant elle n'est pas prsente sur CTAN~! + Rcuprez plutt le fichier l'adresse + \href{http://download.tuxfamily.org/tehessinmath/les\_sources/tableauVariation.mp}{http://download.tuxfamily.org/tehessinmath/les\_sources/tableauVariation.mp}. + +Cela ne posera de problmes que si vous utilisez l'environnement TVZ. + \end{DANGER} + \end{figure} + + + +La version 4.01 n'est malheureusement plus compatible avec les versions +antrieures car une option supplmentaire a t ajoute pour traiter les +fonctions trigonomtriques. + +Une possibilit a de plus t ajoute pour rduire la taille des +tableaux. + +Les tableaux de signes courts (TSc) ont un argument de plus pour traiter +les valeurs interdites (version 4.01). + + +Une extension pour une compilation via Xe\TeX{} a t +cr~:~\verb+tablor-xetex.sty+ (version 4.01) ne fonctionnant que sous +unix. + + + +Un environnement TVPC a t cr pour traiter les fonctions +prolongeables par continuit (version 4.02). + + +Une possibilit a t ajoute pour donner un nom une fonction +ncessitant l'emploi d'une macro \LaTeX{} (version 4.02b). + + +Les frontires des zones interdites sont assorties de doubles +barres si ncessaire. (version 4.03) + + +Un nouvel environnement TVIex est cr pour avoir les racines des +valeurs intermdiaires sous forme exacte quand c'est possible.(version 4.04) + +Un bug dans tous les TVI est corrig.(Version 4.04). + +Un bug d une mise jour de XCAS (version 4.04-b compatible avec les +prcdentes). + +Des bugs dans TVapp et TVIapp corrigs (version 4.04-c... puis 4.04-d). + +Bug dans TVc (version 4.04-h) + +Nouvel environnement TVS pour des tableaux de variations de fonctions +dont on ne connait qu'une liste d'images (version 4.05). + + +Petites modifs dans le code pour s'adapter aux nouvelles versions de +MetaPOST et pour contrer certains bugs dus certaines configurations +personnelles de xcas (4.05-b). + + +Cration de l'option windows : on peu maintenant dclarer l'utilisation +de l'OS windows en option sans aller modifier le fichier tablor.cfg +(version 4.06). + + +Nouveau \verb+tablor.cfg+ : on peut rgler l'epsilon de XCAS qui fixe le +seuil du zro des flottants. Il est rgl $10^{-100}$ par +dfaut. Il faut une version rcente de XCAS, postrieure au 20 novembre +2009. (version tablor : 4.06-c) + + +Tableaux en couleurs ! Merci \texttt{fp} du forum +\href{http://forum.mathematex.net/latex-f6/tableau-de-variations-redige-en-bleu-t10826.html}{\texttt{mathematex}} +(version tablor : 4.07) + +\xcas +\begin{lstlisting}[caption={}] +//reglage de epsilon : seuil du zero de giac +epsilon:=1e-100; +\end{lstlisting} + +\subsection{Professor.sty} + + +\texttt{tablor.sty} a fait des petits... Grce une efficace +collaboration avec Denis \textsc{LE FUR}, vous disposez prsent de +toute une panoplie d'outils similaires pour tracer des courbes, des +histogrammes, des arbres de probabilits, des graphes probabilistes, des +lissages par moyennes mobiles et j'en passe et des meilleures... Allez +dcouvrir ces trsors sur +\href{http://mathsp.tuxfamily.org/spip.php?rubrique46}{http://mathsp.tuxfamily.org/spip.php?rubrique46}. + + + +\subsection{Plugin TeXmacs} + + +Emmanul Corcelle a crit un plugin pour que les utilisateurs de TeXmacs +puissent eux aussi profiter de \texttt{tablor} et +\texttt{professor}. Pour cela visitez le site \href{http://corcelle.wordpress.com/}{http://corcelle.wordpress.com/} + + + + +\section{Comment a marche~?} + +\subsection{Principe gnral} + +On entre une instruction qu'on envoie via \LaTeX{} \texttt{XCAS} qui effectue un certain nombre de +calculs (rsolution d'quations, calcul de limites). \texttt{XCAS} renvoie un rsultat sous la forme +d'un script \texttt{MetaPOST} qui est compil. Un tableau est cr et ensuite insr dans le document +\texttt{tex}. + + +\subsection{Rentrons dans les dtails} + +En utilisant un environnement \texttt{tablor}, de nombreux fichiers sont crs dans le rpertoire +courant puis effacs par la commande \texttt{nettoyer} si vous le souhaitez~: + +\begin{itemize} +\item des fichiers d'extension \texttt{.cxx}~:~il s'agit du fichier le plus important. C'est le + programme \texttt{XCAS} qui ~fabrique~ le tableau. Vous pouvez l'utilisez tel quel dans une + session \texttt{XCAS} ou \texttt{giac}. +\item des fichiers d'extension \texttt{.giac} qui regroupent des instructions lues et excutes par + \texttt{giac}. +Il est trs court~: + + +\xcas + +\begin{lstlisting} +maple_mode(0); // au cas o certains travailleraient en mode maple, mupad ou ti +read("config.cxx"); // pour configurer la 1re colonne (signe de ou sign of etc.) +read("XcasTV.cxx"); // giac charge le programme +read("XCasTV.user"); // giac lit les paramtres rentrs dans le source +tex et fabrique la vole le source MetaPOST. +\end{lstlisting} + +\item des fichiers d'extension \texttt{.user} qui sont crs par \LaTeX{} grce l'environnement + \texttt{VerbatimOut} de l'extension \texttt{fancyvrb} : il s'agit en fait de la commande qui se + trouve par exemple entre \verb+\begin{TV}+ et \verb+\end{TV}+. + + + +\end{itemize} + +\subsection{Code XCAS} + +Toutes les procdures suivent le mme principe~: + +\begin{itemize} +\item la plus grande partie s'occupe de crer les lignes du tableaux + l'aide de nombreux tests et boucles; +\item ensuite, on regroupe ces lignes dans une variable + \texttt{MetaLfc}; + +\item on exporte le tableau l'aide des trois dernires lignes~: + +\xcas + +\begin{lstlisting} +sortie:=fopen("XCasmpfc.mp"); // on cre un fichier XCasmpfc.mp +fprint(sortie,Unquoted,MetaLfc); // on y met MetaLfc +fclose(sortie); // on ferme XCasmpfc.mp +\end{lstlisting} + + + + +\lat +\end{itemize} + + + + +\begin{figure}[!h] + \begin{Idee}{Autres collaborations XCAS/\LaTeX{}} +On peut suivre ce mme principe pour crer d'autres associations de +vos outils prfrs. Voir par exemple~: + +\href{http://gconnan.free.fr/?page=53}{http://gconnan.free.fr/?page=53} + +et + +\href{http://melusine.eu.org/syracuse/giac/}{http://melusine.eu.org/syracuse/giac/} + \end{Idee} + \end{figure} + + + + + +\section{De quoi a-t-on besoin~?} + +\begin{figure}[!h] + \begin{Idee}{Conseils en lignes} + N'hsitez pas explorer la page suivante : + +\href{http://mathsp.tuxfamily.org/spip.php?article186}{http://mathsp.tuxfamily.org/spip.php?article186} + +surtout si vous tes sur XP :-) + +De nombreux problmes ont t rgls sur le forum~: \href{http://gconnan.free.fr/punbb/upload/index.php}{http://gconnan.free.fr/punbb/upload/index.php} + \end{Idee} + \end{figure} + + + \begin{figure}[!h] + \begin{Idee}{MikTeX et TeXLive} + \texttt{tablor} est prsent sur MikTeX et + TeXLive. \texttt{tableauVariation.mp} est sur + MikTeX mais la version n'est pas jour ( la date du 7 fvrier 2009). + \end{Idee} + \end{figure} + + +\begin{itemize} + +\item Il faut avoir install \texttt{XCAS}, logiciel multi-plateforme de calcul et de programmation~: + +\href{http://www-fourier.ujf-grenoble.fr/\%7Eparisse/giac\_fr.html}{http://www-fourier.ujf-grenoble.fr/\%7Eparisse/giac\_fr.html}~; + +\item il faut avoir le fichier de macros \texttt{MetaPOST} +\texttt{tableauVariation.mp} de Frdric Mazoit~: +\href{http://download.tuxfamily.org/tehessinmath/les\_sources/tableauVariation.mp}{http://download.tuxfamily.org/tehessinmath/les\_sources/tableauVariation.mp}~; + +Pour ceux qui sont gure habitus \texttt{MetaPOST}, cela ne pose aucun problme car les +scripts et compilations \texttt{MetaPOST} se font automatiquement. Il suffit de crer dans son +\texttt{texmf} personnel une arborescence du style~: \texttt{./texmfperso/metapost/tablor/} et d'y +placer \texttt{tableauVariation.mp} puis un \texttt{rehash}. C'est exactement la mme dmarche que +pour installer une nouvelle extension \LaTeX{}. + + +\item il faut tre en mode \texttt{shell-escape} pour autoriser + les sorties de la compilation \texttt{tex}. Pour \texttt{emacs}, on rajoute en + fin de fichier \verb+%%% LaTeX-command: "latex --shell-escape" ***+; pour les autres diteurs, il faut modifier + la commande de compilation. Sinon, on peut modifier le fichier \texttt{texmf.cnf} + pour que le mode soit automatis en modifiant la ligne + suivante~:~\texttt{shell-escape t} mais ce n'est pas recommand car il + faut activer le shell-escape le moins possible et toujours sous contrle~; + + + +\begin{figure}[!h] + \begin{Idee}{shell-escape sur KILE} + On peut crer une compilation en allant dans les menus de configuration, l'associer un raccourci clavier et hop, quand on veut une compil rapide c'est facile. + +On va dans \texttt{configuration>kile>outils>nouvel outil} + +On l'appelle par exemple shellEscape et on le base sur LateX + +Ensuite en commande on met \texttt{latex} (ou \texttt{pdflatex}) +et en option \verb+-shell-escape -interaction=nonstopmode '%source'+ +et on clique sur OK. + +Ensuite on va dans \texttt{configuration>raccourci clavier > rechercher sh}. +On tombe sur shellEscape. On clique sur personnaliser et on choisi un raccourci, par exemple +la touche windows et s (S-s en langage emacs...) + +Et voil : quand on veut compiler un document appelant tablor, on appuie sur windows+s. + \end{Idee} + \end{figure} + + + + + + +\begin{figure}[!h] + + \begin{Idee}{shell-escape sur TeXnicCenter} + Pour les utilisateurs de TeXnicCenter, observez cette +\href{http://img221.imageshack.us/img221/27/capture20080114215233hu7.png}{explication} du +paramtrage du \texttt{shell-escape}. On peut par exemple mettre~: + +\texttt{-enable-write18 --shell-escape --src -interaction=nonstopmode "\%Wm"}. + +Sur TeXmaker, c'est \texttt{latex -enable-write18 --shell-escape -interaction=nonstopmode \%.tex}. + +Pour faire comprendre \texttt{Microsoft Windows XP} o trouver \texttt{giac}, vous pouvez modifier le \texttt{path} en suivant +ces instructions~: + +Demarrer->Panneau de configuration->Systme onglet Avanc->Variable d'environnement. Il faut cliquer sur la ligne PATH puis sur le bouton modifier +et l il faut ajouter + +\begin{center} + \verb+;C:\repertoire_d'installation_de_xcas+ +\end{center} + + + +(Merci Gatan et Daniel). +\end{Idee} + + \end{figure} + + + +\item il faut avoir disposition les extensions \texttt{fancyvrb}, + \texttt{filecontents}, \texttt{ifthen} et \texttt{ifpdf}; + +\item pour ceux qui compilent avec \texttt{pdf\LaTeX{}}, il n'y a aucun problme et rien faire car \texttt{tablor} + contient dj ce qu'il faut pour s'adapter~: + \verb+\ifpdf \DeclareGraphicsRule{*}{mps}{*}{} \fi+ + +\item il faut installer le fichier \texttt{tablor.sty} dans son \texttt{texmf} personnel. Pour ceux + qui ont une version rcente de \texttt{MiKTeX} ou \texttt{TeXLive}, + \texttt{tablor} est dj install. Pour les + utilisateurs de \texttt{Unix}, vous devez savoir comment faire... Par commodit, vous pouvez en + profiter pour installer la version \texttt{Unix} de \emph{MiKTeX package manager}. J'ai fait un + petit script pour vous y aider ici : + + \href{http://gconnan.free.fr/?page=52}{http://gconnan.free.fr/?page=52} + +\item il faut installer le fichier de configuration + \texttt{tablor.cfg} dans le mme + rpertoire de \texttt{tablor.sty} ce qui est fait automatiquement + soit par dcompression d'une archive \texttt{tablor.zip} soit par + l'intermdiaire des distributions \texttt{MikTeX} et \texttt{TeXLive}. + + + +\end{itemize} + + + + + + +\begin{figure}[!h] + \begin{DANGER}{Conflit d'extensions} + L'extension \verb+fancybox+ rentre en conflit avec \verb+fancyvrb+ qu'utilise + \verb+tablor+ car elles dfinissent toutes deux diffremment l'environnement \verb+VerbatimOut+. + \end{DANGER} + \end{figure} + + + + \begin{DANGER}{Commandes cres} + Huit nouvelles commandes sont cres~:~\verb+\tv, \tvbis, \nettoyer, \initablor,+ + + \verb+ \dresse, \dressetoile, \executGiacmp+. + Attention aux conflits si de tels noms existent quelque part dans vos + fichiers personnels. + \end{DANGER} + + + + + +\section{Comment l'utiliser~?} + + + +\begin{figure}[!h] + \begin{Idee}{Faut-il savoir utiliser MetaPOST et XCAS~?} + Non~! Tous les appels ces logiciels se font sans aucune + intervention de l'utilisateur. + \end{Idee} + \end{figure} + + + +\subsection{Prambule} + +Les ECM donns en exemple ne dpendent pas du moteur de compilation~:~\texttt{\LaTeX{}+dvi+dvips} ou +\texttt{pdf\LaTeX{}} conviennent. + +Le prambule sera toujours sous Linux ou Mac~: + +\lat + +\begin{lstlisting} +\documentclass{article} +\usepackage{graphicx} +\usepackage[french]{babel} % or eunozer langouage +\usepackage[xcas]{tablor} % xcas en option : cf plus loin +\end{lstlisting} + +Le prambule sera toujours sous Windows~: + +\lat + +\begin{lstlisting} +\documentclass{article} +\usepackage{graphicx} +\usepackage[french]{babel} % or eunozer langouage +\usepackage[xcas,windows]{tablor} % xcas et windows en option : cf plus loin +\end{lstlisting} + + + +% \begin{figure}[!h] +% \begin{Idee} +% Les fontes utilises dans les tableaux sont \verb+[upright]{fourier}+. Il est tout +% fait possible d'utiliser d'autres fontes. Il suffit de modifier le fichier +% \texttt{tablor.sty} en remplaant partout o il apparat \verb+[upright]{fourier}+ par \verb+lmodern+ ou ce +% que vous voulez. Ce n'est pas trs pratique, mais cela vite de le mettre en option +% chaque utilisation et on utilise souvent la mme fonte dans ses documents. +% \end{Idee} +% \end{figure} + + + +\subsection{L'option xcas}\label{option} + + +On met \texttt{xcas} si l'on a install \texttt{giac/XCAS} sur son + ordinateur et on ne met rien si \texttt{giac/XCAS} n'est pas + install ou (et) que l'on a rcupr un + fichier \texttt{tex} avec les fichiers sources \texttt{MetaPOST}; Ainsi, \texttt{tablor} ne fera + pas appel \texttt{giac/XCAS} et se contentera de compiler les fichiers \texttt{MetaPOST}. + + + + +\subsection{L'option windows} + +Si vous utilisez encore Windows\textregistered, dclarez-le en option~:~ + +\begin{lstlisting} +\usepackage[xcas,windows]{tablor} +\end{lstlisting} + +Pour les utilisateurs de Linux et Mac, il n'y a rien dclarer... + +\subsection{Fichier de configuration \texttt{tablor.cfg}} + +\subsubsection*{Contenu} + +{\small + + +\begin{lstlisting} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Fichier de configuration de tablor.sty % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +% La mise jour de ce fichier permet d'adapter certains paramtres du package tablor.sty +% au poste de travail et aux habitudes des utilisateurs. + + +%======================================== +% I - Configuration du prambule MetaPOST +%======================================== + +\begin{filecontents*}{enteteMP.cfg} +input tableauVariation; +verbatimtex +%&latex +\documentclass{article} +\usepackage[upright]{fourier} % ou mathpazo, lmodern, etc. ou rien ! +\usepackage{amsmath} +\renewcommand\mbox[1]{ #1 } % pour les mbox intempestifs de xcas +\renewcommand\cdot{ } % idem pour les cdot +\begin{document} +\catcode`\@=0 % pour utiliser le @ +etex +\end{filecontents*} + + + + +%================================= +% II - Dclaration de l'diteur utilis +% ================================ +% +% Remplacez "emacsclient -c" par la commande qui lance un autre editeur que +% votre diteur favori pour afficher les tableaux a modifier. +% Laissez une espace avant de fermer l'accolade. + +\newcommand{\editeur}{emacsclient -c } + + + + +%================================= +%III - 1ere colonne +%================================= +% +%permet de configurer les termes dans la premiere colonne des +%tableaux : "signe de" ou "sign of" ou "" etc. +% + + + +\begin{VerbatimOut}{config.cxx} + +//reglage de epsilon : seuil du zero de giac +epsilon:=1e-100; + +// POUR LES TV, TVI,TVZ,TVapp,TSq,TSa +// pour la ligne signe +lsic:=" +newLigneSignes(btex $\\hbox{ Signe de }\\atop{\\displaystyle "; + +// POUR LES TV, TVI,TVZ,TVapp +// pour la ligne variation +lvic:=" +newLigneVariations(btex $\\hbox{ Variations de }\\atop{\\displaystyle "; + +\end{VerbatimOut} + + + +%% you may prefer + +% \begin{VerbatimOut}{config.cxx} + +% // FOR TV, TVI,TVZ,TVapp,TSq,TSa +% // for the signs +% lsic:=" +% newLigneSignes(btex $\\hbox{ Sign of }\\atop{\\displaystyle "; + +% // POUR LES TV, TVI,TVZ,TVapp +% // for the variations +% lvic:=" +% newLigneVariations(btex $\\hbox{ Variations of }\\atop{\\displaystyle "; + +%\end{VerbatimOut} + + + +%% ou si vous prfrez que ni signe ni variation n'apparaissent + + + +% \begin{VerbatimOut}{config.cxx} + +% // POUR LES TV, TVI,TVZ,TVapp,TSq,TSa +% // pour la ligne signe +% lsic:=" +% newLigneSignes(btex ${\\displaystyle "; + +% // POUR LES TV, TVI,TVZ,TVapp +% // pour la ligne variation +% lvic:=" +% newLigneVariations(btex ${\\displaystyle "; + +% \end{VerbatimOut} + + + +\end{lstlisting} +} + + + +Vous le placerez dans la mme arborescence que \texttt{tablor.sty} et le modifierez si besoin est. + +\subsubsection*{Rle} + +\begin{itemize} +\item La premire partie permet de configurer le prambule \texttt{tex} qui sera utilis par +\texttt{MetaPOST} pour crer les tableaux. La ligne contenant +l'extension des fontes est en particulier optionnelle~:~vous pouvez la +modifier, voire la supprimer selon vos choix de fontes; + + +\item si vous utilisez \texttt{ Microsoft-Windows}, il faudra dcommenter la +ligne spcifie afin que les commandes \texttt{unix} soient remplaces +automatiquement par des commandes \texttt{dos}; + + +\item l'diteur sera appel dans certains cas pour modifier + l'aspect des tableaux dans les fichiers sources \texttt{MetaPOST}. Il faudra choisir un diteur + comme par exemple \texttt{emacs, xemacs, texmaker, vi, winshell, notepad, vim, kate, gedit, + textmate,texshop}, \texttt{kile}, etc. +Pour viter certains problmes, choisissez un autre diteur que celui +que vous utilisez pour \LaTeX{} afin que la fentre s'ouvre sans problme. + +Voir aussi le paragraphe~\ref{modif}; + +\item par dfaut, on voit apparatre dans la premire colonne des tableaux ~signe de ~ ou + ~variations de ~. Vous pouvez modifier ces rglages ici comme indiqu; deux exemples sont + donns~:~en anglais ou en n'crivant que les expressions. + +\item on peut rgler l'epsilon de XCAS qui fixe le +seuil du zro des flottants. Il est rgl $10^{-100}$ par dfaut. +\end{itemize} + + +\subsection{Initialisation de \texttt{tablor} et prfixe des tableaux}\label{prefix} + + +Les fichiers \texttt{MetaPOST} des tableaux sont regroups dans un fichier de suffixe +\texttt{\_Tab.mp}. Le prfixe est par dfaut celui du fichier \texttt{tex} appelant +\texttt{tablor}. Il est possible, pour des raisons de classement personnel, de modifier ce prfixe +la suite du \verb+\begin{document}+ en entrant~: + + \begin{lstlisting} +\initablor + \end{lstlisting} + +si l'on veut avoir comme prfixe le prfixe courant (obtenu par \verb+\jobname+) ou bien~: + + \begin{lstlisting} +\initablor[Waouh] + \end{lstlisting} + +si l'on veut que le fichier \texttt{MetaPOST} des tableaux s'appelle \verb+Waouh\_Tab.mp+ + +\medskip + +Si tout s'est bien pass, on doit supprimer les fichiers \texttt{log} de \texttt{MetaPOST} et clore le +fichier \texttt{\_Tab.mp} en entrant juste avant \verb+\end{document}+ la commande~: + +\begin{lstlisting} + \nettoyer +\end{lstlisting} + + +ou bien, selon les cas~: + +\begin{lstlisting} +\nettoyer[Waouh] + \end{lstlisting} + + + +\medskip + +\textbf{En rsum}, notre fichier \texttt{tex} aura cette ossature~: + + +\begin{lstlisting} +\documentclass{article} +\usepackage{graphicx} +\usepackage[french]{babel} % or eunozer langouage +\usepackage[xcas]{tablor} % options modifiables + +\begin{document} + +\initablor + +... + +\nettoyer + +\end{document} +\end{lstlisting} + + +\section{Facteur de rduction} + +Si vous trouvez le tableau trop grand, vous pouvez utilisez la commande +\verb+\ech{nombre}+ o \texttt{nombre} reprsente le coefficienr de +rduction ou d'agrandissement du tableau. + +Par exemple, comparez~: + + \begin{lstlisting} +\begin{TV} +TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) +\end{TV} + \end{lstlisting} + + \begin{center} + + +\begin{TV} +TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) +\end{TV} + +\end{center} + +et + + \begin{lstlisting} +\ech{0.7} +\begin{TV} +TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) +\end{TV} +\ech{1} + \end{lstlisting} + + \begin{center} + + \ech{0.7} +\begin{TV} +TV([-10,+infinity],[-1,1],"g","t",x^2/(x^2-1),1,n,\tv) +\end{TV} +\ech{1} + +\end{center} + +\begin{figure}[!h] + \begin{DANGER}{Remise l'chelle 1} + N'oubliez pas de remettre l'chelle 1 en entrant la + suite de l'environnement \verb+\ech{1}+ + \end{DANGER} + \end{figure} + + + +\section{Tableaux en couleur} + +Grce la trs efficace intervention de \texttt{fp} du forum +\href{http://forum.mathematex.net/latex-f6/tableau-de-variations-redige-en-bleu-t10826.html}{\texttt{mathematex}}, +on peut prsent avoir des tableaux en couleur. Cette couleur est noire +par dfaut. Si on veut gayer sa prsentation, on utilise la commande +\verb+\coultab{couleur}+ o \verb+couleur+ est le nom de la couleur +dsire selon les standards \textbf{MetaPOST}~: +\begin{itemize} +\item \verb+blue+, \verb+red+, \verb+green+, etc. +\item pour les gris : \verb+0.1white+, \verb+0.2white+, etc. +\item un code RGB : \verb+(0.4,0.2,1)+, etc. +\end{itemize} + +\begin{lstlisting}[caption={}] +\coultab{blue} +\begin{TV} +TV([0,2],[],"f","x",x^2,1,n,\tv) +\end{TV} +\end{lstlisting} + + +\coultab{blue} +\begin{center} + \begin{TV} + TV([0,2],[],"f","x",x^2,1,n,\tv) + \end{TV} + \end{center} +\coultab{black} + + + + + +\section{Nom des fonctions et commandes \LaTeX{}} + +Si vous voulez donner un nom de fonction ncessitant l'emploi d'une +commande \LaTeX{}, il faudra utiliser le caractre \verb+@+ au lieu de +\verb+\+. + +Par exemple, pour nommer une fonction $\varphi$, il faudra entrer +\verb+@varphi+~: + + +\begin{lstlisting} +\begin{TSq} +TSq("@varphi",[-45*x-27],[2-x],[-infinity,+infinity],n,\tv) +\end{TSq} +\end{lstlisting} + + +\begin{center} + +\begin{TSq} +TSq("@varphi",[-45*x-27],[2-x],[-infinity,+infinity],n,\tv) +\end{TSq} + +\end{center} + + + +\section{Utilisation du moteur Xe\LaTeX} + + +On peut prsent compiler via Xe\LaTeX{} en utilisant l'extension ddie +\verb+tablor-xetex.sty+ qui ne fonctionnera que dans un environnement +UNIX puisqu'elle utilise un script \texttt{shell} pour convertir les +sorties MetaPOST en \texttt{pdf} : + + +\begin{lstlisting} + +\ifxetex + +\begin{filecontents*}{convert-mp-pdf.sh} +#!/bin/sh +mpost -interaction nonstopmode $1 ; + +cat>$1.tex<<EOF +\documentclass{article} +\usepackage[T1]{fontenc} +\usepackage[frenchb]{babel} +\usepackage{graphicx} +\usepackage{pst-eps} +\thispagestyle{empty} +\begin{document} +\begin{TeXtoEPS} +\includegraphics{$1.0} +\end{TeXtoEPS} +\end{document} +EOF +latex $1 +dvips -o $1.eps -E $1.dvi +epstopdf $1.eps; +## Fin de convert-mp-pdf.sh +\end{filecontents*} + +%$>> + + +\immediate\write18{chmod 775 ./convert-mp-pdf.sh} + +\fi + +\end{lstlisting} + + + +Il n'y a rien faire. Cette version peut mme tre utilise avec +pdf\LaTeX{} ou pdf\TeX{}~! + + + + +\section{Tableaux des variations} + +\subsection{Tableau standard} + +L'environnement s'appelle \texttt{TV}. On utilise une commande au format \texttt{XCAS}~: + + +\xcas + +\begin{lstlisting} +TV([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,lignes,trigo,\tv) +\end{lstlisting} + +\begin{itemize} + +\item \texttt{[borne inf,borne sup]} dsigne les bornes de l'ensemble de + dfinition. + +On note + $+\infty$~:~\texttt{+infinity} et $-\infty$~:~\texttt{-infinity}. N'oubliez pas + les crochets~! +\item \texttt{[valeurs interdites]} dsigne la liste des valeurs interdites~; +\item \texttt{"nom fonction"} dsigne la lettre reprsentant la fonction telle que vous voulez + qu'elle apparaisse : $f$, $g$, $\varphi$, etc. +\item \texttt{"nom variable"}~:~mme chose pour la variable, selon que vous voulez la dsigner par + $x$, $t$, etc. N'oubliez pas les guillemets~! +\item \texttt{expression en fonction de x} dsigne l'expression de la fonction. Attention~! Utilisez + ici toujours $x$ pour dsigner la variable~; +\item le paramtre \texttt{lignes} est remplacer par 1 si vous voulez voir apparatre une ligne + avec le signe de la drive, par 0 si vous ne voulez pas de cette ligne et par 2 si vous ne voulez + que le signe de la drive~; +\item le paramtre \texttt{trigo} est remplacer par \texttt{t} si la + fonction tudie est trigonomtrique et par tout autre symbole sinon~; +\item on termine par \verb+\tv+, une commande permettant de numroter les tableaux en interne. + +\end{itemize} + +\lat + +Voyons prsent quelques exemples. + +\begin{enumerate} +\item Le tableau de variation sans signe de la drive de la fonction $f~:~x\mapsto x^2$ sur $[-5;7]$. + + +On obtient~: + +\begin{TV} +TV([-5,7],[],"f","x",x^2,0,n,\tv); +\end{TV} + + +aprs avoir entr~: + +\begin{lstlisting} +\begin{TV} +TV([-5,7],[],"f","x",x^2,0,n,\tv) +\end{TV} +\end{lstlisting} + + + +\item Si on veut la mme fonction sur \textbf{R} avec le signe de la drive~: + + \begin{lstlisting} +\begin{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,n,\tv) +\end{TV} + +\item Avec la mme fonction sur \textbf{R} avec uniquement le signe de la drive~: + + + + \begin{lstlisting} +\begin{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,n,\tv) +\end{TV} + + + + +\item Voici ce que cela donne pour $g~:~t\mapsto \frac{t^2}{t^2-1}$ sur $[-10; +\infty[$~: + + \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} + + +\item Pour la fonction $x\mapsto \sin(x)+\frac{1}{2}$ on n'oublie pas le + paramtre \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 problmes pour des quations $f'(x)=0$ que \texttt{XCAS} ne saurait pas rsoudre + de manire formelle. Il faudrait alors utiliser une rsolution numrique et remplacer + \texttt{resoudre} par \texttt{fsolve}. Mais dans les tudes demandes au Bac, l'tude des signes + de la drive est possible formellement. Dans les cas plus exotiques, on peut faire le tableau ~ + la main~. +\end{enumerate} + + + +\subsection{Tableaux dont on ne connat qu'une liste d'images} + +Au dbut du cours de Seconde, il peut tre utile de crer des tableaux +partir de liste d'images. + +On rentre la liste des abscisses, la liste des ordonnes avec +ventuellement les limites gauche et droite des valeurs interdites, +les valeurs interdites ventuelles, le nom de la fonction et le nom de +la variable. + +\subsubsection{Sans valeur interdite} + +\begin{lstlisting} +\begin{TVS} +TVS([1,2,3,4],[-1,5,2,9],[],"f","x",\tv) +\end{TVS} +\end{lstlisting} + +\begin{TVS} +TVS([1,2,3,4],[-1,5,2,9],[],"f","x",\tv) +\end{TVS} + +\subsubsection{Avec valeurs interdites} + + +\begin{lstlisting} + \begin{TVS} +TVS([1,2,3,4],[-1,-infinity,+infinity,2,9],[2],"f","x",\tv) +\end{TVS} +\end{lstlisting} + +\begin{TVS} +TVS([1,2,3,4],[-1,-infinity,+infinity,2,9],[2],"f","x",\tv) +\end{TVS} + + +\begin{lstlisting} + \begin{TVS} +TVS([1,2,3,4],[-1,-infinity,+infinity,2,+infinity],[1,2,4],"f","x",\tv) +\end{TVS} +\end{lstlisting} + + + +\begin{TVS} +TVS([1,2,3,4],[-1,-infinity,+infinity,2,+infinity],[1,2,4],"f","x",\tv) +\end{TVS} + +\subsection{Tableau de variation avec ~zone(s) interdite(s)~} + + +Pour certaines fonctions, tout un (ou plusieurs) intervalle(s) est(sont) exclu(s) de l'ensemble de dfinition. + +Par exemple, la fonction $x\mapsto \sqrt{x^2-1}$ est dfinie sur $]-\infty; -1]\cup[1; ++\infty[$. + +On utilise alors l'environnement \texttt{TVZ} (Z comme zone...). + + +\begin{lstlisting} +\begin{TVZ} + TVZ([-infinity,+infinity],[],[[-1,1]],"@varphi","x",sqrt(x^2-1),1,n,\tv) +\end{TVZ} +\end{lstlisting} + + +\begin{center} + \begin{TVZ} + TVZ([-infinity,+infinity],[],[[-1,1]],"@varphi","x",sqrt(x^2-1),1,n,\tv) +\end{TVZ} +\end{center} + + +\begin{figure}[!h] + \begin{DANGER}{Listes des intervalles interdits} + Le troisime argument est une liste d'intervalles : la liste des ~zones interdites~ + qui peut ventuellemnt se rduire un seul intervalle comme dans l'exemple prcdent. + \end{DANGER} + \end{figure} + +Voici un exemple comportant plusieurs zones interdites~:~$x\mapsto +\ln\big((x-5)^2-1\big)+\ln\big(x^2-1\big)$ + + +\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,n,\tv) +\end{TVZ} +\end{lstlisting} + + + +\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,n,\tv) +\end{TVZ} +\end{center} + + +\subsection{Tableau des variations avec thorme des valeurs intermdiaires} + +Si l'on veut mettre en vidence les solutions de l'quation $f(x)=a$, on utilise l'environnement +\texttt{TVI}. + +La syntaxe est~: + +\begin{lstlisting} +TVI([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,t,a,trigo,\tv) +\end{lstlisting} + +Les paramtres sont les mmes que pour \texttt{TV} mais on ajoute la valeur \texttt{a} bien sr. + + +Par exemple, pour $f~:~x\mapsto \frac{x^2}{x^2-1}$ et l'quation $f(x)=10$ on entre~: + +\begin{lstlisting} +\begin{TVI} +TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,n,\tv) +\end{TVI} +\end{lstlisting} + + +et on obtient~: + +\ech{0.9} +\begin{TVI} +TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,n,\tv) +\end{TVI} +\ech{1} + +Les solutions sont notes $\alpha_1$, $\alpha_2$, etc. + +Si l'quation est plutt $f(x)=-1$~: + + +\begin{lstlisting} +\begin{TVI} +TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,n,\tv) +\end{TVI} +\end{lstlisting} + + +et on obtient~: + +\begin{TVI} +TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,n,\tv) +\end{TVI} + + + + +\subsection{Tableau des variations avec thorme des valeurs + intermdiaires et racines sous forme exacte} + +Si l'on veut mettre en vidence les solutions de l'quation $f(x)=a$ et +qu'on veut faire apparatre les racines sous forme exacte et pas +seulement sous forme d'$\alpha_i$, on utilise l'environnement +\texttt{TVIex}. + +La syntaxe est la mme que \texttt{TVI}~: + +\begin{lstlisting} +TVIex([borne inf,borne sup],[valeurs interdites],"nom fonction","nom variable",expression en fonction de x,t,a,trigo,\tv) +\end{lstlisting} + +Les paramtres sont les mmes que pour \texttt{TV} mais on ajoute la valeur \texttt{a} bien sr. + + +Par exemple, pour $f~:~x\mapsto \frac{x^2}{x^2-1}$ et l'quation $f(x)=10$ on entre~: + +\begin{lstlisting} +\begin{TVIex} +TVIex([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,n,\tv) +\end{TVIex} +\end{lstlisting} + + +et on obtient~: + +\ech{0.9} +\begin{TVIex} +TVIex([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,10,n,\tv) +\end{TVIex} +\ech{1} + +Si l'quation est plutt $f(x)=-1$~: + + +\begin{lstlisting} +\begin{TVIex} +TVIex([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,n,\tv) +\end{TVIex} +\end{lstlisting} + + +et on obtient~: + +\begin{TVIex} +TVIex([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,n,\tv) +\end{TVIex} + +Avec une quation trigonomtrique~: + +\begin{lstlisting} +\begin{TVIex} +TVIex([-pi,pi],[],"@cos","x",cos(x),1,1/2,t,\tv) +\end{TVIex} +\end{lstlisting} + +\begin{TVIex} +TVIex([-pi,pi],[],"@cos","x",cos(x),1,1/2,t,\tv) +\end{TVIex} + + +\begin{figure}[!h] + \begin{DANGER}{Racines formelles non calculables} + XCAS peut ne pas pouvoir trouver une expression exacte des racines + et affichera un message barbare du style~: + +\texttt{Unable to isolate x in ...} + +Le tableau ne sera alors pas construit et vous aurez un message d'erreur. + \end{DANGER} + \end{figure} + + +\subsection{Tableaux de variations avec approximation des zros de la drive} + +Il n'est parfois pas possible d'obtenir une valeur formelle des zros de la drive. On est donc +amen rechercher une approximation numrique de ces zros. Cela est possible grce la commande +\texttt{fsolve} de \texttt{XCAS} utilise bon escient. On appelera les environnements \texttt{TVapp} et +\texttt{TVIapp} ainsi que leurs associs toils. + +Voyons sur un exemple. + +\subsubsection*{Exemple} + +On veut rsoudre l'quation $\ln(x)=\mathrm{e}^{-x}$ sur $]0,+\infty[$. + +Soit $g$ la fonction $x\mapsto x\ln(x)-e^{-x} $. + + +\begin{lstlisting} +\begin{TVapp} +TVapp([0,+infinity],[0],"g","x",x*ln(x)-exp(-x),1,\tv) +\end{TVapp} +\end{lstlisting} + + +\begin{center} +\begin{TVapp} +TVapp([0,+infinity],[0],"g","x",x*ln(x)-exp(-x),1,\tv) +\end{TVapp} +\end{center} + + +\begin{figure}[!h] + \begin{DANGER} + {TVapp et TVIapp ne sont pas infaillibles~!~!} + +Chercher \emph{toutes} les approximations des racines de la drives +c'est se lancer dans la thorie du tout c'est--dire concilier la + recherche de solutions approches pouvant tre extrmement proches +sur des intervalles pouvant tre extrmement tendus. Un concepteur +de logiciel de calcul formel s'y refuse. Je devais m'y coller par souci +d'efficacit. + Normalement, le code +devrait fonctionner pour \emph{la plupart} des cas tudis par des profs pas +trop sadiques. a ralentit lgrement la compilation. Le balayage se +fait avec une prcision de +0,1. C'est sr qu'on peut trouver de nombreux exemples qui ne +fonctionneront pas mais plus on veut resserrer les mailles du filet, +plus on passe de temps les tricoter sauf dans le cas des fonctions +polynomiales grce XCAS. + + Se pose aussi le problme des +images et des tests de signes et de leurs approximations. Par exemple + +\begin{lstlisting} +\begin{TVapp} +TVapp([0,+infinity],[0],"g","x",1/3*x^3-0.0015*x^2+2e-06*x,1,\tv) +\end{TVapp} +\end{lstlisting} + +renvoie un tableau curieux car les images des racines de la drives +sont de l'ordre de $10^{-10}$. + + +% \begin{TVapp} +% TVapp([0,+infinity],[0],"g","x",1/3*x^3-0.0015*x^2+2e-06*x,1,\tv) +% \end{TVapp} + +a peut s'arranger en donnant en argument supplmentaire le nombre de +chiffres affichs. Cela rendrait les diffrentes versions incompatibles +et le jeu n'en vaut pas forcment la chandelle. + \end{DANGER} + \end{figure} + + + + +\subsection{Tableaux de variations de fonctions prolongeables par continuit} + +On peut avoir prolonge une fonction par continuit et donc ne plus +avoir de double barre sur la ligne des variations mais toujours une sur +la ligne du signe de la drive. + +On entre trois listes~: +\begin{enumerate} +\item les bornes de l'intervalle d'tude, comme toujours~; +\item les valeurs o la fonction sera prolonge par continuit~; +\item les valeurs o la fonction n'est pas drivable. +\end{enumerate} + +Cela donne pour $x\mapsto {\rm e}^{-1/x^2}$~: + + +\begin{lstlisting} +\begin{TVPC} +TVPC([-infinity,+infinity],[0],[0],"g","t",e^(-1/x^2),1,n,\tv); +\end{TVPC} +\end{lstlisting} + + +\begin{TVPC} +TVPC([-infinity,+infinity],[0],[0],"g","t",e^(-1/x^2),1,n,\tv); +\end{TVPC} + + + +\subsection{Tableaux de variations et courbes paramtres} + +On peut obtenir le tableau de variations correspondant des courbes paramtres dfinies par un +systme du type~: + +\[\begin{cases} x=f(t) \\ + y=g(t) +\end{cases}\] + +La syntaxe est la suivante~: + +\begin{lstlisting} + \begin{TVP} +TVP(IE,VI,["x","y"],"t",[x(t),y(t)],a,trigo,n,\tv) + \end{TVP} +\end{lstlisting} + + +avec \texttt{IE} l'intervalle d'tude, \texttt{VI} la liste des listes de valeurs interdites +respectives pour les deux fonctions, \texttt{a} pour avoir un tableau complet ou partiel comme dans +les autres "TV", enfin \texttt{trigo} qui vaut \texttt{t} si interviennent des +fonctions trigonomtrqiues, autre chose +sinon. + + +\begin{figure}[!h] + \begin{DANGER}{Version de XCAS} + L'utilisation de TVP implique l'utilisation d'une version de XCAS d'une date postrieure au 14 juin + 2008 ! + \end{DANGER} + \end{figure} + + +\subsubsection{Cas des fonctions trigonomtriques} + +tudions par exemple sur $\left[0\ ;\ \frac{\pi}{2}\right]$ + + +\[ +\begin{cases} x(t)=\cos(3t) \\ + y(t)=\sin(4t) +\end{cases}\] + +\begin{lstlisting} + + \begin{TVP} + 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,t,\tv) + \end{TVP} + + + +\subsubsection{Les autres cas} + + + +tudions par exemple sur $]-\infty\ ;\ +\infty[$ + + +\[ +\begin{cases} +x(t)=\frac{t^2}{(t+1)(t-2)} \\ +y(t)=\frac{t^2(t+2)}{t+1} +\end{cases} +\] + +\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,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,n,\tv) +\end{TVP} + + + +\section{Tableaux de signes} + + +\subsection{Cas du produit de deux facteurs affines} + +Pour tudier le signe de $(-2x+3)(-x+5)$ sur \textbf{R}, on entre~: + +\begin{lstlisting} +\begin{TSa} + TSa(-2,3,-1,5,\tv); +\end{TSa} +\end{lstlisting} + + +On obtient~: + +\begin{TSa} +TSa(-2,3,-1,5,\tv); +\end{TSa} + + +\subsection{Cas du produit d'un nombre quelconque de facteurs quelconques sur un intervalle quelconque} + + + + +\begin{figure}[!h] + \begin{DANGER}{Nouveaut partir de la version 2.08} +Par souci de cohrence avec l'environnement TSq, on doit rajouter maintenant en premier argument le +nom de la fonction produit dans l'environnement TS. + \end{DANGER} + \end{figure} + + + + + + + + +Certains cas pathologiques ne vont pas fonctionner, mais sinon, pour tudier le signe de +\[(-2x+3)(x^2-1)(x^2+1)(x-1)(x^2-2)\] on entre cette fois les expressions sous cette forme en +prcisant l'intervalle d'tude~: + +\begin{lstlisting} +\begin{TS} + TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],n,\tv); +\end{TS} +\end{lstlisting} + +On obtient~: + + +\begin{TS} + TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],n,\tv); +\end{TS} + + + +Ou bien, sur un intervalle born~: + +\begin{lstlisting} +\begin{TS} +TS("f",[x-10,x+10],[-15,10],n,\tv) +\end{TS} +\end{lstlisting} + + +\begin{TS} +TS("f",[x-10,x+10],[-15,10],n,\tv) +\end{TS} + + + +\subsection{Signe d'un quotient} + +On entre dans deux listes diffrentes les facteurs du numrateur et du dnominateur~: + + +\begin{lstlisting} +\begin{TSq} +TSq("nom du quotient",[liste des facteurs du numrateur],[liste des facteurs du dnominateur],[inf,sup],trigo,\tv) +\end{TSq} +\end{lstlisting} + +Par exemple, pour tudier le signe de $\frac{(-2x+3)(-4x+5)}{(x^2-16)(x-2)}$ sur \textbf{R}~: + +\begin{lstlisting} +\begin{TSq} +TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],n,\tv) +\end{TSq} +\end{lstlisting} + + + + +\begin{TSq} +TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],n,\tv) +\end{TSq} + + Sur un intervalle born~: + +\begin{lstlisting} +\begin{TSq} +TSq("Q",[x-10,x-5],[x+10,x+3],[-10,10],n,\tv) +\end{TSq} +\end{lstlisting} + + +\begin{TSq} +TSq("Q",[x-10,x-5],[x+10,x+3],[-10,10],n,\tv) +\end{TSq} + + + + +\subsection{Signe d'une seule expression} + + +On utilise l'environnement \texttt{TSc} comme \emph{Tableau de Signe court} en prcisant +l'expression tudie, l'intervalle considr et les valeurs interdites~: + +\begin{lstlisting} +\begin{TSc} +TSc((x-10)*(x+5),[-10,10],[],n,\tv) +\end{TSc} +\end{lstlisting} + + + +\begin{TSc} +TSc((x-10)*(x+5),[-10,10],[],n,\tv) +\end{TSc} + +avec valeurs interdites~: + +\begin{lstlisting} +\begin{TSc} +TSc((x+10)/((x-5)*(x-2)),[-10,5],[2,5],n,\tv) +\end{TSc} +\end{lstlisting} + + +\begin{TSc} +TSc((x+10)/((x-5)*(x-2)),[-10,5],[2,5],n,\tv) +\end{TSc} + +valeurs interdites et fonction trigonomtrique~: + +\begin{lstlisting} +\begin{TSc} +TSc(tan(x),[0,2*pi],[pi/2,3*pi/2],t,\tv) +\end{TSc} +\end{lstlisting} + + +\begin{TSc} +TSc(tan(x),[0,2*pi],[pi/2,3*pi/2],t,\tv) +\end{TSc} + + +\section{Comment modifier les tableaux partir des fichiers MetaPOST~?}\label{modif} + + +\subsection{Tableau par tableau} + +Il est impossible de prvoir toutes les requtes des diffrents utilisateurs. Le style du tableau +produit peut nanmoins vous dplaire. Vous pouvez le modifier en intervenant directement sur le +fichier \texttt{MetaPOST} cr pour chaque tableau. Pour cela, il suffit d'ajouter une toile au nom de +l'environnement utilis et de donner un numro votre nouvelle figure pour qu'elle ne soit pas +crase par les compilations suivantes. Numrotez partir de 100 par exemple. + +Si vous tapez~: + +\begin{lstlisting} +\begin{TV*}{100} + TV([-1,+infinity],[],"f","x",x-ln(x+1),1,n,\tv) +\end{TV*} +\end{lstlisting} + +l'diteur que vous avez mis en option (voir le paragraphe~\ref{option}) est directement lanc et le fichier +\texttt{MetaPOST} correspondant votre tableau qui portera le numro 100 +est affich. Vous pouvez alors le modifier, taper sur \Ctrl + \keystroke{S} pour l'enregistrer et +\Ctrl + \keystroke{Q} pour fermer l'diteur\footnote{Ces combinaisons de touches correspondent la + plupart des diteurs mais ne sont pas universelles : vrifiez pour celui que vous avez choisi.}. La compilation s'achve alors automatiquement comme +pour un environnement non toil. + +\begin{figure}[!h] + \begin{DANGER}{Choix de l'diteur} + vitez de choisir votre diteur habituel~:~sur + \texttt{Linux} prenez par exemple \texttt{gedit} ou + \texttt{kate}, sur \texttt{Windows} prenez + \texttt{wordpad}, etc. + \end{DANGER} + \end{figure} + + + +Par exemple, je tape~: + +\begin{lstlisting} +\begin{TS*}{100} + TS("F",[3*x+2,5*x^2-1],[-50,50],n,\tv) +\end{TS*} +\end{lstlisting} + + +et apparat une fentre de l'diteur (ici \TeX maker) avec le fichier correspondant au tableau. Je le modifie +volont~: + +\begin{center} + \includegraphics[height=9cm]{capture.eps} +\end{center} + + +Je tape sur \Ctrl + \keystroke{S} puis \Ctrl + \keystroke{Q} et la compilation reprend +automatiquement pour m'afficher le tableau voulu~: + + +\begin{center} + \begin{TS*}{105} + TS("F",[3*x+2,5*x^2-1],[-50,50],n,\tv) + \end{TS*} +\end{center} + + + +Une fois la modification faite, on ne vous redemandera pas d'effectuer de modifications, sauf si +vous changez le numro de la figure. + +\subsection{Traitement global dans un unique fichier MetaPOST}\label{global} + +Un fichier \texttt{prfixe\_Tab.mp} est cr o sont copis les sources de chaque tableau. Vous pouvez +ainsi retravailler globalement sur les tableaux si besoin ou les transmettre une personne n'ayant +pas install \texttt{XCAS}. Voir le paragraphe~\ref{prefix} pour plus de dtails. + + +\section{Merci...} + +\begin{itemize} + +\item \href{http://frederic.mazoit.free.fr/LaTeX\_metapost/tableauVariations/}{Frdric \textsc{Mazoit}} pour son fichier \texttt{tableauVariation.mp}; + +\item \href{http://www.yvesdelhaye.be/?Generateur-d-interrogations-le}{Yves \textsc{Delhaye}} pour ses ides sur le \texttt{shell-escape} + +\item \href{http://www-fourier.ujf-grenoble.fr/\%7Eparisse/giac\_fr.html}{Bernard + \textsc{Parisse}} pour \texttt{XCAS}; + +\item Jean-Michel \textsc{Boucart} pour ses prcieuses et efficaces + amliorations de la partie \LaTeX{} du code. + + +\end{itemize} + + +\section{Erreurs habituelles} + + +Avez-vous rendu possible le \texttt{shell-escape}~? Avez-vous install +toutes les extensions listes en dbut de ce document~? Est-ce que \texttt{XCAS} + est dans votre \texttt{PATH}~? + +La premire chose est d'analyser le fichier \texttt{log}. + +En cas de problme, n'hsitez pas me contacter l'adresse indique +sur mon site en joignant le fichier \texttt{log}. + + + +\section{\texttt{Tablor} et Emacs} + +Pour les heureux utilisateurs de tempo, voici quelques lignes pour faciliter votre vie rajouter +dans un fichier \texttt{latex-tempo}: + +\begin{lstlisting} +;; +;; TABLOR +;;; +;cas tableau de variation + ("TV" (& > "\\begin{center}"n> + "\\begin{TV}" n> +"TV(["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"]," + "["(p "liste de valeurs interdites (,) :")"]," + "\""(p "nom de la fonction :")"\"," + "\""(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:oui, n:non) :")"," + "\\tv)" n> + "\\end{TV}" n> + "\\end{center}" > % )) + ;cas TVI + ("TVI" (& > "\\begin{center}"n> + "\\begin{TVI}" n> +"TVI(["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"]," + "["(p "liste de valeurs interdites (,) :")"]," + "\""(p "nom de la fonction :")"\"," + "\""(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:oui, n:non) :")"," + ""(p "f(x)=l pour la valeur l :")"," + "\\tv)" n> + "\\end{TVI}" n> + "\\end{center}" > % )) + ;cas signe produit + ("TS" (& > "\\begin{center}"n> + "\\begin{TS}" n> + "TS(\""(p "nom du produit :")"\"," + "["(p "liste des facteurs (,) :")"]," + "["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"]," + ""(p "trigo ? (t:oui, n:non) :")"," + "\\tv)" n> + "\\end{TS}" n> + "\\end{center}" > % )) + ;cas signe quotient + ("TSq" (& > "\\begin{center}"n> + "\\begin{TSq}" n> + "TSq(\""(p "nom du quotient :")"\"," + "["(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:oui, n:non) :")"," + "\\tv)" n> + "\\end{TSq}" n> + "\\end{center}" > % )) + +; Tableau signe court + ("TSc" (& > "\\begin{center}"n> + "\\begin{TSc}" n> + "TSc("(p "expression :")",""[" +(p "debut de l'intervalle:")"," +(p "fin de l'intervalle:")"],""[" +(p "liste de valeurs interdites (,) :")"],""" +(p "trigo ? (t:oui, n:non) :")"," + "\\tv)" n> + "\\end{TSc}" n> + "\\end{center}" > % )) + + ;cas tableau de variation avec zone interdite + ("TVZ" (& > "\\begin{center}"n> + "\\begin{TV}" n> +"TVZ(["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"]," + "["(p "liste de valeurs interdites (,) :")"]," + "["(p "liste des zones interdites ([,],[,]) :")"]," + "\""(p "nom de la fonction :")"\"," + "\""(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:oui, n:non) :")"," + "\\tv)" n> + "\\end{TV}" n> + "\\end{center}" > % )) +;cas TVP + ("TVP" (& > "\\begin{center}"n> + "\\begin{TVI}" n> +"TVP(["(p "debut de l'intervalle:")","(p "fin de l'intervalle:")"]," + "[["(p "liste de valeurs interdites de x(t)(,) :")"]," + "["(p "liste de valeurs interdites de y(t)(,) :")"]]," + "[\""(p "nom de la fonction x :")"\"," + "\""(p "nom de la fonction y :")"\"]," + "\""(p "nom de la variable :")"\"," + "["(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 "t si fonctions trigo, n sinon :")"," + "\\tv)" n> + "\\end{TVP}" n> + "\\end{center}" > % )) +\end{lstlisting} + +Merci \href{http://phil.pham.free.fr/}{Phil Pham}. + + +\section{Galerie} + +Voici quelques exemples de tableaux~: + +\begin{lstlisting} +\begin{TVI} +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,n,\tv) +\end{TVI} + + +\begin{lstlisting} +\begin{TVI} +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,n,\tv) +\end{TVI} + + +\begin{lstlisting} +\begin{TVI} +TVI([0,+infinity],[0],"@ln","x",ln(x),1,2,n,\tv) +\end{TVI} +\end{lstlisting} + +\begin{TVI} +TVI([0,+infinity],[0],"@ln","x",ln(x),1,2,n,\tv) +\end{TVI} + +\stepcounter{TVn} + +\begin{lstlisting} +\begin{TV} +TV([1,+infinity],[],"-@ln","x",-ln(x),1,n,\tv) +\end{TV} +\end{lstlisting} + +\begin{TV} +TV([1,+infinity],[],"-@ln","x",-ln(x),1,n,\tv) +\end{TV} + + + +\begin{lstlisting} +\begin{TVI} +TVI([-pi,pi],[],"@cos","x",cos(x),1,1/2,t,\tv) +\end{TVI} +\end{lstlisting} + +\begin{TVI} +TVI([-pi,pi],[],"@cos","x",cos(x),1,1/2,t,\tv) +\end{TVI} + +\begin{lstlisting} +\begin{TV} +TV([0,2*pi],[],"@cos","x",cos(x),1,t,\tv) +\end{TV} +\end{lstlisting} + +\begin{TV} +TV([0,2*Pi],[],"@cos","x",cos(x),1,t,\tv) +\end{TV} + + + + + + +\begin{lstlisting} +\begin{TVI} +TVI([0,pi],[pi/2],"@tan","t",tan(x),1,7,t,\tv) +\end{TVI} +\end{lstlisting} + +\begin{TVI} +TVI([0,pi],[pi/2],"@tan","t",tan(x),1,7,t,\tv) +\end{TVI} + + +\begin{lstlisting} +\begin{TVIex} +TVIex([0,pi],[pi/2],"@tan","t",tan(x),1,7,t,\tv) +\end{TVIex} +\end{lstlisting} + +\begin{TVIex} +TVIex([0,pi],[pi/2],"@tan","t",tan(x),1,7,t,\tv) +\end{TVIex} + + +\begin{lstlisting} +\begin{TVI} +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,n,\tv) +\end{TVI} + + + + +\begin{lstlisting} +\begin{TVIex} +TVIex([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,n,\tv) +\end{TVIex} +\end{lstlisting} + +\begin{TVIex} +TVIex([-1,1],[],"f","x",(1-x)*sqrt(1-x^2),1,1,n,\tv) +\end{TVIex} + + + + + +\begin{lstlisting} +\begin{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,n,\tv) +\end{TV} + + +\begin{lstlisting} +\begin{TS} +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],n,\tv); +\end{TS} + +\begin{lstlisting} +\begin{TVI} +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,n,\tv) +\end{TVI} + + + + +\begin{lstlisting} +\begin{TVI} +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,n,\tv) +\end{TVI} + +\stepcounter{TVn} + + +\begin{lstlisting} +\begin{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,n,\tv) +\end{TV} + + + + + +\begin{lstlisting} +\begin{TVI} +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,n,\tv) +\end{TVI} + +\begin{lstlisting} +\begin{TVI} +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,n,\tv) +\end{TVI} + + +\begin{lstlisting} +\begin{TVIex} +TVIex([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,n,\tv) +\end{TVIex} +\end{lstlisting} + + + +\begin{TVIex} +TVIex([0,+infinity],[0],"f","x",ln(x)-(ln(x))^2,1,-1,n,\tv) +\end{TVIex} + + + +\begin{lstlisting} +\begin{TSc} +TSc((x-10)*(x+10),[-10,10],[],n,\tv) +\end{TSc} +\end{lstlisting} + + + +\begin{TSc} +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,n,\tv) +\end{TVZ} +\end{lstlisting} + + \begin{TVZ} + 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],[[-1,1]],"f","x",ln(x^2-1),1,n,\tv) +\end{TVZ} + \end{lstlisting} + + \begin{TVZ} + TVZ([-infinity,+infinity],[-1,1],[[-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,t,\tv) +\end{TVP} + \end{lstlisting} + + + +\begin{TVP} +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,t,\tv) +\end{TVP} +\end{lstlisting} + + +\begin{TVP} +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]],"f","x",sqrt((x-5)^2-1)+sqrt(x^2-1),1,n,\tv) +% \end{TVZ} +% \end{lstlisting} + + + +% \begin{center} +% \begin{TVZ} +% 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} + + + +\begin{lstlisting} + \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} + + +\begin{center} +\begin{TS} + TS(" f ",[cos(x)-1/2,sin(x)+1/2],[0,2*pi],t,\tv) +\end{TS} +\end{center} + +% \begin{lstlisting} +% \begin{TVIapp} +% TVIapp([-1,+infinity],[-1,0],"g'","x",diff(ln(x+1)/x^2,x),1,0,\tv) +% \end{TVIapp} +% \end{lstlisting} + +% \begin{center} +% \begin{TVIapp} +% TVIapp([-1,+infinity],[-1,0],"g'","x",diff(ln(x+1)/x^2,x),1,0,\tv) +% \end{TVIapp} +% \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,n,\tv) +% \end{TV} + +% \VF +% \begin{itemize} + +% \item[\ldots] 5 n'a pas d'antcdent \Rep +% \item[\ldots] 5 n'a pas d'image \Rep +% \item[\ldots] 5 a deux antcdents \Rep +% \item[\ldots] 5 a une image suprieure celle de $\sqrt{2}$\Rep + +% \end{itemize} + + + +% \item Soit $f$ la fonction dfinie par $f~:~x\mapsto 3x^3-5x^2+2x-7$. Les tableaux suivants peuvent +% correspondre $f$~: + +% \VF + +% \begin{enumerate} + + +% \item Tableau 1 \Rep + +% \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 + +% \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 + +% \begin{TSc} +% TSc(-3*x^3+5*x^2-2*x+7,[-20,20],n,\tv) +% \end{TSc} + + +% \item Tableau 4 \Rep + +% \begin{TSc} +% TSc(3*x^3-5*x^2+2*x-7,[-20,20],n,\tv) +% \end{TSc} + + +% \end{enumerate} + +% \end{enumerate} + +% \end{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,n,\tv) +% \end{TV} + +% \VF +% \begin{itemize} + +% \item[\ldots] 5 n'a pas d'antcdent \Rep +% \item[\ldots] 5 n'a pas d'image \Rep +% \item[\ldots] 5 a deux antcdents \Rep +% \item[\ldots] 5 a une image suprieure celle de $\sqrt{2}$\Rep + +% \end{itemize} + + + +% \item Soit $f$ la fonction dfinie par $f~:~x\mapsto 3x^3-5x^2+2x-7$. Les tableaux suivants peuvent-ils +% correspondre la fonction $f$~: + +% \VF + +% \begin{enumerate} + + +% \item Tableau 1 \Rep + + +% \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 + +% \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 + +% \begin{TSc} +% TSc(-3*x^3+5*x^2-2*x+7,[-20,20],n,\tv) +% \end{TSc} + + +% \item Tableau 4 \Rep + +% \begin{TSc} +% TSc(3*x^3-5*x^2+2*x-7,[-20,20],n,\tv) +% \end{TSc} + + +% \end{enumerate} + +% \end{enumerate} + + + +% \begin{lstlisting} +% On considre la fonction $f$ dfinie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$ + +% tudions sa drive~: + + +% \begin{TVIapp} +% TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv) +% \end{TVIapp} + +% On en dduit 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} + +% On considre la fonction $f$ dfinie sur \textbf{R} par $f(x)=\frac{1}{2}\bigl(x+(1-x){\rm e}^{2x}\bigr)$ + +% tudions sa drive~: + + +% \begin{TVIapp} +% TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv) +% \end{TVIapp} + +% On en dduit 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} + + + + +\pagebreak + +\tableofcontents + +\nettoyer + + + +%\bouger{/home/moi/Desktop/} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: |