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authorNorbert Preining <preining@logic.at>2008-01-19 14:55:20 +0000
committerNorbert Preining <preining@logic.at>2008-01-19 14:55:20 +0000
commit9bca56189bb3edc83bf64b0088ef5a52b07e3b36 (patch)
treeddd6f446085e1b22c5bf2a9c75aeaf828b53d882 /Master/texmf-dist/doc/latex/tablor/tablor.html
parent53f5c9b6fd4fe0cde4c661cc8d252d571392b66f (diff)
new package tablor, put into mathextra
git-svn-id: svn://tug.org/texlive/trunk@6313 c570f23f-e606-0410-a88d-b1316a301751
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+<!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: #f5deb3;
+ background-color: #000000;
+ 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;
+ }
+ .flyspell-duplicate {
+ /* flyspell-duplicate-face */
+ color: #cdad00;
+ font-weight: bold;
+ text-decoration: underline;
+ }
+ .flyspell-incorrect {
+ /* flyspell-incorrect-face */
+ color: #ff4500;
+ font-weight: bold;
+ text-decoration: underline;
+ }
+ .font-latex-bold {
+ /* font-latex-bold-face */
+ color: #6b8e23;
+ font-weight: bold;
+ }
+ .font-latex-math {
+ /* font-latex-math-face */
+ color: #ffa500;
+ }
+ .font-latex-sedate {
+ /* font-latex-sedate-face */
+ color: #d3d3d3;
+ }
+ .font-latex-subscript {
+ /* font-latex-subscript-face */
+ font-size: 80%;
+ }
+ .font-latex-warning {
+ /* font-latex-warning-face */
+ color: #ff0000;
+ 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>{<span class="flyspell-incorrect">tablor</span>}
+ [17/01/2008 v1.2
+ la machine &#224; cr&#233;er des tableaux de signes et variations]
+
+
+
+<span class="comment-delimiter">%% </span><span class="comment">Cr&#233;e 5 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"><span class="flyspell-duplicate">TSa</span></span><span class="comment">(-2,3,-1,5,1);
+</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([-2*x+3,x^2-1,x^2+1,x-1,x^2-2],2);
+</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],3)
+</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="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))^2,1,4)
+</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 avec valeurs </span><span class="comment"><span class="flyspell-incorrect">interm&#233;diares</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">{TVI}
+</span><span class="comment-delimiter">%</span><span class="comment"><span class="flyspell-duplicate">TVI</span></span><span class="comment">([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,1)
+</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="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>{
+<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{rm XCasmp.mp* XCasmp.log XCasmp?.mp* XCasmp?.log XCasmpTV.mp* XCasmpTV.<span class="flyspell-duplicate">log</span> *.out <span class="flyspell-duplicate">XCasmpTVI</span>.<span class="flyspell-duplicate">mp</span>* <span class="flyspell-duplicate">XCasmpTVI</span>.<span class="flyspell-duplicate">log</span>
+ *.in *.meta *<span class="flyspell-incorrect">mpx</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">\bouger</span></span><span class="function-name">}</span>[1]{
+<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{cp <span class="flyspell-duplicate">XCas</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">\recup</span></span><span class="function-name">}</span>[2]{
+<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="flyspell-duplicate">cp</span> #1 #2}}
+
+
+
+<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVn</span></span><span class="function-name">}</span>
+
+
+<span class="font-latex-sedate"><span class="keyword">\usepackage</span></span><span class="function-name">{fancyvrb}</span>
+<span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\usepackage</span></span><span class="comment">[upright]{fourier}
+</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="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="flyspell-incorrect">giac</span> &lt;#1 } }
+<span class="font-latex-sedate">\makeatother</span>
+
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTV.meta}
+TV(L,F,nom,<span class="flyspell-duplicate">nomv</span>,f,ftt,<span class="flyspell-duplicate">nmr</span>):={
+<span class="flyspell-duplicate">nl</span>:=<span class="flyspell-duplicate">size</span>(L);
+f:=unapply(f,x);
+<span class="flyspell-duplicate">fp</span>:=fonction_derivee(f);
+Z:=concat(L,F);
+S:=resoudre(fp(x),x);
+ si size(S)&gt;0 alors pour j de 0 jusque size(S)-1 faire
+ kk:=(evalf(S[j])&gt;=evalf(L[0])) and (evalf(S[j])&lt;=evalf(L[<span class="flyspell-duplicate">nl</span>-1]));
+ if(kk==1){Z:=append(Z,simplifier(S[j]))};
+ <span class="flyspell-duplicate">fpour</span>
+ <span class="flyspell-duplicate">fsi</span>;
+
+Z:=sort(Z);
+nz:=size(Z);
+ si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1;
+ fsi;
+pour u de 1 jusque nz-2 faire
+ si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1;
+ fsi;
+<span class="flyspell-duplicate">fpour</span>;
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";<span class="flyspell-duplicate">lsp</span>:=" ";
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);";<span class="flyspell-duplicate">fpour</span>;
+
+ k0:= evalf(limite(f(x),x=Z[0],1))&gt; evalf(limite(f(x),x=Z[1],-1));
+ kz:=evalf(limite(f(x),x=Z[nz-1],-1))&gt; evalf(limite(f(x),x=Z[<span class="flyspell-duplicate">nz</span>-2],1));
+
+<span class="flyspell-duplicate">lsi</span>:="newLigneSignes(btex <span class="font-latex-math">$\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$</span> <span class="flyspell-duplicate">etex</span>);"+
+ if(Z[0]==-infinity){if(sign(evalf(<span class="flyspell-duplicate">fp</span>(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}<span class="flyspell-duplicate">else</span>{"moins;"}}<span class="flyspell-duplicate">else</span>{if(<span class="flyspell-duplicate">member</span>(Z[0],F)==0){
+ if(<span class="flyspell-duplicate">sign</span>(<span class="flyspell-duplicate">fp</span>(Z[0]+10^(-5)))==1){"plus;"}<span class="flyspell-duplicate">else</span>{"moins;"}}<span class="flyspell-duplicate">else</span>{"<span class="flyspell-duplicate">nonDefBarre</span>;"+
+ if(<span class="flyspell-duplicate">sign</span>(<span class="flyspell-duplicate">fp</span>((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}
+
+if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))&gt;0;
+ lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+
+ if(ksp==1){"plus;"}else{"moins;"}
+ }; }
+
+<span class="flyspell-duplicate">lsf</span>:=if(member(Z[nz-1],F)==0){""}else{"<span class="flyspell-duplicate">nomDefBarre</span>;"}
+<span class="flyspell-duplicate">lm</span>0:=limite(f(x),x=Z[0],1)==-<span class="flyspell-duplicate">infinity</span>;
+ li:="newLigneVariations(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Variations de }\\atop{\\displaystyle \\Mathbold{"+nom+"}}$</span> <span class="flyspell-duplicate">etex</span>);"+
+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"}
+ else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"}+
+ if(k0==1){"1"}<span class="flyspell-duplicate">else</span>{"0"}+
+ ");";
+
+ if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){ krm:=evalf(limite(f(x),x=Z[r-1],1))&lt; evalf(limite(f(x),x=Z[r],-1));
+ krp:=evalf(limite(f(x),x=Z[r],1))&gt; evalf(limite(f(x),x=Z[r+1],-1)) ;
+ lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-<span class="flyspell-duplicate">infinity</span>;
+ lp:=lp+if(member(Z[r],F)){
+ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}
+ else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span> etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}<span class="flyspell-duplicate">else</span>{if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}}
+ }; }
+
+<span class="flyspell-duplicate">lnz</span>:=limite(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>;
+ lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"}+
+ if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"};
+
+
+<span class="flyspell-duplicate">intro</span>:="input <span class="flyspell-duplicate">tableauVariation</span>;
+ <span class="flyspell-duplicate">verbatimtex</span>
+<span class="comment-delimiter">%</span><span class="comment">&amp;latex
+</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>}
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span>
+ <span class="flyspell-duplicate">etex</span>
+
+"
+
+
+<span class="flyspell-duplicate">MetaL</span>:= if(ftt==0){if(nz&gt;2){intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+li+
+<span class="flyspell-duplicate">lp</span>+
+<span class="flyspell-duplicate">lf</span>
++"<span class="flyspell-duplicate">endTableau</span>;
+<span class="flyspell-duplicate">end</span>";}else{intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+li+
+<span class="flyspell-duplicate">lf</span>
++"<span class="flyspell-duplicate">endTableau</span>;
+<span class="flyspell-duplicate">end</span>";}}<span class="flyspell-duplicate">else</span>{
+if(nz&gt;2){intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+<span class="flyspell-duplicate">lsi</span>+lsp+<span class="flyspell-duplicate">lsf</span>+
+li+
+<span class="flyspell-duplicate">lp</span>+
+<span class="flyspell-duplicate">lf</span>
++"<span class="flyspell-duplicate">endTableau</span>;
+<span class="flyspell-duplicate">end</span>";}else{intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+<span class="flyspell-duplicate">lsi</span>+<span class="flyspell-duplicate">lsf</span>+
+li+
+<span class="flyspell-duplicate">lf</span>
++"<span class="flyspell-duplicate">endTableau</span>;
+<span class="flyspell-duplicate">end</span>";}
+}
+
+<span class="flyspell-duplicate">return</span>(<span class="flyspell-duplicate">MetaL</span>);
+ }:;
+
+
+
+<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">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVI.<span class="flyspell-duplicate">meta</span>}
+
+
+<span class="flyspell-duplicate">TVI</span>(L,F,nom,nomv,f,ftt,ao,<span class="flyspell-duplicate">nmr</span>):={
+<span class="flyspell-duplicate">nl</span>:=<span class="flyspell-duplicate">size</span>(L);
+f:=unapply(f,x);
+<span class="flyspell-duplicate">fp</span>:=fonction_derivee(f);
+Z:=concat(L,F);
+S:=resoudre(fp(x),x);
+ si size(S)&gt;0 alors pour j de 0 jusque size(S)-1 faire
+ <span class="flyspell-duplicate">kk</span>:=(<span class="flyspell-duplicate">evalf</span>(S[j])&gt;=<span class="flyspell-duplicate">evalf</span>(L[0])) and (<span class="flyspell-duplicate">evalf</span>(S[j])&lt;=<span class="flyspell-duplicate">evalf</span>(L[<span class="flyspell-duplicate">nl</span>-1]));
+ if(<span class="flyspell-duplicate">kk</span>==1){Z:=append(Z,simplifier(S[j]))};
+ <span class="flyspell-duplicate">fpour</span>
+ <span class="flyspell-duplicate">fsi</span>;
+
+Z:=sort(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+ si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1;
+ <span class="flyspell-duplicate">fsi</span>;
+pour u de 1 jusque nz-2 faire
+ si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1;
+ <span class="flyspell-duplicate">fsi</span>;
+<span class="flyspell-duplicate">fpour</span>;
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";<span class="flyspell-duplicate">lsp</span>:=" ";
+
+
+
+LI:=limite(f(x),x,Z[0],1);
+<span class="flyspell-duplicate">LF</span>:=limite(f(x),x,Z[<span class="flyspell-duplicate">nz</span>-1],-1);
+<span class="flyspell-duplicate">LP</span>:=<span class="flyspell-duplicate">NULL</span>;
+if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){LP:=LP,if(member(Z[r],F)){limite(f(x),x,Z[r],-1),limite(f(x),x,Z[r],1)}else{f(Z[r])}}};
+if(nz&gt;2){ LL:=[LI,LP,LF]}else{LL:=[LI,<span class="flyspell-duplicate">LF</span>]};
+
+<span class="flyspell-duplicate">NL</span>:=size(<span class="flyspell-duplicate">LL</span>);
+A:=NULL;aa:=1;<span class="flyspell-duplicate">kk</span>:=0;
+
+if(NL==nz){for(k:=0;k&lt;nz-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-<span class="flyspell-duplicate">ao</span>))==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> <span class="flyspell-duplicate">etex</span>);"}}
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> <span class="flyspell-duplicate">etex</span>);"};
+
+if(NL&gt;nz){for(k:=0;k&lt;NL-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-<span class="flyspell-duplicate">ao</span>))==0.0);
+<span class="flyspell-duplicate">TestL</span>:=(abs(LL[k])==abs(LL[k+1]));
+if(TestS==0){ if( TestL==1 ){l0:=l0}<span class="flyspell-duplicate">else</span>{
+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);";<span class="flyspell-duplicate">aa</span>:=aa+1;kk:=kk+1}}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=<span class="flyspell-duplicate">kk</span>+1}}
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> <span class="flyspell-duplicate">etex</span>);"};
+
+
+
+<span class="flyspell-duplicate">TestS</span>:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-<span class="flyspell-duplicate">ao</span>))==0.0);
+ k0:= evalf(limite(f(x),x=Z[0],1))&gt; evalf(limite(f(x),x=Z[1],-1));
+ kz:=evalf(limite(f(x),x=Z[nz-1],-1))&gt; evalf(limite(f(x),x=Z[<span class="flyspell-duplicate">nz</span>-2],1));
+
+<span class="flyspell-duplicate">lsi</span>:="newLigneSignes(btex <span class="font-latex-math">$\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$</span> <span class="flyspell-duplicate">etex</span>);"+
+ if(Z[0]==-<span class="flyspell-duplicate">infinity</span>){if(<span class="flyspell-duplicate">sign</span>(<span class="flyspell-duplicate">evalf</span>(<span class="flyspell-duplicate">fp</span>(if(Z[1]==+<span class="flyspell-duplicate">infinity</span>){0}<span class="flyspell-duplicate">else</span>{Z[1]-10^(-5)})))==1){"plus;"}<span class="flyspell-duplicate">else</span>{"moins;"}}<span class="flyspell-duplicate">else</span>{if(<span class="flyspell-duplicate">member</span>(Z[0],F)==0){
+ if(<span class="flyspell-duplicate">sign</span>(<span class="flyspell-duplicate">fp</span>((Z[0]+10^(-10))))==1){"plus;"}<span class="flyspell-duplicate">else</span>{"moins;"}}<span class="flyspell-duplicate">else</span>{"<span class="flyspell-duplicate">nonDefBarre</span>;"+
+ if(<span class="flyspell-duplicate">sign</span>(<span class="flyspell-duplicate">fp</span>(10^(-10)+Z[0]))==1){"plus;"}<span class="flyspell-duplicate">else</span>{"moins;"} }}+if(<span class="flyspell-duplicate">TestS</span>==0){"<span class="flyspell-duplicate">valBarre</span>(<span class="flyspell-duplicate">btex</span><span class="font-latex-math">$ $</span> <span class="flyspell-duplicate">etex</span>);"+ if(<span class="flyspell-duplicate">sign</span>(<span class="flyspell-duplicate">fp</span>(10^(-10)+Z[0]))==1){"plus;"}<span class="flyspell-duplicate">else</span>{"moins;"}}<span class="flyspell-duplicate">else</span>{" "};
+
+
+
+
+
+if(nz&gt;2){rr:=1; if(nz==NL){for(r:=1; r&lt;=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(<span class="flyspell-duplicate">evalf</span>(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-<span class="flyspell-duplicate">ao</span>))==0.0);
+ ksp:=evalf(fp(Z[r]+0.01))&gt;0;
+ TestL:=(abs(LL[r])==abs(LL[r+1]));
+ lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+
+ if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex <span class="font-latex-math">$ $</span> etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}<span class="flyspell-duplicate">else</span>{" "};
+ }}
+<span class="flyspell-duplicate">else</span>{for(r:=1; r&lt;=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))&gt;0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-<span class="flyspell-duplicate">ao</span>))==0.0);
+ TestL:=(abs(LL[r])==abs(LL[r+1]));
+ if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+
+ if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex <span class="font-latex-math">$ $</span> etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=<span class="flyspell-duplicate">rr</span>+1;}
+ } else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+
+ if(kspp==1){"plus;"}else{"moins;"};rr:=<span class="flyspell-duplicate">rr</span>+1;}
+}}
+ };
+
+
+
+lsf:=if(member(Z[nz-1],F)==0){""}else{"<span class="flyspell-duplicate">nomDefBarre</span>;"}
+lm0:=limite(f(x),x=Z[0],1)==-<span class="flyspell-duplicate">infinity</span>;
+
+TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-<span class="flyspell-duplicate">ao</span>))==0.0);
+
+ li:="newLigneVariations(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Variations de }\\atop{\\displaystyle \\Mathbold{"+nom+"}}$</span> <span class="flyspell-duplicate">etex</span>);"+
+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}
+ else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"}+
+ if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}<span class="flyspell-duplicate">else</span>{" "};
+
+
+ if(nz&gt;2){if(nz==NL){for(r:=1; r&lt;=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(<span class="flyspell-duplicate">evalf</span>(LL[r+1]-ao))==0.0);
+ krm:=evalf(limite(f(x),x=Z[r-1],1))&lt; evalf(limite(f(x),x=Z[r],-1));
+ krp:=evalf(limite(f(x),x=Z[r],1))&gt; evalf(limite(f(x),x=Z[r+1],-1)) ;
+ lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-<span class="flyspell-duplicate">infinity</span>;
+ lp:=lp+if(member(Z[r],F)) {
+ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+ else{"valPos(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span>
+ etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}<span class="flyspell-duplicate">else</span>{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(<span class="flyspell-duplicate">btex</span>
+ <span class="font-latex-math">$ "+ao+" $</span> <span class="flyspell-duplicate">etex</span>,0.5);"
+ }else{" "};
+};//for
+}else{rr:=1;for(r:=1; r&lt;=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-<span class="flyspell-duplicate">ao</span>))==0.0);
+ krm:=evalf(limite(f(x),x=Z[rr-1],1))&lt; evalf(limite(f(x),x=Z[<span class="flyspell-duplicate">rr</span>],-1));
+ krp:=evalf(limite(f(x),x=Z[rr],1))&gt; evalf(limite(f(x),x=Z[<span class="flyspell-duplicate">rr</span>+1],-1)) ;
+ lmrm:=limite(f(x),x=Z[rr],-1)==-infinity;lmrp:=limite(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
+if(TestS==0){if( TestL==1 ){lp:=lp}else{ lp:=lp+if(member(Z[rr],F)) {
+ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}
+ else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[rr])))+"$</span>
+ etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(<span class="flyspell-duplicate">btex</span>
+ <span class="font-latex-math">$ "+ao+" $</span> <span class="flyspell-duplicate">etex</span>,0.5);
+ ";rr:=<span class="flyspell-duplicate">rr</span>+1;
+}// else <span class="flyspell-incorrect">testL</span>==1
+}//<span class="flyspell-duplicate">testS</span>==0
+<span class="flyspell-duplicate">else</span>{lp:=lp+if(member(Z[rr],F)){
+ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+ else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[rr])))+"$</span>
+ etex,"+if(sign(<span class="flyspell-duplicate">evalf</span>(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);
+ "}}};rr:=<span class="flyspell-duplicate">rr</span>+1;
+}//else <span class="flyspell-duplicate">testS</span>==0
+}//for nz&lt;<span class="flyspell-duplicate">NL</span>
+}// else nz&lt;<span class="flyspell-duplicate">NL</span>
+//if nz=NL
+};//if <span class="flyspell-duplicate">nz</span>&gt;2
+
+
+lnz:=limite(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>;
+ lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+
+ if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"};
+
+
+
+<span class="flyspell-duplicate">intro</span>:="
+input <span class="flyspell-duplicate">tableauVariation</span>;
+<span class="flyspell-duplicate">verbatimtex</span>
+<span class="comment-delimiter">%</span><span class="comment">&amp;latex
+</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>}
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span>
+ <span class="flyspell-duplicate">etex</span>
+
+";
+
+
+<span class="flyspell-duplicate">MetaL</span>:= if(ftt==0){if(nz&gt;2){intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+li+
+<span class="flyspell-duplicate">lp</span>+
+<span class="flyspell-duplicate">lf</span>
++"endTableau;
+<span class="flyspell-duplicate">end</span>";}else{intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+li+
+<span class="flyspell-duplicate">lf</span>
++"endTableau;
+<span class="flyspell-duplicate">end</span>";}}else{
+if(nz&gt;2){intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+<span class="flyspell-duplicate">lsi</span>+lsp+lsf+
+li+
+<span class="flyspell-duplicate">lp</span>+
+<span class="flyspell-duplicate">lf</span>
++"endTableau;
+<span class="flyspell-duplicate">end</span>";}else{intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+<span class="flyspell-duplicate">lsi</span>+lsf+
+li+
+<span class="flyspell-duplicate">lf</span>
++"endTableau;
+<span class="flyspell-duplicate">end</span>";}
+};
+
+<span class="flyspell-duplicate">return</span>(<span class="flyspell-duplicate">MetaL</span>);
+ }:;
+
+
+
+<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">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignL.meta}
+<span class="flyspell-duplicate">TS</span>(L,nmr):={
+L:=apply(f-&gt;unapply(f,x),L)
+n:=size(L);
+Z:=<span class="flyspell-duplicate">NULL</span>;
+
+
+pour k de 0 jusque n-1 faire
+ S:=resoudre(L[k](x),x);
+ si size(S)&gt;0 alors pour j de 0 jusque size(S)-1 faire
+ Z:=Z,simplifier(S[j]);
+ <span class="flyspell-duplicate">fpour</span>;
+ fsi;
+<span class="flyspell-duplicate">fpour</span>;
+Z:=sort(Z);
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+pour u de 1 jusque nz-2 faire
+ si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=<span class="flyspell-duplicate">nz</span>-1;
+ fsi;
+<span class="flyspell-duplicate">fpour</span>;
+nz:=size(Z);
+l0:=" ";li:=" ";lr:=" ";
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);";<span class="flyspell-duplicate">fpour</span>;
+
+
+
+for(p:=0;p&lt;=n-1;p++){<span class="flyspell-duplicate">lp</span>:=" ";
+ li:=li+"newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$</span> etex);"+
+ if(L[p](Z[0]-1.0)&gt;0){"plus;"}else{"moins;"}+
+ for(r:=0; r&lt;=nz-2;r++){
+ lp:=lp+if(simplifier(L[p](Z[r]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+
+ if(L[p]((Z[r]+Z[r+1])*.5)&gt;0){"plus;"}else{"moins;"}}+
+ if(simplifier(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+
+ if(L[p](Z[nz-1]+1.0)&gt;0){"plus;"}else{"moins;"}
+ };
+
+
+pour t de 0 jusque nz-2 faire
+ lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"
+ fpour
+
+<span class="flyspell-duplicate">MetaL</span>:=" input <span class="flyspell-duplicate">tableauVariation</span>;
+ <span class="flyspell-duplicate">verbatimtex</span>
+<span class="comment-delimiter">%</span><span class="comment">&amp;latex
+</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>}
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span>
+ etex
+ beginTableau("+nmr+")
+<span class="flyspell-duplicate">newLigneVariables</span>(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
+ val(btex <span class="font-latex-math">$-\\infty$</span> etex);"+l0+"val(btex <span class="font-latex-math">$+\\infty$</span> <span class="flyspell-duplicate">etex</span>);"+
+ li
+ +
+ " newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe du }\\atop{{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> produit}}$</span> etex);"+
+ if(product(L[s](Z[0]-1.0),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"+
+ lr+
+ if(product(L[s](Z[nz-1]+1.0),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+"
+<span class="flyspell-duplicate">endTableau</span>;
+<span class="flyspell-duplicate">end</span>"
+;
+return(<span class="flyspell-duplicate">MetaL</span>);
+ }:;
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+
+
+
+
+
+
+
+
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignQ.meta}
+<span class="flyspell-duplicate">TSq</span>(nomf,L,Fo,nmr):={
+L:=apply(f-&gt;unapply(f,x),L);
+<span class="flyspell-duplicate">Fo</span>:=apply(f-&gt;unapply(f,x),Fo);
+L:=concat(L,Fo);
+n:=size(L);
+Z:=NULL;
+m:=size(Fo);
+F:=<span class="flyspell-duplicate">NULL</span>;
+
+
+
+pour k de 0 jusque n-1 faire
+ S:=resoudre(L[k](x),x);
+ si size(S)&gt;0 alors pour j de 0 jusque size(S)-1 faire
+ Z:=Z,simplifier(S[j]);
+ <span class="flyspell-duplicate">fpour</span>;
+ fsi;
+<span class="flyspell-duplicate">fpour</span>;
+
+
+pour k de 0 jusque m-1 faire
+ SF:=resoudre(Fo[k](x),x);
+ si size(SF)&gt;0 alors pour j de 0 jusque size(SF)-1 faire
+ F:=F,simplifier(SF[j]);
+ fpour;
+ fsi;
+<span class="flyspell-duplicate">fpour</span>;
+
+
+
+Z:=sort(Z); // on classe les z&#233;ros dans l'ordre croissant
+nz:=size(Z);
+pour u de 1 jusque nz-2 faire
+ si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1; // pour les z&#233;ros en double
+ fsi;
+fpour;
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+l0:=" ";li:=" ";lr:=" ";
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);";<span class="flyspell-duplicate">fpour</span>;
+
+
+
+for(p:=0;p&lt;=n-1;p++){lp:=" ";
+ li:=li+"newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$</span> <span class="flyspell-duplicate">etex</span>);"+
+ if(L[p](Z[0]-1.0)&gt;0){"plus;"}else{"moins;"}+
+ for(r:=0; r&lt;=nz-2;r++){
+ lp:=lp+if(simplifier(L[p](Z[r]))==0){"
+ <span class="flyspell-duplicate">valBarre</span>(btex 0 etex);"}else{"barre;"}+
+ if(L[p]((Z[r]+Z[r+1])*.5)&gt;0){"plus;"}else{"moins;"}}+
+ if(simplifier(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+
+ if(L[p](Z[nz-1]+1.0)&gt;0){"plus;"}else{"moins;
+ "}
+ };
+
+
+pour t de 0 jusque nz-2 faire
+ lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+if(member(Z[t+1],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}
+ fpour
+
+<span class="flyspell-duplicate">MetaL</span>:=" input <span class="flyspell-duplicate">tableauVariation</span>;
+ <span class="flyspell-duplicate">verbatimtex</span>
+<span class="comment-delimiter">%</span><span class="comment">&amp;latex
+</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>}
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span>
+ etex
+ beginTableau("+nmr+")
+<span class="flyspell-duplicate">newLigneVariables</span>(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
+ val(btex <span class="font-latex-math">$-\\infty$</span> etex);"+l0+"val(btex <span class="font-latex-math">$+\\infty$</span> <span class="flyspell-duplicate">etex</span>);"+
+ li
+ +
+ " newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> "+nomf+"(x) }$</span> etex);"+
+ if(product(L[s](Z[0]-1.0),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+if(member(Z[0],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+
+ lr+
+ if(product(L[s](Z[nz-1]+1.0),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+"
+<span class="flyspell-duplicate">endTableau</span>;
+<span class="flyspell-duplicate">end</span>"
+;
+return(<span class="flyspell-duplicate">MetaL</span>);
+ }:;
+
+
+<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">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSign.meta}
+<span class="flyspell-duplicate">TSa</span>(a,b,c,d,nmr):={
+zA:=resoudre(a*x+b=0,x)[0];
+<span class="flyspell-duplicate">zB</span>:=resoudre(c*x+d=0,x)[0];
+<span class="flyspell-duplicate">zmin</span>:=min(zA,zB);
+<span class="flyspell-duplicate">zmax</span>:=max(zA,zB);
+ Meta:= " input <span class="flyspell-duplicate">tableauVariation</span>;
+ verbatimtex
+<span class="comment-delimiter">%</span><span class="comment">&amp;latex
+</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>}
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span>
+ <span class="flyspell-duplicate">etex</span>
+ beginTableau("+<span class="flyspell-duplicate">nmr</span>+")
+ newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> <span class="flyspell-duplicate">etex</span>);
+ val(btex <span class="font-latex-math">$-\\infty$</span> etex);val(btex <span class="font-latex-math">$"+latex(zmin)+"$</span> etex);
+val(btex <span class="font-latex-math">$"+latex(zmax)+"$</span>etex);
+val(btex <span class="font-latex-math">$+\\infty$</span> etex);
+ newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+"}}$</span> <span class="flyspell-duplicate">etex</span>);"
+ + if(a&gt;0){"moins;"}else{"plus;"}+
+ if(zmin==zA){"valBarre(btex 0 etex);"}else{"barre;"}+
+ if(zmin==zA){si a&gt;0 alors "plus;"; sinon "moins;";fsi}
+ else{si a&gt;0 alors "moins;"; sinon "plus;"; <span class="flyspell-duplicate">fsi</span>}+
+ if(zmin==zA){"barre;"}else{"valBarre(btex 0 etex);"}+
+ if(a&gt;0){"plus;"}else{"moins;"}
+ +" newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+"}}$</span> <span class="flyspell-duplicate">etex</span>);"
+ + if(c&gt;0){"moins"}else{"plus"}+";"+
+ if(zmin==zB){"valBarre(btex 0 etex);"}else{"barre;"}+
+ if(zmin==zB){si c&gt;0 alors "plus;"; sinon "moins;";<span class="flyspell-duplicate">fsi</span>}
+ else{si c&gt;0 alors "moins;"; sinon "plus;"; fsi}+
+ if(zmin==zB){"barre;"}else{"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"}+
+ if(c&gt;0){"plus;"}else{"moins;"}
+
+ +" newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{("+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> <span class="flyspell-duplicate">etex</span>);"
+ + si a*c&gt;0 alors plus; sinon moins;fsi+";"+
+ "valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"+
+ si a*c&gt;0 alors moins; sinon plus;<span class="flyspell-duplicate">fsi</span>+";"+
+ "valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"+
+ si a*c&gt;0 alors plus; sinon moins;fsi+";"+"
+endTableau;
+<span class="flyspell-duplicate">end</span>"
+;
+<span class="flyspell-duplicate">return</span>(<span class="flyspell-duplicate">Meta</span>);
+ }:;
+<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">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCas.in}
+<span class="flyspell-duplicate">maple</span>_mode(0);
+read("XcasTabSign.meta");
+Sortie:=fopen("XCasmp.mp");
+vect.xcas.out := read("XCas.out");
+<span class="flyspell-duplicate">vxo</span> := vect.xcas.out;
+<span class="flyspell-duplicate">dim</span>.vxo := dim(vxo);
+<span class="flyspell-duplicate">nbr</span>.line.vxo := dim.vxo;
+Resultat:=cat(" ");
+<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt);
+Resultat:=cat(Resultat,RslT);
+<span class="flyspell-duplicate">fprint</span>(Sortie,Unquoted,Resultat);
+<span class="flyspell-duplicate">fclose</span>(Sortie);
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSa}</span>
+{<span class="font-latex-sedate">\stepcounter</span>{TVn}<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCas.out}}
+{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+ <span class="font-latex-sedate">\executGiacmp</span>{XCas.in}
+
+ <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost <span class="flyspell-duplicate">XCasmp</span>}
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span>
+ <span class="font-latex-sedate">\includegraphics</span>{XCasmp.<span class="font-latex-sedate">\theTVn</span>}
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span>
+
+}
+
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasQ.in}
+<span class="flyspell-duplicate">maple</span>_mode(0);
+<span class="flyspell-duplicate">read</span>("XcasTabSignQ.meta");
+Sortie:=fopen("XCasmpQ.mp");
+<span class="flyspell-duplicate">vect</span>.xcas.out := read("XCasQ.out");
+vxo := vect.xcas.out;
+<span class="flyspell-duplicate">dim</span>.vxo := dim(vxo);
+<span class="flyspell-duplicate">nbr</span>.line.vxo := dim.vxo;
+<span class="flyspell-duplicate">Resultat</span>:=cat(" ");
+<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt);
+<span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,RslT);
+fprint(Sortie,Unquoted,Resultat);
+<span class="flyspell-duplicate">fclose</span>(Sortie);
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TSq</span></span><span class="function-name">}</span>
+{<span class="font-latex-sedate">\stepcounter</span>{TVn}<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasQ.out}}
+{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+ <span class="font-latex-sedate">\executGiacmp</span>{XCasQ.in}
+
+ <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost <span class="flyspell-duplicate">XCasmpQ</span>}
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span>
+ <span class="font-latex-sedate">\includegraphics</span>{XCasmpQ.<span class="font-latex-sedate">\theTVn</span>}
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span>
+
+}
+
+
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasL.in}
+<span class="flyspell-duplicate">maple</span>_mode(0);
+<span class="flyspell-duplicate">read</span>("XcasTabSignL.meta");
+Sortie:=fopen("XCasmpL.mp");
+<span class="flyspell-duplicate">vect</span>.xcas.out := read("XCasL.out");
+vxo := vect.xcas.out;
+<span class="flyspell-duplicate">dim</span>.vxo := dim(vxo);
+<span class="flyspell-duplicate">nbr</span>.line.vxo := dim.vxo;
+<span class="flyspell-duplicate">Resultat</span>:=cat(" ");
+<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt);
+<span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,RslT);
+fprint(Sortie,Unquoted,Resultat);
+<span class="flyspell-duplicate">fclose</span>(Sortie);
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TS</span></span><span class="function-name">}</span>
+{<span class="font-latex-sedate">\stepcounter</span>{TVn}<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasL.out}}
+{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+ <span class="font-latex-sedate">\executGiacmp</span>{XCasL.in}
+
+ <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost <span class="flyspell-duplicate">XCasmpL</span>}
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span>
+ <span class="font-latex-sedate">\includegraphics</span>{XCasmpL.<span class="font-latex-sedate">\theTVn</span>}
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span>
+
+}
+
+
+
+
+
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTV.in}
+<span class="flyspell-duplicate">maple</span>_mode(0);
+read("XcasTV.meta");
+Sortie:=fopen("XCasmpTV.mp");
+<span class="flyspell-duplicate">vect</span>.xcas.out := read("XCasTV.out");
+<span class="flyspell-duplicate">vxo</span> := vect.xcas.out;
+<span class="flyspell-duplicate">dim</span>.vxo := dim(vxo);
+<span class="flyspell-duplicate">nbr</span>.line.vxo := dim.vxo;
+Resultat:=cat(" ");
+<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt);
+<span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,<span class="flyspell-duplicate">RslT</span>);
+fprint(Sortie,Unquoted,Resultat);
+<span class="flyspell-duplicate">fclose</span>(Sortie);
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TV}</span>
+{<span class="font-latex-sedate">\stepcounter</span>{TVn}<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTV.out}}
+{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+ <span class="font-latex-sedate">\executGiacmp</span>{XCasTV.in}
+
+ <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost <span class="flyspell-duplicate">XCasmpTV</span>}
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span>
+ <span class="font-latex-sedate">\includegraphics</span>{XCasmpTV.<span class="font-latex-sedate">\theTVn</span>}
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span>
+
+}
+
+
+
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{<span class="flyspell-incorrect">XCasTVI</span>.in}
+maple_mode(0);
+<span class="flyspell-duplicate">read</span>("<span class="flyspell-duplicate">XcasTVI</span>.<span class="flyspell-duplicate">meta</span>");
+Sortie:=<span class="flyspell-duplicate">fopen</span>("<span class="flyspell-incorrect">XCasmpTVI</span>.mp");
+<span class="flyspell-duplicate">vect</span>.xcas.out := read("<span class="flyspell-duplicate">XCasTVI</span>.out");
+vxo := vect.xcas.out;
+dim.vxo := dim(<span class="flyspell-duplicate">vxo</span>);
+nbr.line.vxo := dim.<span class="flyspell-duplicate">vxo</span>;
+<span class="flyspell-duplicate">Resultat</span>:=<span class="flyspell-duplicate">cat</span>(" ");
+rslt := vxo[0]; RslT:=cat(<span class="flyspell-duplicate">rslt</span>);
+<span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,<span class="flyspell-duplicate">RslT</span>);
+fprint(Sortie,Unquoted,Resultat);
+fclose(Sortie);
+<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVI</span></span><span class="function-name">}</span>
+{<span class="font-latex-sedate">\stepcounter</span>{TVn}<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{<span class="flyspell-duplicate">XCasTVI</span>.out}}
+{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+ <span class="font-latex-sedate">\executGiacmp</span>{<span class="flyspell-duplicate">XCasTVI</span>.in}
+
+ <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost <span class="flyspell-duplicate">XCasmpTVI</span>}
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span>
+ <span class="font-latex-sedate">\includegraphics</span>{<span class="flyspell-duplicate">XCasmpTVI</span>.<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="comment-delimiter">%%</span><span class="comment">
+</span><span class="comment-delimiter">%% </span><span class="comment">Zi </span><span class="comment"><span class="flyspell-duplicate">end</span></span><span class="comment">
+</span></pre>
+ </body>
+</html>