%&plain %% ========= quelques macros pour tableaux ============== %% ========== (preconisees par R. Seroul) =============== \def \tvi {% trait vertical invisible \vrule height 12pt depth 5pt width 0pt} \def \tv {% trait vertical taille reglable \tvi \vrule } \def \hfq {% hfill quad -> un separateur \hfill \quad } \def \cc#1{% case centree \hfq #1% \hfq } \def \doublevrule{% \vrule \hskip.31em \vrule } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% quelques macros pour les caracteres 'fleches' %% fichier : arrows.tex %% format : plain.tex %% auteur : jean-paul Vignault %% date : 1 janvier 2000 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \font \tenline = line10 \font \tenlinew = linew10 \newdimen \tmpdimen \newbox \tmpbox % ============ Série 6 ============== %% rapport largeur/hauteur = 3/5 = 0.6, dp = 0 \def \srightuuuparrow{% \hbox{\tenline \kern 0.15999pt \char20 \kern -3.7pt \raise 2.6pt \hbox{\char21} \kern 0.1pt }} \def \rightuuuparrow{% \hbox{\tenline \kern 0.15999pt \char20 \raise 10pt \hbox{\char20} \kern -3.7pt \raise 12.6pt \hbox{\char21} \kern 0.1pt }} \def \mrightuuuparrow{% \hbox{\tenline \kern 0.15999pt \char20 \raise 10pt \hbox{\char20} \raise 20pt \hbox{\char20} \kern -3.7pt \raise 22.6pt \hbox{\char21} \kern 0.1pt }} \def \brightuuuparrow{% \hbox{\tenline \kern 0.15999pt \char20 \raise 10pt \hbox{\char20} \raise 20pt \hbox{\char20} \raise 30pt \hbox{\char20} \kern -3.7pt \raise 32.6pt \hbox{\char21} \kern 0.1pt }} \def \bbrightuuuparrow{% \hbox{\tenline \kern 0.15999pt \char20 \raise 10pt \hbox{\char20} \raise 20pt \hbox{\char20} \raise 30pt \hbox{\char20} \raise 40pt \hbox{\char20} \kern -3.7pt \raise 42.6pt \hbox{\char21} \kern 0.1pt }} \def \suuup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 12.6pt \hbox{\tvi height \tmpdimen #1} } \def \uuup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 22.6pt \hbox{\tvi height \tmpdimen #1} } \def \muuup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 32.6pt \hbox{\tvi height \tmpdimen #1} } \def \buuup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 42.6pt \hbox{\tvi height \tmpdimen #1} } \def \bbuuup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 52.6pt \hbox{\tvi height \tmpdimen #1} } \def \suuucenter#1{% \vbox to 12.6pt{% \vfil \hbox{#1} \vfil }} \def \uuucenter#1{% \vbox to 22.6pt{% \vfil \hbox{#1} \vfil }} \def \muuucenter#1{% \vbox to 32.6pt{% \vfil \hbox{#1} \vfil }} \def \buuucenter#1{% \vbox to 42.6pt{% \vfil \hbox{#1} \vfil }} \def \bbuuucenter#1{% \vbox to 52.6pt{% \vfil \hbox{#1} \vfil }} % ============= serie 4 ============== %% La encore, le rapport largeur/hauteur doit etre de 3/5 \def \srightdddownarrow{% \hbox{\tenline \kern 0.3pt \raise 2.6pt \hbox{\char84} \kern -4pt \char85 \kern 0.26pt }} \def \rightdddownarrow{% \hbox{\tenline \kern 0.3pt \raise 12.6pt \hbox{\char84} \raise 2.6pt \hbox{\char84} \kern -4pt \char85 \kern 0.26pt }} \def \mrightdddownarrow{% \hbox{\tenline \kern 0.3pt \raise 22.6pt \hbox{\char84} \raise 12.6pt \hbox{\char84} \raise 2.6pt \hbox{\char84} \kern -4pt \char85 \kern 0.26pt }} \def \brightdddownarrow{% \hbox{\tenline \kern 0.3pt \raise 32.6pt \hbox{\char84} \raise 22.6pt \hbox{\char84} \raise 12.6pt \hbox{\char84} \raise 2.6pt \hbox{\char84} \kern -4pt \char85 \kern 0.26pt }} \def \bbrightdddownarrow{% \hbox{\tenline \kern 0.3pt \raise 42.6pt \hbox{\char84} \raise 32.6pt \hbox{\char84} \raise 22.6pt \hbox{\char84} \raise 12.6pt \hbox{\char84} \raise 2.6pt \hbox{\char84} \kern -4pt \char85 \kern 0.26pt }} % ============= serie 5 ============== %% rapport largeur/hauteur = 5/3 % \kern 0.15999pt % \char20 % \kern -3.7pt \raise 2.6pt \hbox{\char21} % \kern 0.1pt \def \srightddownarrow{% \hbox{\tenline \kern 0.3pt \raise 1.56pt \hbox{\char98} \kern -8pt \char126 \kern 0.3pt }} \def \rightddownarrow{% \hbox{\tenline \kern 0.3pt \raise 7.56pt \hbox{\char98} \raise 1.56pt \hbox{\char98} \kern -8pt \char126 \kern 0.3pt }} \def \mrightddownarrow{% \hbox{\tenline \kern 0.3pt \raise 13.56pt \hbox{\char98} \raise 7.56pt \hbox{\char98} \raise 1.56pt \hbox{\char98} \kern -8pt \char126 \kern 0.3pt }} \def \brightddownarrow{% \hbox{\tenline \kern 0.3pt \raise 19.56pt \hbox{\char98} \raise 13.56pt \hbox{\char98} \raise 7.56pt \hbox{\char98} \raise 1.56pt \hbox{\char98} \kern -8pt \char126 \kern 0.3pt }} \def \bbrightddownarrow{% \hbox{\tenline \kern 0.3pt \raise 25.56pt \hbox{\char98} \raise 19.56pt \hbox{\char98} \raise 13.56pt \hbox{\char98} \raise 7.56pt \hbox{\char98} \raise 1.56pt \hbox{\char98} \kern -8pt \char126 \kern 0.3pt }} % ============= serie 2 ============== %% rapport largeur/hauteur = 5/3 \def \srightuuparrow{% \hbox{\tenline \kern 0.3pt \char34 \kern -8pt \raise 0.06pt \hbox{\char62} \kern 0.3pt }} \def \rightuuparrow{% \hbox{\tenline \kern 0.3pt \char34 \raise 6pt \hbox{\char34} \kern -8pt \raise 6.06pt \hbox{\char62} \kern 0.3pt }} \def \mrightuuparrow{% \hbox{\tenline \kern 0.3pt \char34 \raise 6pt \hbox{\char34} \raise 12pt \hbox{\char34} \kern -8pt \raise 12.06pt \hbox{\char62} \kern 0.3pt }} \def \brightuuparrow{% \hbox{\tenline \kern 0.3pt \char34 \raise 6pt \hbox{\char34} \raise 12pt \hbox{\char34} \raise 18pt \hbox{\char34} \kern -8pt \raise 18.06pt \hbox{\char62} \kern 0.3pt }} \def \bbrightuuparrow{% \hbox{\tenline \kern 0.3pt \char34 \raise 6pt \hbox{\char34} \raise 12pt \hbox{\char34} \raise 18pt \hbox{\char34} \raise 24pt \hbox{\char34} \kern -8pt \raise 24.06pt \hbox{\char62} \kern 0.3pt }} \def \suucenter#1{% \vbox to 7.56pt{% \vfil \hbox{#1} \vfil }} \def \uucenter#1{% \vbox to 13.56pt{% \vfil \hbox{#1} \vfil }} \def \muucenter#1{% \vbox to 19.56pt{% \vfil \hbox{#1} \vfil }} \def \buucenter#1{% \vbox to 25.56pt{% \vfil \hbox{#1} \vfil }} \def \bbuucenter#1{% \vbox to 31.56pt{% \vfil \hbox{#1} \vfil }} \def \suup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 7.56pt \hbox{\tvi height \tmpdimen #1} } \def \uup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 13.56pt \hbox{\tvi height \tmpdimen #1} } \def \muup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 19.56pt \hbox{\tvi height \tmpdimen #1} } \def \buup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 25.56pt \hbox{\tvi height \tmpdimen #1} } \def \bbuup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 31.56pt \hbox{\tvi height \tmpdimen #1} } % ============= serie 3 ============== % rapport largeur/hauteur = 4 \def \srightdownarrow{% \hbox{\tenline \kern 1pt \raise 1.5pt \hbox{\char88} \kern -6pt \char113 \kern 1pt }} \def \rightdownarrow{% \hbox{\tenline \kern 1pt \raise 4pt\hbox{\char88} \raise 1.5pt \hbox{\char88} \kern -6pt \char113 \kern 1pt }} \def \mrightdownarrow{% \hbox{\tenline \kern 1pt \raise 6.5pt\hbox{\char88} \raise 4pt\hbox{\char88} \raise 1.5pt \hbox{\char88} \kern -6pt \char113 \kern 1pt }} \def \brightdownarrow{% \hbox{\tenline \kern 1pt \raise 9pt\hbox{\char88} \raise 6.5pt\hbox{\char88} \raise 4pt\hbox{\char88} \raise 1.5pt \hbox{\char88} \kern -6pt \char113 \kern 1pt }} \def \bbrightdownarrow{% \hbox{\tenline \kern 1pt \raise 11.5pt\hbox{\char88} \raise 9pt\hbox{\char88} \raise 6.5pt\hbox{\char88} \raise 4pt\hbox{\char88} \raise 1.5pt \hbox{\char88} \kern -6pt \char113 \kern 1pt }} \def \down#1{% \lower 2pt \hbox{#1}} \def \bbucenter#1{% \vbox to 14pt{% \vfil \hbox{#1} \vfil }} \def \bbup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 14pt \hbox{\tvi height \tmpdimen #1} } % ============= serie 1 ============== % rapport largeur/hauteur = 4 \def \srightuparrow{% \raise 0.2pt \hbox{\tenline \kern 1pt \char24 \kern -6pt \raise .46667pt \hbox{\char49} \kern 1pt }} \def \rightuparrow{% \raise 0.2pt \hbox{\tenline \kern 1pt \char24 \raise 2.5pt \hbox{\char24} \kern -6pt \raise 2.96667pt \hbox{\char49} \kern 1pt }} \def \mrightuparrow{% \raise 0.2pt \hbox{\tenline \kern 1pt \char24 \raise 2.5pt \hbox{\char24} \raise 5pt \hbox{\char24} \kern -6pt \raise 5.46667pt \hbox{\char49} \kern 1pt }} \def \brightuparrow{% \raise 0.2pt \hbox{\tenline \kern 1pt \char24 \raise 2.5pt \hbox{\char24} \raise 5pt \hbox{\char24} \raise 7.5pt \hbox{\char24} \kern -6pt \raise 7.96667pt \hbox{\char49} \kern 1pt }} \def \bbrightuparrow{% \raise 0.2pt \hbox{\tenline \kern 1pt \char24 \raise 2.5pt \hbox{\char24} \raise 5pt \hbox{\char24} \raise 7.5pt \hbox{\char24} \raise 10pt \hbox{\char24} \kern -6pt \raise 10.46667pt \hbox{\char49} \kern 1pt }} \def \sucenter#1{% \vbox to 4pt{% \vfil \hbox{#1} \vfil }} \def \mucenter#1{% \vbox to 6.5pt{% \vfil \hbox{#1} \vfil }} \def \ucenter#1{% \vbox to 9pt{% \vfil \hbox{#1} \vfil }} \def \bucenter#1{% \vbox to 11.5pt{% \vfil \hbox{#1} \vfil }} \def \sup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 4pt \hbox{\tvi height \tmpdimen #1}} \def \up#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 6.5pt \hbox{\tvi height \tmpdimen #1}} \def \mup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 9pt \hbox{\tvi height \tmpdimen #1}} \def \bup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 11.5pt \hbox{\tvi height \tmpdimen #1}} \def \bbup#1{% \setbox \tmpbox \hbox{#1} \tmpdimen = \ht \tmpbox \advance \tmpdimen by 2pt \raise 14pt \hbox{\tvi height \tmpdimen #1}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% exemples d'utilisation %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\newpage{\vfill\eject} \nopagenumbers %%%%%% exemple 1 %%%%% $$\vcenter {\offinterlineskip \def \cc#1{ \hfil #1 \hfil } \halign { % preamble \cc {$#$}& #\tv && \cc {$#$} \cr x&& 0&& 2&& +\infty \cr \noalign {\hrule height 1pt } x-2&& & -& 0& + \cr \noalign {\hrule } x&& 0& +& \tv & + \cr \noalign {\hrule height 1pt} f' (x)&& \doublevrule & -& 0& + \cr \noalign {\hrule height 1pt} \buucenter {$f (x)$}&& \doublevrule & \brightddownarrow & \down{$\matrix {1-4\ln 2 \cr \approx -1, 77\cr }$}& \brightuuparrow & \buup {\phantom {1}} \cr }} $$ \newpage %%%%%% exemple 2 %%%%% $$\vcenter {\offinterlineskip \def \cc#1{ \hfil #1 \hfil } \halign { % preamble \cc {$#$}& #\tv && \cc {$#$} \cr x&& -\infty && 3/7 \cr \noalign {\hrule height 1pt } 3-7x&& & +& 0 \cr \noalign {\hrule } -7&& & - \cr \noalign {\hrule height 1pt} f' (x)&& & -& \doublevrule \cr \noalign {\hrule height 1pt} \bucenter {$f (x)$}&& \bup {\phantom {1}} & \brightdownarrow & \doublevrule \cr }} $$ \newpage %%%%%% exemple 3 %%%%% $$\vcenter {\offinterlineskip \def \cc#1{ \hfil #1 \hfil } \halign { % preamble \cc {$#$}& #\tv && \cc {$#$} \cr x&& 0&&& e^{1/2}&& +\infty \cr \noalign {\hrule height 1pt } 1 - 2\ln x&& && +& 0& - \cr \noalign {\hrule } x^2&& 0&& +& \tv & + \cr \noalign {\hrule height 1pt} f' (x)&& \doublevrule && +& 0& - \cr \noalign {\hrule height 1pt} \buucenter {$f (x)$}&& \doublevrule & \down {$-\infty $}& \brightuuparrow & \buup {$2(e^{-1/2}-1) \approx -0, 79$}& \brightddownarrow & \down {$-2$} \cr }} $$ \newpage %%%%%% exemple 4 %%%%% $$\vcenter {\offinterlineskip \def \cc#1{ \hfil #1 \hfil } \halign { % preamble \cc {$#$}& #\tv && \cc {$#$} \cr x&& -\infty && 0&& +\infty \cr \noalign {\hrule height 1pt } f' (x)&& &-& 0& + \cr \noalign {\hrule height 1pt} \buucenter {$f (x)$}&& & \brightddownarrow & \down{$0$}& \brightuuparrow & \buup {\phantom {1}} \cr }} $$ \newpage %%%%%% exemple 5 %%%%% $$\vcenter {\offinterlineskip \def \cc#1{ \hfil #1 \hfil } \halign { % preamble \cc {$#$}& #\tv && \cc {$#$} \cr x&& -\infty && 0&& +\infty \cr \noalign {\hrule height 1pt } f' (x)&& &+& 0& + \cr \noalign {\hrule height 1pt} \buucenter {$f (x)$}&& & \brightuparrow & \buucenter{$2$}& \bup {\brightuparrow }& \buup {\phantom {1}} \cr }} $$ \newpage %%%%%% exemple 6 %%%%% $$\vcenter {\offinterlineskip \def \cc#1{ \hfil #1 \hfil } \halign { % preamble \cc {$#$}& #\tv && \cc {$#$} \cr x&& -3&& -1&& 1&& 3& \cr \noalign {\hrule height 1pt} \buucenter {$f (x)$}&& \down {?}& \brightuuparrow & \buup {$3$}& \brightddownarrow & \down{$-1$}& \brightuuparrow & \buup {?} \cr }} $$ \newpage %%%%%% exemple 7 %%%%% $$ \vcenter{ \def \hfq{\hfil \ } \offinterlineskip \halign{ % preamble &\hfq #\hfq \cr $t$& \vrule depth 5pt & $-1$&& $0$&& $1$&& $2$& \cr \noalign{\hrule} $x' (t)$& \vrule height 10pt depth 3pt & $-2$& $-$& $0$& $+$& $2$& $+$& $4$& \cr \noalign{\hrule} \bbuucenter{$x (t)$}& \vrule& \bbup{$2$}& \brightdownarrow & \down{$1\strut $}& \brightuparrow & \bup{$2$}& \bup{\brightuparrow} & \bup{\bup{$5$}} \cr \noalign{\hrule} $y' (t)$& \vrule height 10pt depth 3pt & $-4$& $-$& $-2$& $-$& $0$& $+$& $2$& \cr \noalign{\hrule} \bbuucenter{$x (t)$}& \vrule& \bbuup{$5$}& \bbup{\brightdownarrow} & \bup{$2$}& \brightdownarrow & \down{$1$}& \bbrightuparrow & \bbup{$2$} \cr }} $$ \newpage %%%%%% exemple 8 %%%%% $$ \vcenter { \def \hfq {\hfil \ } \offinterlineskip \halign { % preamble &\hfq #\hfq \cr $t$& \vrule depth 5pt & $-\infty $&& $-7/3$&& $0$&& $1$&& $+\infty $& \cr \noalign{\hrule} $x' (t)$& \vrule height 10pt depth 3pt & & $-$& $\approx -9, 33$& $-$& $0$& $+$& $1$& $+$&& \cr \noalign{\hrule} \bbuucenter{$x (t)$}& \vrule& \bbuup{$+\infty $}& \bbup{\brightdownarrow} & \bup{$\approx 14, 9$}& \brightdownarrow & \down{$4\strut $}& \bbrightuparrow & \bbup{$6$}& \bbup {\bbrightuparrow }& \bbup {\bbup {$+\infty $}} \cr \noalign{\hrule} $y' (t)$& \vrule height 10pt depth 3pt & & $+$& $0$& $-$& $-7$& $-$& $0$& $+$&& \cr \noalign{\hrule} \bbuucenter{$y (t)$}& \vrule& \down {$-\infty $}& \brightuuparrow & \bbuup {$\approx 18, 52$}& \bbup {\brightdownarrow }& \bbup {$4$}& \brightdownarrow & \down{$0$}& \bbrightuuparrow & \bbuup{$+\infty $} \cr }} $$ \bye