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-rw-r--r--Master/texmf-dist/doc/latex/tablor/Figures.zipbin142673 -> 148920 bytes
-rw-r--r--Master/texmf-dist/doc/latex/tablor/tablor.html1102
-rw-r--r--Master/texmf-dist/doc/latex/tablor/tablor.pdfbin287467 -> 299304 bytes
-rw-r--r--Master/texmf-dist/doc/latex/tablor/tablor.tex87
-rw-r--r--Master/texmf-dist/tex/latex/tablor/tablor.sty624
5 files changed, 1566 insertions, 247 deletions
diff --git a/Master/texmf-dist/doc/latex/tablor/Figures.zip b/Master/texmf-dist/doc/latex/tablor/Figures.zip
index 9e1f9648f9b..3203b1f239b 100644
--- a/Master/texmf-dist/doc/latex/tablor/Figures.zip
+++ b/Master/texmf-dist/doc/latex/tablor/Figures.zip
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.html b/Master/texmf-dist/doc/latex/tablor/tablor.html
index e26383d0ea4..f102f34fba8 100644
--- a/Master/texmf-dist/doc/latex/tablor/tablor.html
+++ b/Master/texmf-dist/doc/latex/tablor/tablor.html
@@ -31,6 +31,12 @@
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;
@@ -83,13 +89,13 @@
<pre>
<span class="font-latex-sedate">\NeedsTeXFormat</span>{LaTeX2e}[1995/12/01]
-<span class="font-latex-sedate">\ProvidesPackage</span>{<span class="flyspell-duplicate">tablor</span>}[19/03/2008 v1.9 la machine &#224; cr&#233;er des tableaux de signes et variations]
+<span class="font-latex-sedate">\ProvidesPackage</span>{<span class="flyspell-duplicate">tablor</span>}[24/03/2008 v2.01 la machine &#224; cr&#233;er 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 </span><span class="font-latex-sedate"><span class="comment">\copyright</span></span><span class="comment">
-</span><span class="comment-delimiter">% </span><span class="comment">avec l'efficace participation de Jean-Michel Boucart
+</span><span class="comment-delimiter">% </span><span class="comment">avec l'efficace participation de Jean-Michel </span><span class="comment"><span class="flyspell-incorrect">Boucart</span></span><span class="comment">
</span>
-<span class="comment-delimiter">%% </span><span class="comment">Cr&#233;e 10 environnements :
+<span class="comment-delimiter">%% </span><span class="comment">Cr&#233;e 14 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">);
@@ -107,15 +113,27 @@
</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,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
+</span><span class="comment-delimiter">% </span><span class="comment">TV([0,+</span><span class="comment"><span class="flyspell-duplicate">infinity</span></span><span class="comment">],[0],"h","x",ln(x)-(ln(x))^2,1,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
</span><span class="comment-delimiter">% </span><span class="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 interm&#233;diares
+</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">TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">)
</span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TVI}
</span><span class="comment-delimiter">%%%</span><span class="comment">
+</span><span class="comment-delimiter">% </span><span class="comment">tableau de variations avec f' sans z&#233;ro 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 z&#233;ro 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"><span class="flyspell-duplicate">TVIapp</span></span><span class="comment">([0,+</span><span class="comment"><span class="flyspell-duplicate">infinity</span></span><span class="comment">],[0],"g","x",</span><span class="comment"><span class="flyspell-duplicate">ln</span></span><span class="comment">(x)-x*</span><span class="comment"><span class="flyspell-duplicate">exp</span></span><span class="comment">(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 &#233;toil&#233;s qui permet l'affichage interm&#233;diaire du
</span><span class="comment-delimiter">% </span><span class="comment">fichier metapost pour le modifier
</span><span class="comment-delimiter">%</span><span class="comment">
@@ -133,17 +151,17 @@
<span class="font-latex-sedate">\RequirePackage</span>{ifthen}
<span class="font-latex-sedate">\RequirePackage</span>{fancyvrb}
-<span class="font-latex-sedate">\RequirePackage</span>{ifpdf}
+<span class="font-latex-sedate">\RequirePackage</span>{<span class="flyspell-duplicate">ifpdf</span>}
<span class="comment-delimiter">% </span><span class="comment">option xcas pr&#233;sent
</span>
-<span class="font-latex-sedate">\newboolean</span>{xcas}<span class="font-latex-sedate">\setboolean</span>{xcas}{false}
+<span class="font-latex-sedate">\newboolean</span>{xcas}<span class="font-latex-sedate">\setboolean</span>{xcas}{<span class="flyspell-duplicate">false</span>}
<span class="font-latex-sedate">\DeclareOption</span>{xcas}{<span class="font-latex-sedate">\setboolean</span>{xcas}{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="comment-delimiter">%% </span><span class="comment">Initialisation du choix </span><span class="comment"><span class="flyspell-incorrect">d'OS</span></span><span class="comment">
+</span><span class="font-latex-sedate">\newboolean</span>{windows}<span class="font-latex-sedate">\setboolean</span>{windows}{<span class="flyspell-duplicate">false</span>}
<span class="comment-delimiter">%% </span><span class="comment">on configure tablor dans un fichier ext&#233;rieur pour la plateforme
@@ -153,15 +171,15 @@
</span>
<span class="font-latex-sedate">\ProcessOptions</span><span class="font-latex-sedate">\relax</span>
-<span class="comment-delimiter">%% </span><span class="comment">pour ceux compilant via pdflatex
+<span class="comment-delimiter">%% </span><span class="comment">pour ceux compilant via </span><span class="comment"><span class="flyspell-incorrect">pdflatex</span></span><span class="comment">
</span>
<span class="font-latex-sedate">\ifpdf</span>
-<span class="font-latex-sedate">\DeclareGraphicsRule</span>{*}{mps}{*}{}
+<span class="font-latex-sedate">\DeclareGraphicsRule</span>{*}{<span class="flyspell-incorrect">mps</span>}{*}{}
<span class="font-latex-sedate">\fi</span>
<span class="comment-delimiter">%% </span><span class="comment">pour nettoyer les fichiers auxiliaires
</span>
-<span class="font-latex-sedate">\AtEndDocument</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> tete.* *.user XCas* Xcas* *.mpx}}
+<span class="font-latex-sedate">\AtEndDocument</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> tete.* *.user XCas* Xcas* *.<span class="flyspell-incorrect">mpx</span>}}
@@ -169,7 +187,7 @@
</span><span class="comment-delimiter">%% </span><span class="comment">de tous les tableaux produits
</span>
<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{tete.mp}
- input tableauVariation;
+ input <span class="flyspell-duplicate">tableauVariation</span>;
verbatimtex
<span class="comment-delimiter">%</span><span class="comment">&amp;latex
</span> <span class="font-latex-sedate"><span class="keyword">\documentclass</span></span><span class="function-name">{article}</span>
@@ -187,17 +205,17 @@
</span>
<span class="comment-delimiter">%% </span><span class="comment">D&#233;finit des commandes disque selon l'OS utilis&#233;
-</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{windows}}<span class="comment">%
+</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{<span class="flyspell-duplicate">windows</span>}}<span class="comment">%
</span> {<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\rem</span></span><span class="function-name">}</span>{DEL } <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cat</span></span><span class="function-name">}</span>{TYPE }
<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{COPY }}<span class="comment">%
</span> {<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\rem</span></span><span class="function-name">}</span>{rm }<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cat</span></span><span class="function-name">}</span>{cat }
- <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{cp }}
+ <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{<span class="flyspell-duplicate">cp</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}
-<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{echo end &gt;&gt; #1.Tab.mp}
+<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{echo end &gt;&gt; #1.Tab.<span class="flyspell-duplicate">mp</span>}
}
@@ -210,7 +228,7 @@
<span class="comment-delimiter">%% </span><span class="comment">initialise les compteurs
</span>
-<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{TVn}</span>
+<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVn</span></span><span class="function-name">}</span>
<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\tv</span></span><span class="function-name">}</span>{<span class="font-latex-sedate">\theTVn</span>}
<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{TVnbis}</span>
@@ -229,7 +247,7 @@
</span>{<span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\Tableaux</span>.Tab.mp}<span class="comment">% Si Tableaux.mp est pr&#233;sent...
</span> {<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> <span class="font-latex-sedate">\Tableaux</span>.Tab.mp}}<span class="comment">% le d&#233;truire
</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> -f tete.mp <span class="font-latex-sedate">\Tableaux</span>.Tab.mp}<span class="comment">% Reconstituer l'ent&#234;te de Tableaux.mp
+</span> <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cp</span> -f tete.mp <span class="font-latex-sedate">\Tableaux</span>.Tab.mp}<span class="comment">% Reconstituer l'ent&#234;te de Tableaux.</span><span class="comment"><span class="flyspell-duplicate">mp</span></span><span class="comment">
</span>}
{<span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\Tableaux</span>.Tab.mp}<span class="comment">% Sans l'option XCas, si
</span> <span class="comment">% Tableaux.mp existe
@@ -246,7 +264,7 @@
<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{<span class="flyspell-duplicate">giac</span> #1 }}<span class="comment">%
</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{giac &lt;#1 }}}
<span class="font-latex-sedate">\makeatother</span>
@@ -255,7 +273,7 @@
<span class="comment-delimiter">%%%</span><span class="comment">
</span><span class="comment-delimiter">%</span><span class="comment">
-</span><span class="comment-delimiter">%%% </span><span class="comment">LES SCRIPTS GIAC/XCAS
+</span><span class="comment-delimiter">%%% </span><span class="comment">LES SCRIPTS GIAC/</span><span class="comment"><span class="flyspell-incorrect">XCAS</span></span><span class="comment">
</span><span class="comment-delimiter">%</span><span class="comment">
</span><span class="comment-delimiter">%%%</span><span class="comment">
</span>
@@ -271,7 +289,7 @@
</span>
<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTV.cxx}
-TV(L,F,nom,nomv,f,ftt,nmr):={
+<span class="flyspell-duplicate">TV</span>(L,F,nom,nomv,f,ftt,nmr):={
nl:=size(L);
f:=unapply(f,x);
fp:=fonction_derivee(f);
@@ -288,19 +306,19 @@ nz:=size(Z);
si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1;
fsi;
pour u de 1 jusque nz-2 faire
- si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1;
+ si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1;
fsi;
fpour;
nz:=size(Z);
l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" ";
pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);
-";fpour;
+";<span class="flyspell-duplicate">fpour</span>;
k0:= evalf(limite(f(x),x=Z[0],1))&gt; evalf(limite(f(x),x=Z[1],-1));
kz:=evalf(limite(f(x),x=Z[nz-1],-1))&gt; evalf(limite(f(x),x=Z[nz-2],1));
lsi:="
-newLigneSignes(btex <span class="font-latex-math">$\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$</span> etex);"+
+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(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
if(sign(fp(Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
@@ -315,9 +333,9 @@ lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;
"}
lm0:=limite(f(x),x=Z[0],1)==-infinity;
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> etex);"+
+<span class="flyspell-duplicate">newLigneVariations</span>(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> etex);"+
if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}
- else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}+
+ 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"}+
");";
@@ -327,13 +345,13 @@ newLigneVariations(btex <span class="font-latex-math">$\\hbox{\</span><span clas
lp:=lp+if(member(Z[r],F)){
"limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span>
- etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+ etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);
"}}}
}; }
lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+
- if(kz==1){"1);"}else{"0);
+ if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);
"};
@@ -345,26 +363,26 @@ intro:="input tableauVariation;
<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span>
<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#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;
+ <span class="flyspell-duplicate">etex</span>;
"
MetaL:=if(ftt==2){if(nz&gt;2){intro+"beginTableau("+nmr+")"+
l0+lsi+lsp+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
end
";}else{
intro+"beginTableau("+nmr+")"+
l0+
lsi+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
end";
}
}else{ if(ftt==0){if(nz&gt;2){intro+"beginTableau("+nmr+")"+
l0+
li+
-lp+
+<span class="flyspell-duplicate">lp</span>+
lf
+"
endTableau;
@@ -375,22 +393,22 @@ lf
+"
endTableau;
end";}}else{
-if(nz&gt;2){intro+"beginTableau("+nmr+")"+
+if(nz&gt;2){intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
l0+
lsi+lsp+lsf+
li+
lp+
lf
+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
end";}else{intro+"beginTableau("+nmr+")"+
l0+
lsi+lsf+
li+
-lf
+<span class="flyspell-duplicate">lf</span>
+"
endTableau;
-end";}
+<span class="flyspell-duplicate">end</span>";}
}}
@@ -399,30 +417,30 @@ MetaLfc:=if(ftt==2){if(nz&gt;2){"
beginTableau("+nmr+")"+
l0+lsi+lsp+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
";}else{
intro+"beginTableau("+nmr+")"+
l0+
lsi+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
";
}
}else{ if(ftt==0){if(nz&gt;2){"beginTableau("+nmr+")"+
l0+
li+
-lp+
+<span class="flyspell-duplicate">lp</span>+
lf
+"
endTableau;
-";}else{"beginTableau("+nmr+")"+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
l0+
li+
lf
+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
";}}else{
if(nz&gt;2){"beginTableau("+nmr+")"+
@@ -430,34 +448,267 @@ if(nz&gt;2){"beginTableau("+nmr+")"+
lsi+lsp+lsf+
li+
lp+
-lf
+<span class="flyspell-duplicate">lf</span>
+"
endTableau;
";}else{"beginTableau("+nmr+")"+
l0+
+<span class="flyspell-duplicate">lsi</span>+lsf+
+li+
+lf
++"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}
+}}
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+<span class="flyspell-duplicate">fclose</span>(sortie);
+
+
+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="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>{<span class="flyspell-duplicate">XcasTVapp</span>.<span class="flyspell-duplicate">cxx</span>}
+
+
+
+
+
+
+
+TVapp(L,F,nom,nomv,f,ftt,nmr):={
+
+
+<span class="flyspell-duplicate">nl</span>:=size(L);
+f:=unapply(f,x);
+fp:=fonction_derivee(f);
+z0:=concat(L,F);z:=sort(z0);
+nz:=size(z);
+if(L==[-infinity,+infinity]){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..100);}
+<span class="flyspell-duplicate">else</span>{if(L[0]==-infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..L[1]);}
+else{if(L[1]==+infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=L[0]..100);}
+else{S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=z[0]..z[nz-1])}}};
+si size(S)&gt;0 alors pour j de 0 jusque size(S)-1 faire
+ kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])&gt;=L[0]) and (evalf(S[j])&lt;=L[1]);
+ if(kk==1){if(kok==1){z:=append(z,simplifier(S[j]))}};
+ fpour;
+<span class="flyspell-duplicate">fsi</span>;
+
+
+S:=NULL;
+S:=S,z[0];
+for(j:=1;j&lt;size(z);j++){
+ if(z[j]!=undef and (abs(z[j])&gt;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&lt;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])+"$</span> <span class="flyspell-duplicate">etex</span>);
+";<span class="flyspell-duplicate">fpour</span>;
+
+ k0:= evalf(limite(f(x),x=Z[0],1))&gt; evalf(limite(f(x),x=Z[1],-1));
+ kz:=evalf(limite(f(x),x=Z[nz-1],-1))&gt; evalf(limite(f(x),x=Z[nz-2],1));
+
+lsi:="
+<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$</span> <span class="flyspell-duplicate">etex</span>);"+
+ if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
+ if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+ if(sign(fp(Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"+
+ if(sign(fp((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}
+
+if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))&gt;0;
+ lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+
+ if(ksp==1){"plus;"}else{"moins;"}
+ }; }
+
+lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;
+"}
+lm0:=limite(f(x),x=Z[0],1)==-<span class="flyspell-duplicate">infinity</span>;
+ li:="
+<span class="flyspell-duplicate">newLigneVariations</span>(btex <span class="font-latex-math">$\\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+"}}$</span> etex);"+
+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}
+ else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"}+
+ if(k0==1){"1"}else{"0"}+
+ ");";
+
+ if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){ krm:=evalf(limite(f(x),x=Z[r-1],1))&lt; evalf(limite(f(x),x=Z[r],-1));
+ krp:=evalf(limite(f(x),x=Z[r],1))&gt; evalf(limite(f(x),x=Z[r+1],-1)) ;
+ lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+ lp:=lp+if(member(Z[r],F)){
+ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+ else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span>
+ etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);
+"}}}
+ }; }
+
+lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
+ lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"}+
+ if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);
+"};
+
+
+intro:="input tableauVariation;
+ <span class="flyspell-duplicate">verbatimtex</span>
+<span class="comment-delimiter">%</span><span class="comment">&amp;latex
+</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#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>;
+
+"
+
+
+MetaL:=if(ftt==2){if(nz&gt;2){intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+lsi+lsp+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
+end
+";}else{
+intro+"beginTableau("+nmr+")"+
+ l0+
+<span class="flyspell-duplicate">lsi</span>+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
+end";
+}
+}else{ if(ftt==0){if(nz&gt;2){intro+"beginTableau("+nmr+")"+
+ l0+
+li+
+<span class="flyspell-duplicate">lp</span>+
+lf
++"
+endTableau;
+end";}else{intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+li+
+lf
++"
+endTableau;
+end";}}else{
+if(nz&gt;2){intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+lsi+lsp+lsf+
+li+
+lp+
+<span class="flyspell-duplicate">lf</span>
++"
+<span class="flyspell-duplicate">endTableau</span>;
+end";}else{intro+"beginTableau("+nmr+")"+
+ l0+
lsi+lsf+
li+
+<span class="flyspell-duplicate">lf</span>
++"
+endTableau;
+<span class="flyspell-duplicate">end</span>";}
+}}
+
+
+
+MetaLfc:=if(ftt==2){if(nz&gt;2){"
+
+beginTableau("+nmr+")"+
+ l0+lsi+lsp+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}else{
+intro+"beginTableau("+nmr+")"+
+ l0+
+lsi+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";
+}
+}else{ if(ftt==0){if(nz&gt;2){"beginTableau("+nmr+")"+
+ l0+
+li+
+<span class="flyspell-duplicate">lp</span>+
+lf
++"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+li+
lf
+"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}}else{
+if(nz&gt;2){"beginTableau("+nmr+")"+
+ l0+
+lsi+lsp+lsf+
+li+
+<span class="flyspell-duplicate">lp</span>+
+<span class="flyspell-duplicate">lf</span>
++"
endTableau;
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+<span class="flyspell-duplicate">lsi</span>+lsf+
+li+
+lf
++"
+<span class="flyspell-duplicate">endTableau</span>;
+
";}
}}
sortie:=fopen("XCasmpfc.mp");
-fprint(sortie,Unquoted,MetaLfc);
-fclose(sortie);
+<span class="flyspell-duplicate">fprint</span>(sortie,Unquoted,MetaLfc);
+<span class="flyspell-duplicate">fclose</span>(sortie);
-return(MetaL);
+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="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 interm&#233;diaires
@@ -467,52 +718,52 @@ return(MetaL);
-<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVI.cxx}
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVI.<span class="flyspell-duplicate">cxx</span>}
TVI(L,F,nom,nomv,f,ftt,ao,nmr):={
-nl:=size(L);
+<span class="flyspell-duplicate">nl</span>:=size(L);
f:=unapply(f,x);
-fp:=fonction_derivee(f);
+<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[nl-1]));
if(kk==1){Z:=append(Z,simplifier(S[j]))};
- fpour
+ <span class="flyspell-duplicate">fpour</span>
fsi;
Z:=sort(Z);
-nz:=size(Z);
- si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1;
+<span class="flyspell-duplicate">nz</span>:=size(Z);
+ si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1;
fsi;
pour u de 1 jusque nz-2 faire
si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1;
fsi;
-fpour;
+<span class="flyspell-duplicate">fpour</span>;
nz:=size(Z);
-l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" ";
+l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";<span class="flyspell-duplicate">lsp</span>:=" ";
LI:=limite(f(x),x,Z[0],1);
LF:=limite(f(x),x,Z[nz-1],-1);
-LP:=NULL;
+<span class="flyspell-duplicate">LP</span>:=NULL;
if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){LP:=LP,if(member(Z[r],F)){limite(f(x),x,Z[r],-1),limite(f(x),x,Z[r],1)}else{f(Z[r])}}};
-if(nz&gt;2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
+if(nz&gt;2){ LL:=[LI,LP,LF]}else{LL:=[LI,<span class="flyspell-duplicate">LF</span>]};
NL:=size(LL);
-A:=NULL;aa:=1;kk:=0;
+A:=NULL;aa:=1;<span class="flyspell-duplicate">kk</span>:=0;
if(NL==nz){for(k:=0;k&lt;nz-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
if(TestS==0){A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"}}
l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);"};
if(NL&gt;nz){for(k:=0;k&lt;NL-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
-TestL:=(abs(LL[k])==abs(LL[k+1]));
+<span class="flyspell-duplicate">TestL</span>:=(abs(LL[k])==abs(LL[k+1]));
if(TestS==0){ if( TestL==1 ){l0:=l0}else{
A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;kk:=kk+1}}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=kk+1}}
-l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> <span class="flyspell-duplicate">etex</span>);
"};
@@ -521,29 +772,29 @@ TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))=
k0:= evalf(limite(f(x),x=Z[0],1))&gt; evalf(limite(f(x),x=Z[1],-1));
kz:=evalf(limite(f(x),x=Z[nz-1],-1))&gt; evalf(limite(f(x),x=Z[nz-2],1));
-lsi:="
+<span class="flyspell-duplicate">lsi</span>:="
newLigneSignes(btex <span class="font-latex-math">$\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$</span> etex);"+
if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
if(sign(fp((Z[0]+10^(-10))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
- if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex<span class="font-latex-math">$ $</span> etex);"+ if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "};
+ if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex<span class="font-latex-math">$ $</span> etex);"+ if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"}}<span class="flyspell-duplicate">else</span>{" "};
-if(nz&gt;2){rr:=1; if(nz==NL){for(r:=1; r&lt;=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+if(nz&gt;2){rr:=1; if(nz==NL){for(r:=1; r&lt;=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-<span class="flyspell-duplicate">ao</span>))==0.0);
ksp:=evalf(fp(Z[r]+0.01))&gt;0;
TestL:=(abs(LL[r])==abs(LL[r+1]));
lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex <span class="font-latex-math">$ $</span> etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "};
}}
-else{for(r:=1; r&lt;=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))&gt;0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+<span class="flyspell-duplicate">else</span>{for(r:=1; r&lt;=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))&gt;0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
TestL:=(abs(LL[r])==abs(LL[r+1]));
if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
- if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex <span class="font-latex-math">$ $</span> etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
- } else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
- if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
+ if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex <span class="font-latex-math">$ $</span> etex);"+if(<span class="flyspell-duplicate">kspp</span>==1){"plus;"}else{"moins;"};rr:=rr+1;}
+ } else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"nonDefBarre;"}+
+ if(kspp==1){"plus;"}else{"moins;"};rr:=<span class="flyspell-duplicate">rr</span>+1;}
}}
};
@@ -552,158 +803,448 @@ else{for(r:=1; r&lt;=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))&gt;0;TestS:=(sign(eva
lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;"}
lm0:=limite(f(x),x=Z[0],1)==-infinity;
-TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
+<span class="flyspell-duplicate">TestS</span>:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-<span class="flyspell-duplicate">ao</span>))==0.0);
li:="
newLigneVariations(btex <span class="font-latex-math">$\\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+"}}$</span> etex);
"+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}
else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}+
- if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}else{" "};
+ if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}<span class="flyspell-duplicate">else</span>{" "};
- if(nz&gt;2){if(nz==NL){for(r:=1; r&lt;=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+ if(nz&gt;2){if(nz==NL){for(r:=1; r&lt;=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-<span class="flyspell-duplicate">ao</span>))==0.0);
krm:=evalf(limite(f(x),x=Z[r-1],1))&lt; evalf(limite(f(x),x=Z[r],-1));
krp:=evalf(limite(f(x),x=Z[r],1))&gt; evalf(limite(f(x),x=Z[r+1],-1)) ;
- lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+ lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-<span class="flyspell-duplicate">infinity</span>;
lp:=lp+if(member(Z[r],F)) {
- "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}
else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span>
etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
<span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"
}else{" "};
};//for
-}else{rr:=1;for(r:=1; r&lt;=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+}else{rr:=1;for(r:=1; r&lt;=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(<span class="flyspell-duplicate">evalf</span>(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-<span class="flyspell-duplicate">ao</span>))==0.0);
krm:=evalf(limite(f(x),x=Z[rr-1],1))&lt; evalf(limite(f(x),x=Z[rr],-1));
- krp:=evalf(limite(f(x),x=Z[rr],1))&gt; evalf(limite(f(x),x=Z[rr+1],-1)) ;
+ krp:=evalf(limite(f(x),x=Z[rr],1))&gt; evalf(limite(f(x),x=Z[<span class="flyspell-duplicate">rr</span>+1],-1)) ;
lmrm:=limite(f(x),x=Z[rr],-1)==-infinity;lmrp:=limite(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
if(TestS==0){if( TestL==1 ){lp:=lp}else{ lp:=lp+if(member(Z[rr],F)) {
- "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}
else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[rr])))+"$</span>
- etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
+ etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[<span class="flyspell-duplicate">rr</span>]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
<span class="font-latex-math">$ "+ao+" $</span> etex,0.5);
";rr:=rr+1;
-}// else testL==1
+}// else <span class="flyspell-duplicate">testL</span>==1
}//testS==0
else{lp:=lp+if(member(Z[rr],F)){
"limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[rr])))+"$</span>
- etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+ etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);
"}}};rr:=rr+1;
}//else testS==0
}//for nz&lt;NL
-}// else nz&lt;NL
+}// else nz&lt;<span class="flyspell-duplicate">NL</span>
//if nz=NL
-};//if nz&gt;2
+};//if <span class="flyspell-duplicate">nz</span>&gt;2
lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
- lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+
+ lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+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)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"}+
if(kz==1){"1);"}else{"0);"};
-intro:="
+<span class="flyspell-duplicate">intro</span>:="
input tableauVariation;
-verbatimtex
+<span class="flyspell-duplicate">verbatimtex</span>
<span class="comment-delimiter">%</span><span class="comment">&amp;latex
</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span>
<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span>
<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span>
<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#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;
+ <span class="flyspell-duplicate">etex</span>;
";
-MetaL:= if(ftt==2){if(nz&gt;2){intro+"beginTableau("+nmr+")"+
+<span class="flyspell-duplicate">MetaL</span>:= if(ftt==2){if(nz&gt;2){intro+"beginTableau("+nmr+")"+
l0+lsi+lsp+lsf+"
endTableau;
end";}else{
-intro+"beginTableau("+nmr+")"+
+<span class="flyspell-duplicate">intro</span>+"beginTableau("+nmr+")"+
l0+
-lsi+lsf+"
+<span class="flyspell-duplicate">lsi</span>+lsf+"
endTableau;
-end";
+<span class="flyspell-duplicate">end</span>";
}
}else{
-if(ftt==0){if(nz&gt;2){intro+"beginTableau("+nmr+")"+
+if(ftt==0){if(nz&gt;2){intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
l0+
li+
lp+
-lf
+<span class="flyspell-duplicate">lf</span>
+"
endTableau;
-end";}else{intro+"beginTableau("+nmr+")"+
+<span class="flyspell-duplicate">end</span>";}else{intro+"beginTableau("+nmr+")"+
l0+
li+
-lf
+<span class="flyspell-duplicate">lf</span>
+"
endTableau;
-end";}}else{
+<span class="flyspell-duplicate">end</span>";}}else{
if(nz&gt;2){intro+"beginTableau("+nmr+")"+
l0+
lsi+lsp+lsf+
li+
lp+
-lf
+<span class="flyspell-duplicate">lf</span>
+"
endTableau;
-end";}else{intro+"beginTableau("+nmr+")"+
+end";}else{intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
l0+
lsi+lsf+
li+
lf
+"
endTableau;
-end";}
+<span class="flyspell-duplicate">end</span>";}
}};
MetaLfc:= if(ftt==2){if(nz&gt;2){"beginTableau("+nmr+")"+
l0+lsi+lsp+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
";}else{
"beginTableau("+nmr+")"+
l0+
lsi+lsf+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
";
}
}else{
-if(ftt==0){if(nz&gt;2){"beginTableau("+nmr+")"+
+if(ftt==0){if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
l0+
li+
-lp+
+<span class="flyspell-duplicate">lp</span>+
lf
+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
-";}else{"beginTableau("+nmr+")"+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
l0+
li+
lf
+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
";}}else{
if(nz&gt;2){"beginTableau("+nmr+")"+
l0+
+<span class="flyspell-duplicate">lsi</span>+lsp+lsf+
+li+
+<span class="flyspell-duplicate">lp</span>+
+<span class="flyspell-duplicate">lf</span>
++"
+endTableau;
+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+lsi+lsf+
+li+
+lf
++"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}
+}};
+
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+<span class="flyspell-duplicate">fclose</span>(sortie);
+
+
+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="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,<span class="flyspell-duplicate">nmr</span>):={
+
+
+<span class="flyspell-duplicate">nl</span>:=size(L);
+f:=unapply(f,x);
+fp:=fonction_derivee(f);
+z0:=concat(L,F);z:=sort(z0);
+nz:=size(z);
+if(L==[-infinity,+infinity]){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..100);}
+else{if(L[0]==-infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..L[1]);}
+else{if(L[1]==+infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=L[0]..100);}
+else{S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=z[0]..z[nz-1])}}};
+si size(S)&gt;0 alors pour j de 0 jusque size(S)-1 faire
+ kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])&gt;=L[0]) and (evalf(S[j])&lt;=L[1]);
+ if(kk==1){if(kok==1){z:=append(z,simplifier(S[j]))}};
+ fpour;
+<span class="flyspell-duplicate">fsi</span>;
+
+
+S:=NULL;
+S:=S,z[0];
+for(j:=1;j&lt;size(z);j++){
+ if(z[j]!=undef and (abs(z[j])&gt;1e-15 or z[j]==0)){
+ S:=S,z[j]};
+}
+z:=[S];
+
+
+
+Z:=sort(z);
+nz:=size(Z);
+
+S:=<span class="flyspell-duplicate">NULL</span>;
+S:=S,Z[0];
+for(j:=1;j&lt;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+"$</span> etex);";lp:=" "; lf:=" ";<span class="flyspell-duplicate">lsp</span>:=" ";
+
+
+
+LI:=limite(f(x),x,Z[0],1);
+LF:=limite(f(x),x,Z[nz-1],-1);
+<span class="flyspell-duplicate">LP</span>:=NULL;
+if(nz&gt;2){ for(r:=1; r&lt;=nz-2;r++){LP:=LP,if(member(Z[r],F)){limite(f(x),x,Z[r],-1),limite(f(x),x,Z[r],1)}else{f(Z[r])}}};
+if(nz&gt;2){ LL:=[LI,LP,LF]}else{LL:=[LI,<span class="flyspell-duplicate">LF</span>]};
+
+NL:=size(LL);
+A:=NULL;aa:=1;<span class="flyspell-duplicate">kk</span>:=0;
+
+if(NL==nz){for(k:=0;k&lt;nz-1;k++){<span class="flyspell-duplicate">TestS</span>:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
+if(TestS==0){A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"}}
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> <span class="flyspell-duplicate">etex</span>);"};
+
+if(NL&gt;nz){for(k:=0;k&lt;NL-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
+<span class="flyspell-duplicate">TestL</span>:=(abs(LL[k])==abs(LL[k+1]));
+if(TestS==0){ if( TestL==1 ){l0:=l0}else{
+A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;kk:=<span class="flyspell-duplicate">kk</span>+1}}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=kk+1}}
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> <span class="flyspell-duplicate">etex</span>);
+"};
+
+
+
+<span class="flyspell-duplicate">TestS</span>:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-<span class="flyspell-duplicate">ao</span>))==0.0);
+ k0:= evalf(limite(f(x),x=Z[0],1))&gt; evalf(limite(f(x),x=Z[1],-1));
+ kz:=evalf(limite(f(x),x=Z[nz-1],-1))&gt; evalf(limite(f(x),x=Z[nz-2],1));
+
+lsi:="
+<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$</span> etex);"+
+ if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}<span class="flyspell-duplicate">else</span>{"moins;"}}else{if(member(Z[0],F)==0){
+ if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+ if(sign(fp((Z[0]+10^(-10))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
+ if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex<span class="font-latex-math">$ $</span> etex);"+ if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"}}<span class="flyspell-duplicate">else</span>{" "};
+
+
+
+
+
+if(nz&gt;2){rr:=1; if(nz==NL){for(r:=1; r&lt;=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-<span class="flyspell-duplicate">ao</span>))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+ ksp:=evalf(fp(Z[r]+0.01))&gt;0;
+ TestL:=(abs(LL[r])==abs(LL[r+1]));
+ lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+
+ if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex <span class="font-latex-math">$ $</span> etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}<span class="flyspell-duplicate">else</span>{" "};
+ }}
+else{for(r:=1; r&lt;=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))&gt;0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+ TestL:=(abs(LL[r])==abs(LL[r+1]));
+ if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+ if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex <span class="font-latex-math">$ $</span> etex);"+if(<span class="flyspell-duplicate">kspp</span>==1){"plus;"}else{"moins;"};rr:=rr+1;}
+ } else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+
+ if(kspp==1){"plus;"}else{"moins;"};rr:=<span class="flyspell-duplicate">rr</span>+1;}
+}}
+ };
+
+
+
+<span class="flyspell-duplicate">lsf</span>:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;"}
+lm0:=limite(f(x),x=Z[0],1)==-infinity;
+
+<span class="flyspell-duplicate">TestS</span>:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-<span class="flyspell-duplicate">ao</span>))==0.0);
+
+ li:="
+newLigneVariations(btex <span class="font-latex-math">$\\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+"}}$</span> etex);
+"+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}
+ else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"}+
+ if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}<span class="flyspell-duplicate">else</span>{" "};
+
+
+ if(nz&gt;2){if(nz==NL){for(r:=1; r&lt;=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(<span class="flyspell-duplicate">evalf</span>(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+ krm:=evalf(limite(f(x),x=Z[r-1],1))&lt; evalf(limite(f(x),x=Z[r],-1));
+ krp:=evalf(limite(f(x),x=Z[r],1))&gt; evalf(limite(f(x),x=Z[r+1],-1)) ;
+ lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+ lp:=lp+if(member(Z[r],F)) {
+ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}
+ else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span>
+ etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(<span class="flyspell-duplicate">btex</span>
+ <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"
+ }else{" "};
+};//for
+}else{rr:=1;for(r:=1; r&lt;=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+ krm:=evalf(limite(f(x),x=Z[rr-1],1))&lt; evalf(limite(f(x),x=Z[rr],-1));
+ krp:=evalf(limite(f(x),x=Z[rr],1))&gt; evalf(limite(f(x),x=Z[<span class="flyspell-duplicate">rr</span>+1],-1)) ;
+ lmrm:=limite(f(x),x=Z[rr],-1)==-infinity;lmrp:=limite(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
+if(TestS==0){if( TestL==1 ){lp:=lp}else{ lp:=lp+if(member(Z[rr],F)) {
+ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}
+ else{"valPos(btex <span class="font-latex-math">$"+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+" $</span> etex,0.5);
+ ";rr:=rr+1;
+}// else <span class="flyspell-duplicate">testL</span>==1
+}//testS==0
+else{lp:=lp+if(member(Z[rr],F)){
+ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}}
+ else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[rr])))+"$</span>
+ etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);
+ "}}};rr:=<span class="flyspell-duplicate">rr</span>+1;
+}//else testS==0
+}//for nz&lt;NL
+}// else nz&lt;<span class="flyspell-duplicate">NL</span>
+//if nz=NL
+};//if <span class="flyspell-duplicate">nz</span>&gt;2
+
+
+lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
+ lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+
+ if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"};
+
+
+
+<span class="flyspell-duplicate">intro</span>:="
+input tableauVariation;
+<span class="flyspell-duplicate">verbatimtex</span>
+<span class="comment-delimiter">%</span><span class="comment">&amp;latex
+</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span>
+ <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#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>;
+
+";
+
+
+MetaL:= if(ftt==2){if(nz&gt;2){intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+lsi+lsp+lsf+"
+endTableau;
+end";}else{
+<span class="flyspell-duplicate">intro</span>+"beginTableau("+nmr+")"+
+ l0+
+lsi+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
+<span class="flyspell-duplicate">end</span>";
+}
+}else{
+if(ftt==0){if(nz&gt;2){intro+"beginTableau("+nmr+")"+
+ l0+
+li+
+lp+
+<span class="flyspell-duplicate">lf</span>
++"
+endTableau;
+end";}else{intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+li+
+<span class="flyspell-duplicate">lf</span>
++"
+endTableau;
+end";}}else{
+if(nz&gt;2){intro+"beginTableau("+nmr+")"+
+ l0+
lsi+lsp+lsf+
li+
lp+
-lf
+<span class="flyspell-duplicate">lf</span>
+"
endTableau;
+end";}else{intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+lsi+lsf+
+li+
+<span class="flyspell-duplicate">lf</span>
++"
+endTableau;
+<span class="flyspell-duplicate">end</span>";}
+}};
+
+
+MetaLfc:= if(ftt==2){if(nz&gt;2){"beginTableau("+nmr+")"+
+ l0+lsi+lsp+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}<span class="flyspell-duplicate">else</span>{
+"beginTableau("+nmr+")"+
+ l0+
+lsi+lsf+"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";
+}
+}else{
+if(ftt==0){if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+li+
+lp+
+<span class="flyspell-duplicate">lf</span>
++"
+<span class="flyspell-duplicate">endTableau</span>;
";}else{"beginTableau("+nmr+")"+
l0+
-lsi+lsf+
li+
lf
+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
+";}}else{
+if(nz&gt;2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+lsi+lsp+lsf+
+li+
+<span class="flyspell-duplicate">lp</span>+
+lf
++"
+<span class="flyspell-duplicate">endTableau</span>;
+
+";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+
+ l0+
+lsi+lsf+
+li+
+<span class="flyspell-duplicate">lf</span>
++"
+<span class="flyspell-duplicate">endTableau</span>;
";}
}};
@@ -715,7 +1256,7 @@ fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);
-return(MetaL);
+<span class="flyspell-duplicate">return</span>(<span class="flyspell-duplicate">MetaL</span>);
}:;
@@ -724,6 +1265,16 @@ return(MetaL);
+
+
+
+
+
+
+
+
+
+
<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">
@@ -734,7 +1285,7 @@ return(MetaL);
<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignL.cxx}
-TS(L,D,nmr):={
+<span class="flyspell-duplicate">TS</span>(L,D,nmr):={
L:=apply(f-&gt;unapply(f,x),L)
n:=size(L);
Z:=NULL;
@@ -754,7 +1305,7 @@ if(nz&gt;2){pour u de 1 jusque nz-2 faire
si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1;
fsi;
fpour;};
-nz:=size(Z);
+<span class="flyspell-duplicate">nz</span>:=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])+"$</span> etex);";
for(p:=0;p&lt;=n-1;p++){li:=li+"
@@ -763,14 +1314,14 @@ if(mini!=-infinity and L[p](mini)==0){"
valBarre(btex 0 etex);"}else{"
"}+
if(L[p]((mini+maxi)*0.5&gt;0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){"
- valBarre(btex 0 etex);"}else{"
+ valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
"}
}
lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)&gt;0){"plus;"}else{"moins;"};
MetaL:=" input tableauVariation;
- verbatimtex
+ <span class="flyspell-duplicate">verbatimtex</span>
<span class="comment-delimiter">%</span><span class="comment">&amp;latex
</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span>
<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span>
@@ -788,14 +1339,14 @@ newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex
valBarre(btex 0 etex);"}else{"
"}+ lf+
if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
- valBarre(btex 0 etex);"}else{"
+ valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
"}+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
end"
;
-MetaLfc:=" beginTableau("+nmr+")
+<span class="flyspell-duplicate">MetaLfc</span>:=" beginTableau("+nmr+")
newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
"+l0+li+
"
@@ -806,7 +1357,7 @@ newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex
if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
valBarre(btex 0 etex);"}else{"
"}+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
"
;
@@ -818,11 +1369,11 @@ pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+
l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);";
-for(p:=0;p&lt;=n-1;p++){lp:="";
+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(mini!=-infinity and L[p](mini)==0){"
- valBarre(btex 0 etex);"}else{"
+ valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
"}+
if(L[p](Z[0]-0.01)&gt;0){"plus;"}else{"moins;"};
@@ -835,7 +1386,7 @@ newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="f
li:=li+lp+ if(simplifier(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+
if(L[p](Z[nz-1]+1.0)&gt;0){"plus;"}else{"moins;
"}+if(maxi!=+infinity and L[p](maxi)==0){"
- valBarre(btex 0 etex);"}else{"
+ valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
"}
};
@@ -852,7 +1403,7 @@ MetaL:=" input tableauVariation;
<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span>
<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>}
<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span>
- etex;
+ <span class="flyspell-duplicate">etex</span>;
beginTableau("+nmr+")
newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
"+l0+
@@ -863,37 +1414,37 @@ newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex
if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){"
valBarre(btex 0 etex);"}else{"
"}+
- if(product(L[s](Z[0]-0.01),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"+
+ if(product(L[s](Z[0]-0.01),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"+
lr+
if(product(L[s](Z[nz-1]+0.01),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+
if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
valBarre(btex 0 etex);"}else{"
"}+"
endTableau;
-end"
+<span class="flyspell-duplicate">end</span>"
;
MetaLfc:=" beginTableau("+nmr+")
-newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
+<span class="flyspell-duplicate">newLigneVariables</span>(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
"+l0+
li
+
"
newLigneSignes(btex <span class="font-latex-math">$\\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}}$</span> etex);"+
if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){"
- valBarre(btex 0 etex);"}else{"
+ valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
"}+
if(product(L[s](Z[0]-0.01),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"+
lr+
if(product(L[s](Z[nz-1]+0.01),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+
if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
- valBarre(btex 0 etex);"}else{"
+ valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
"}+"
endTableau;
";
}
sortie:=fopen("XCasmpfc.mp");
-fprint(sortie,Unquoted,MetaLfc);
+<span class="flyspell-duplicate">fprint</span>(sortie,Unquoted,MetaLfc);
fclose(sortie);
return(MetaL);
}:;
@@ -910,7 +1461,7 @@ return(MetaL);
<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignQ.cxx}
-TSq(nomf,L,Fo,D,nmr):={
+<span class="flyspell-duplicate">TSq</span>(nomf,L,Fo,D,nmr):={
L:=apply(f-&gt;unapply(f,x),L);
Fo:=apply(f-&gt;unapply(f,x),Fo);
L:=concat(L,Fo);
@@ -927,7 +1478,7 @@ pour k de 0 jusque n-1 faire
if(S[j]&gt;mini and S[j]&lt;maxi){Z:=Z,simplifier(S[j]);}
fpour;
fsi;
-fpour;
+<span class="flyspell-duplicate">fpour</span>;
pour k de 0 jusque m-1 faire
@@ -946,31 +1497,31 @@ nz:=size(Z);
if(nz&gt;2){pour u de 1 jusque nz-2 faire
si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1; // pour les z&#233;ros en double
fsi;
-fpour;}
+<span class="flyspell-duplicate">fpour</span>;}
Z:=sort(Z);
nz:=size(Z);
if(nz&gt;2){pour u de 1 jusque nz-2 faire
- si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1;
+ si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=<span class="flyspell-duplicate">nz</span>-1;
fsi;
fpour;};
nz:=size(Z);
-if(nz==0){li:="";l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);";
+if(nz==0){li:="";l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> <span class="flyspell-duplicate">etex</span>);";
for(p:=0;p&lt;=n-1;p++){li:=li+"
-newLigneSignes(btex <span class="font-latex-math">$\\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))+"}}$</span> etex);"+
+<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\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))+"}}$</span> <span class="flyspell-duplicate">etex</span>);"+
if(mini!=-infinity and L[p](mini)==0){"
valBarre(btex 0 etex);"}else{"
"}+
-if(L[p]((mini+maxi)*0.5&gt;0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){"
+if(L[p]((mini+maxi)*0.5&gt;0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](<span class="flyspell-duplicate">maxi</span>)==0){"
valBarre(btex 0 etex);"}else{"
"}
}
lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)&gt;0){"plus;"}else{"moins;"};
-MetaL:=" input tableauVariation;
+<span class="flyspell-duplicate">MetaL</span>:=" input tableauVariation;
verbatimtex
<span class="comment-delimiter">%</span><span class="comment">&amp;latex
</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span>
@@ -981,25 +1532,25 @@ MetaL:=" input tableauVariation;
etex;
beginTableau("+nmr+")
-newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
+newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> <span class="flyspell-duplicate">etex</span>);
"+l0+li+
"
newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe }\\atop{{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> de "+nomf+"(x)}}$</span> etex);"+
if(member(mini,FF)==0){if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){"
valBarre(btex 0 etex);"}else{"
- "}}else{"nonDefBarre;"}+ lf+
+ "}}else{"nonDefBarre;"}+ <span class="flyspell-duplicate">lf</span>+
if(member(maxi,FF)==0){if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
valBarre(btex 0 etex);"}else{"
"}}else{"nonDefBarre;"}+"
endTableau;
-end"
+<span class="flyspell-duplicate">end</span>"
;
MetaLfc:="
-beginTableau("+nmr+")
+<span class="flyspell-duplicate">beginTableau</span>("+nmr+")
newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
"+l0+li+
"
@@ -1010,7 +1561,7 @@ newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex
if(member(maxi,FF)==0){if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
valBarre(btex 0 etex);"}else{"
"}}else{"nonDefBarre;"}+"
-endTableau;
+<span class="flyspell-duplicate">endTableau</span>;
"
;
@@ -1018,20 +1569,20 @@ endTableau;
-}else{
+}<span class="flyspell-duplicate">else</span>{
l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);";li:=" ";lr:=" ";
pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);
";fpour;
-l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);";
+l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> <span class="flyspell-duplicate">etex</span>);";
-for(p:=0;p&lt;=n-1;p++){lp:="";
+for(p:=0;p&lt;=n-1;p++){<span class="flyspell-duplicate">lp</span>:="";
li:=li+"
newLigneSignes(btex <span class="font-latex-math">$\\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))+"}}$</span> etex);"+
if(mini!=-infinity and L[p](mini)==0){"
- valBarre(btex 0 etex);"}else{"
+ valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
"}+
if(L[p](Z[0]-0.01)&gt;0){"plus;"}else{"moins;"};
@@ -1044,7 +1595,7 @@ newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="f
li:=li+lp+ 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;
"}+if(maxi!=+infinity and L[p](maxi)==0){"
- valBarre(btex 0 etex);"}else{" "}
+ valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" "}
};
@@ -1054,8 +1605,8 @@ pour t de 0 jusque nz-2 faire
if(member(Z[t+1],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"}
fpour
-MetaL:=" input tableauVariation;
-verbatimtex
+<span class="flyspell-duplicate">MetaL</span>:=" input tableauVariation;
+<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>
@@ -1069,9 +1620,9 @@ newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex
li
+
"
- newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe }\\atop{{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> de"+nomf+"(x)}}$</span> etex);"+
+ newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de}\\atop{{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> "+nomf+"(x)}}$</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{"
+ valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
"}}else{"nonDefBarre;"}+
if(product(L[s](Z[0]-0.01),s,0,n-1)&gt;0){"plus;"}else{"moins;"}+
if(member(Z[0],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"}+
@@ -1079,8 +1630,8 @@ newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex
if(product(L[s](Z[nz-1]+0.01),s,0,n-1)&gt;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;
-end"
+<span class="flyspell-duplicate">endTableau</span>;
+<span class="flyspell-duplicate">end</span>"
;
@@ -1088,22 +1639,22 @@ end"
MetaLfc:="
beginTableau("+nmr+")
-newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
+newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> <span class="flyspell-duplicate">etex</span>);
"+l0+
li
+
"
- newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe }\\atop{{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> de"+nomf+"(x)}}$</span> etex);"+
+ newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de}\\atop{{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> "+nomf+"(x)}}$</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;"}+
+ "}}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+
if(product(L[s](Z[0]-0.01),s,0,n-1)&gt;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)&gt;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;
+<span class="flyspell-duplicate">endTableau</span>;
"
@@ -1114,14 +1665,14 @@ endTableau;
sortie:=fopen("XCasmpfc.mp");
-fprint(sortie,Unquoted,MetaLfc);
+<span class="flyspell-duplicate">fprint</span>(sortie,Unquoted,MetaLfc);
fclose(sortie);
-return(MetaL);
+return(<span class="flyspell-duplicate">MetaL</span>);
}:;
<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
@@ -1137,13 +1688,13 @@ return(MetaL);
<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSign.cxx}
-TSa(a,b,c,d,nmr):={
-zA:=resoudre(a*x+b=0,x)[0];
+<span class="flyspell-duplicate">TSa</span>(a,b,c,d,nmr):={
+<span class="flyspell-duplicate">zA</span>:=resoudre(a*x+b=0,x)[0];
zB:=resoudre(c*x+d=0,x)[0];
zmin:=min(zA,zB);
-zmax:=max(zA,zB);
+zmax:=max(zA,<span class="flyspell-duplicate">zB</span>);
Meta:= " input tableauVariation;
- verbatimtex
+ <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>
@@ -1155,12 +1706,12 @@ zmax:=max(zA,zB);
newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</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);
+val(btex <span class="font-latex-math">$+\\infty$</span> <span class="flyspell-duplicate">etex</span>);
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> etex);"
+ 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;"; 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;"}
+"
@@ -1169,20 +1720,20 @@ newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="f
if(zmin==zB){"valBarre(btex 0 etex);"}else{"barre;"}+
if(zmin==zB){si c&gt;0 alors "plus;"; sinon "moins;";fsi}
else{si c&gt;0 alors "moins;"; sinon "plus;"; fsi}+
- if(zmin==zB){"barre;"}else{"valBarre(btex 0 etex);"}+
+ if(zmin==zB){"barre;"}else{"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"}+
if(c&gt;0){"plus;"}else{"moins;"}
+"
newLigneSignes(btex <span class="font-latex-math">$\\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> etex);"
- + si a*c&gt;0 alors plus; sinon moins;fsi+";"+
+ + si a*c&gt;0 alors plus; sinon moins;<span class="flyspell-duplicate">fsi</span>+";"+
"valBarre(btex 0 etex);"+
- si a*c&gt;0 alors moins; sinon plus;fsi+";"+
+ si a*c&gt;0 alors moins; sinon plus;<span class="flyspell-duplicate">fsi</span>+";"+
"valBarre(btex 0 etex);"+
si a*c&gt;0 alors plus; sinon moins;fsi+";"+"
endTableau;
-end"
+<span class="flyspell-duplicate">end</span>"
;
-return(Meta);
+return(<span class="flyspell-duplicate">Meta</span>);
}:;
<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
@@ -1198,8 +1749,8 @@ return(Meta);
-<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{<span class="flyspell-duplicate">XcasTSc</span>.<span class="flyspell-duplicate">cxx</span>}
-TSc(g,D,nmr):={
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{<span class="flyspell-duplicate">XcasTSc</span>.cxx}
+<span class="flyspell-duplicate">TSc</span>(g,D,nmr):={
f:=unapply(g,x);
Z:=NULL;
mini:=D[0]; maxi:=D[1];lm:=" ";
@@ -1210,13 +1761,13 @@ li:=if(mini!=-infinity and f(mini)==0){"
valBarre(btex 0 etex);"}else{"
"}+
if(mini!=-infinity or maxi!=+infinity){if(f((mini+maxi)*0.5&gt;0)){"plus;"}else{"moins;"}}else{if(f(0)&gt;0){"plus;"}else{"moins;"}};
-lf:=if(maxi!=+infinity and f(maxi)==0){"
- valBarre(btex 0 etex);"}else{"
+<span class="flyspell-duplicate">lf</span>:=if(maxi!=+infinity and f(maxi)==0){"
+ valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
"};
}
else{pour j de 0 jusque size(S)-1 faire
if(S[j]&gt;mini and S[j]&lt;maxi){Z:=Z,simplifier(S[j])};
- fpour;
+ <span class="flyspell-duplicate">fpour</span>;
Z:=sort(Z);
@@ -1224,7 +1775,7 @@ nz:=size(Z);
if(nz&gt;2){pour u de 1 jusque nz-2 faire
si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1;
fsi;
-fpour;}
+<span class="flyspell-duplicate">fpour</span>;}
nz:=size(Z);
@@ -1234,32 +1785,32 @@ li:=if(mini!=-infinity and f(mini)==0){"
valBarre(btex 0 etex);"}else{"
"}+
if(f((mini+maxi)*0.5&gt;0)){"plus;"}else{"moins;"};
-lf:=if(maxi!=+infinity and f(maxi)==0){"
+<span class="flyspell-duplicate">lf</span>:=if(maxi!=+infinity and f(maxi)==0){"
valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
"};
}else{
l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);";li:=" ";
-pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> <span class="flyspell-duplicate">etex</span>);
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex);
";
-fpour;
+<span class="flyspell-duplicate">fpour</span>;
l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);";
li:= if(mini!=-infinity and f(mini)==0){"
valBarre(btex 0 etex);"}else{"
"}+
-if(f(Z[0]-0.01)&gt;0){"plus;"}else{"moins;"}+"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);";
+if(f(Z[0]-0.01)&gt;0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);";
lm:=if(nz&gt;=2){for(r:=0; r&lt;=nz-2;r++){lm:=lm+if(f((Z[r]+Z[r+1])*.5)&gt;0){"plus;"}else{"moins;"}+
"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"
- }}<span class="flyspell-duplicate">else</span>{" "};
+ }}else{" "};
-lf:=if(f(Z[nz-1]+1.0)&gt;0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
+<span class="flyspell-duplicate">lf</span>:=if(f(Z[nz-1]+1.0)&gt;0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{"
"};
}};
-MetaL:=" input tableauVariation;
+<span class="flyspell-duplicate">MetaL</span>:=" input tableauVariation;
verbatimtex
<span class="comment-delimiter">%</span><span class="comment">&amp;latex
</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span>
@@ -1269,7 +1820,7 @@ MetaL:=" input tableauVariation;
<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span>
etex;
beginTableau("+nmr+")
-newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
+<span class="flyspell-duplicate">newLigneVariables</span>(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
"+l0+"
<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\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(f(x))+"}}$</span> etex);"+
li+lm+lf
@@ -1279,10 +1830,10 @@ endTableau;
;
-<span class="flyspell-duplicate">MetaLfc</span>:="
+MetaLfc:="
-beginTableau("+nmr+")
-newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex);
+<span class="flyspell-duplicate">beginTableau</span>("+nmr+")
+newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> <span class="flyspell-duplicate">etex</span>);
"+l0+"
newLigneSignes(btex <span class="font-latex-math">$\\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(f(x))+"}}$</span> etex);"+
li+lm+lf
@@ -1302,7 +1853,7 @@ fclose(sortie);
-<span class="flyspell-duplicate">return</span>(<span class="flyspell-duplicate">MetaL</span>);
+return(MetaL);
}:;
<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
@@ -1328,19 +1879,19 @@ fclose(sortie);
</span> <span class="comment">% exporter le source mp
</span> <span class="comment">% puis lancer metapost pour cr&#233;er
</span> <span class="comment">% l'image du tableau
-</span> <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab.mp}
+</span> <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> XCasmpfc.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab.<span class="flyspell-duplicate">mp</span>}
<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost -interaction=batchmode -jobname=<span class="font-latex-sedate">\Tableaux</span>.Tab XCasmp#1}}<span class="comment">%
</span> {<span class="comment">% sinon, si le tableau est absent, alerte.
</span> <span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\Tableaux</span>.Tab.<span class="font-latex-sedate">\theTVn</span>}{}{<span class="comment">%
</span> <span class="font-latex-sedate">\PackageError</span>{tablor}{Tableau absent non
reconstituable.}{Pour compiler il faut, soit les fichiers de
tableaux, soit le fichier <span class="font-latex-sedate">\Tableaux</span>.Tab.mp, soit disposer de
- XCas.}}}
+ <span class="flyspell-duplicate">XCas</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="font-latex-sedate">\Tableaux</span>.Tab.<span class="font-latex-sedate">\theTVn</span>}
<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span>
-<span class="font-latex-sedate">\stepcounter</span>{TVn}}
+<span class="font-latex-sedate">\stepcounter</span>{<span class="flyspell-duplicate">TVn</span>}}
<span class="comment-delimiter">%%</span><span class="comment">
@@ -1353,21 +1904,22 @@ fclose(sortie);
<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\dressetoile</span></span><span class="function-name">}</span>[1]{<span class="comment">%
</span><span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\Tableaux</span>.Tab.<span class="font-latex-sedate">\theTVn</span>}{<span class="comment">% Test sur l'existence du tableau
</span><span class="comment-delimiter">% </span><span class="comment">Si oui, inclusion du fichier source de sauvegarde mp dans Tableaux
-</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> TSav-<span class="font-latex-sedate">\theTVn</span>.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab.mp}}
+</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cat</span> <span class="flyspell-duplicate">TSav</span>-<span class="font-latex-sedate">\theTVn</span>.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab.mp}}
<span class="comment-delimiter">% </span><span class="comment">Si non, lancement des op&#233;rations de fabrication
</span>{<span class="font-latex-sedate">\executGiacmp</span>{XCas#1.giac}<span class="comment">%
</span><span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\editeur</span> XCasmpfc.mp}
<span class="comment">% Modification avec l'&#233;diteur choisi
</span>
-<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cp</span> -f XCasmpfc.mp TSav-<span class="font-latex-sedate">\theTVn</span>.mp} <span class="comment">% Sauvegarde du
+<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cp</span> -f XCasmpfc.mp <span class="flyspell-duplicate">TSav</span>-<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 ult&#233;rieure 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> XCasmpfc.mp &gt;&gt; <span class="font-latex-sedate">\Tableaux</span>.Tab.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{mpost -interaction=batchmode <span class="font-latex-sedate">\Tableaux</span>.Tab}<span class="comment">% Reconstitution des tableaux
+</span>
+<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost -interaction=batchmode <span class="font-latex-sedate">\Tableaux</span>.Tab}<span class="comment">% Reconstitution des tableaux
</span> <span class="comment">% et cr&#233;ation du dernier. L'option
</span> <span class="comment">% pallie l'absence de end en fin de
</span> <span class="comment">% fichier
@@ -1376,7 +1928,7 @@ fclose(sortie);
<span class="font-latex-sedate">\includegraphics</span>{<span class="font-latex-sedate">\Tableaux</span>.Tab.<span class="font-latex-sedate">\theTVn</span>}
<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span>
-<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVnbis</span></span><span class="variable-name">}</span> <span class="comment">% Restauration du compteur TVn
+<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVnbis</span></span><span class="variable-name">}</span> <span class="comment">% Restauration du compteur </span><span class="comment"><span class="flyspell-duplicate">TVn</span></span><span class="comment">
</span>}
@@ -1389,7 +1941,7 @@ fclose(sortie);
</span><span class="comment-delimiter">%%</span><span class="comment">
</span><span class="comment-delimiter">%%%</span><span class="comment">
</span><span class="comment-delimiter">%%%</span><span class="comment">
-</span><span class="comment-delimiter">%%% </span><span class="comment">les "giac" qui permettent d'ex&#233;cuter la commande rentr&#233;e dans le fichier tex
+</span><span class="comment-delimiter">%%% </span><span class="comment">les "giac" qui permettent d'ex&#233;cuter la commande rentr&#233;e dans le fichier </span><span class="comment"><span class="flyspell-duplicate">tex</span></span><span class="comment">
</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 &#233;toil&#233;es permettent de modifier le code metapost produit initialement
</span><span class="comment-delimiter">%%%</span><span class="comment">
@@ -1398,21 +1950,21 @@ fclose(sortie);
<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCas.giac}
-maple_mode(0);
+<span class="flyspell-duplicate">maple</span>_mode(0);
read("XcasTabSign.cxx");
-Sortie:=fopen("XCasmp.mp");
+Sortie:=fopen("XCasmp.<span class="flyspell-duplicate">mp</span>");
vect.xcas.user := read("XCas.user");
-vxo := vect.xcas.user;
+<span class="flyspell-duplicate">vxo</span> := vect.xcas.user;
dim.vxo := dim(vxo);
-nbr.line.vxo := dim.vxo;
+<span class="flyspell-duplicate">nbr</span>.line.vxo := dim.vxo;
Resultat:=cat(" ");
-rslt := vxo[0]; RslT:=cat(rslt);
+<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt);
Resultat:=cat(Resultat,RslT);
-fprint(Sortie,Unquoted,Resultat);
+<span class="flyspell-duplicate">fprint</span>(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">{TSa}</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">TSa</span></span><span class="function-name">}</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>&#163;&#181;]{XCas.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>{}
@@ -1428,48 +1980,48 @@ fclose(Sortie);
<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasQ.giac}
maple_mode(0);
-read("XcasTabSignQ.cxx");
+<span class="flyspell-duplicate">read</span>("XcasTabSignQ.cxx");
Sortie:=fopen("XCasmpQ.mp");
-vect.xcas.user := read("XCasQ.user");
-vxo := vect.xcas.user;
-dim.vxo := dim(vxo);
+<span class="flyspell-duplicate">vect</span>.xcas.user := read("XCasQ.user");
+<span class="flyspell-duplicate">vxo</span> := vect.xcas.user;
+<span class="flyspell-duplicate">dim</span>.vxo := dim(vxo);
nbr.line.vxo := dim.vxo;
-Resultat:=cat(" ");
+<span class="flyspell-duplicate">Resultat</span>:=cat(" ");
rslt := vxo[0]; RslT:=cat(rslt);
-Resultat:=cat(Resultat,RslT);
+<span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,RslT);
fprint(Sortie,Unquoted,Resultat);
-fclose(Sortie);
+<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">{TSq}</span><span class="comment">%
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TSq</span></span><span class="function-name">}</span><span class="comment">%
</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>&#163;&#181;]{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>{Q}}
-<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSq*}</span>[1]<span class="comment">%
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TSq</span></span><span class="function-name">*}</span>[1]<span class="comment">%
</span>{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
-<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
+<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{</span><span class="variable-name"><span class="flyspell-duplicate">TVn</span></span><span class="variable-name">}{#1}</span>
<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>&#163;&#181;]{XCasQ.user}}
{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{Q}}
<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasL.giac}
maple_mode(0);
-read("XcasTabSignL.cxx");
+<span class="flyspell-duplicate">read</span>("XcasTabSignL.cxx");
Sortie:=fopen("XCasmpL.mp");
-vect.xcas.user := read("XCasL.user");
+<span class="flyspell-duplicate">vect</span>.xcas.user := read("XCasL.user");
vxo := vect.xcas.user;
-dim.vxo := dim(vxo);
-nbr.line.vxo := dim.vxo;
-Resultat:=cat(" ");
+<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(" ");
rslt := vxo[0]; RslT:=cat(rslt);
-Resultat:=cat(Resultat,RslT);
+<span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,RslT);
fprint(Sortie,Unquoted,Resultat);
-fclose(Sortie);
+<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">{TS}</span><span class="comment">%
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TS</span></span><span class="function-name">}</span><span class="comment">%
</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>&#163;&#181;]{XCasL.user}}
{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{L}}
@@ -1482,60 +2034,101 @@ fclose(Sortie);
<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTSc.giac}
-maple_mode(0);
+<span class="flyspell-duplicate">maple</span>_mode(0);
read("XcasTSc.cxx");
Sortie:=fopen("XCasmpTSc.mp");
vect.xcas.user := read("XCasTSc.user");
-vxo := vect.xcas.user;
+<span class="flyspell-duplicate">vxo</span> := vect.xcas.user;
dim.vxo := dim(vxo);
-nbr.line.vxo := dim.vxo;
+<span class="flyspell-duplicate">nbr</span>.line.vxo := dim.vxo;
Resultat:=cat(" ");
-rslt := vxo[0]; RslT:=cat(rslt);
+<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt);
Resultat:=cat(Resultat,RslT);
-fprint(Sortie,Unquoted,Resultat);
+<span class="flyspell-duplicate">fprint</span>(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">{TSc*}</span>[1]<span class="comment">%
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TSc</span></span><span class="function-name">*}</span>[1]<span class="comment">%
</span>{<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
-<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
+<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{</span><span class="variable-name"><span class="flyspell-duplicate">TVn</span></span><span class="variable-name">}{#1}</span>
<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>&#163;&#181;]{XCasTSc.user}}
-{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{TSc}}
+{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="flyspell-duplicate">TSc</span>}}
<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSc}</span><span class="comment">%
</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>&#163;&#181;]{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>{TSc}}
+{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{<span class="flyspell-duplicate">TSc</span>}}
<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTV.giac}
-maple_mode(0);
+<span class="flyspell-duplicate">maple</span>_mode(0);
read("XcasTV.cxx");
Sortie:=fopen("XCasmpTV.mp");
-vect.xcas.user := read("XCasTV.user");
-vxo := vect.xcas.user;
+<span class="flyspell-duplicate">vect</span>.xcas.user := read("XCasTV.user");
+<span class="flyspell-duplicate">vxo</span> := vect.xcas.user;
dim.vxo := dim(vxo);
-nbr.line.vxo := dim.vxo;
+<span class="flyspell-duplicate">nbr</span>.line.vxo := dim.vxo;
Resultat:=cat(" ");
-rslt := vxo[0]; RslT:=cat(rslt);
+<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt);
Resultat:=cat(Resultat,RslT);
-fprint(Sortie,Unquoted,Resultat);
+<span class="flyspell-duplicate">fprint</span>(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">{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>&#163;&#181;]{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>{TV}}
+<span class="font-latex-sedate">\dresse</span>{<span class="flyspell-duplicate">TV</span>}}
-<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TV*}</span>[1]{<span class="comment">%
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TV</span></span><span class="function-name">*}</span>[1]{<span class="comment">%
</span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVnbis}{</span><span class="font-latex-sedate"><span class="variable-name">\theTVn</span></span><span class="variable-name">}</span>
-<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{#1}</span>
+<span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{</span><span class="variable-name"><span class="flyspell-duplicate">TVn</span></span><span class="variable-name">}{#1}</span>
<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>&#163;&#181;]{XCasTV.user}}<span class="comment">%
-</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{TV}}
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="flyspell-duplicate">TV</span>}}
+
+
+
+
+
+
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVapp.giac}
+maple_mode(0);
+<span class="flyspell-duplicate">read</span>("XcasTVapp.cxx");
+Sortie:=fopen("XCasmpTVapp.mp");
+vect.xcas.user := read("XCasTVapp.user");
+<span class="flyspell-duplicate">vxo</span> := vect.xcas.user;
+dim.vxo := dim(vxo);
+nbr.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);
+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">{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>&#163;&#181;]{XCasTVapp.user}}<span class="comment">%
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
+<span class="font-latex-sedate">\dresse</span>{TVapp}}
+
+<span class="font-latex-sedate"><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">{</span><span class="variable-name"><span class="flyspell-duplicate">TVn</span></span><span class="variable-name">}{#1}</span>
+<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>&#163;&#181;]{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="flyspell-duplicate">TVapp</span>}}
+
+
+
+
+
+
+
+
+
<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVI.giac}
@@ -1543,13 +2136,13 @@ maple_mode(0);
read("XcasTVI.cxx");
Sortie:=fopen("XCasmpTVI.mp");
vect.xcas.user := read("XCasTVI.user");
-vxo := vect.xcas.user;
+<span class="flyspell-duplicate">vxo</span> := vect.xcas.user;
dim.vxo := dim(vxo);
nbr.line.vxo := dim.vxo;
Resultat:=cat(" ");
-rslt := vxo[0]; RslT:=cat(rslt);
+<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt);
Resultat:=cat(Resultat,RslT);
-fprint(Sortie,Unquoted,Resultat);
+<span class="flyspell-duplicate">fprint</span>(Sortie,Unquoted,Resultat);
fclose(Sortie);
<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span>
@@ -1560,11 +2153,40 @@ fclose(Sortie);
<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"><span class="keyword">\setcounter</span></span><span class="variable-name">{</span><span class="variable-name"><span class="flyspell-duplicate">TVn</span></span><span class="variable-name">}{#1}</span>
<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>&#163;&#181;]{XCasTVI.user}}<span class="comment">%
-</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{TVI}}
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dressetoile</span>{<span class="flyspell-duplicate">TVI</span>}}
+
+
+
+
+<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVIapp.giac}
+maple_mode(0);
+read("XcasTVIapp.cxx");
+Sortie:=fopen("XCasmpTVIapp.mp");
+<span class="flyspell-duplicate">vect</span>.xcas.user := read("XCasTVIapp.user");
+vxo := vect.xcas.user;
+dim.vxo := dim(vxo);
+nbr.line.vxo := dim.vxo;
+Resultat:=cat(" ");
+rslt := vxo[0]; RslT:=cat(rslt);
+<span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,RslT);
+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">TVIapp</span></span><span class="function-name">}</span><span class="comment">%
+</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>&#163;&#181;]{XCasTVIapp.user}}<span class="comment">%
+</span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="font-latex-sedate">\dresse</span>{TVIapp}}
+
+
+<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVIapp</span></span><span class="function-name">*}</span>[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>&#163;&#181;]{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="flyspell-duplicate">TVIapp</span>}}
@@ -1573,7 +2195,7 @@ fclose(Sortie);
<span class="comment-delimiter">%%</span><span class="comment">
-</span><span class="comment-delimiter">%% </span><span class="comment">Zi end -&gt; enjoy :)
+</span><span class="comment-delimiter">%% </span><span class="comment">Zi end -&gt; </span><span class="comment"><span class="flyspell-incorrect">enjoy</span></span><span class="comment"> :)
</span></pre>
</body>
</html>
diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.pdf b/Master/texmf-dist/doc/latex/tablor/tablor.pdf
index b1975418732..f9eb59537b8 100644
--- a/Master/texmf-dist/doc/latex/tablor/tablor.pdf
+++ b/Master/texmf-dist/doc/latex/tablor/tablor.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.tex b/Master/texmf-dist/doc/latex/tablor/tablor.tex
index 211b1339708..3678920eda9 100644
--- a/Master/texmf-dist/doc/latex/tablor/tablor.tex
+++ b/Master/texmf-dist/doc/latex/tablor/tablor.tex
@@ -25,7 +25,7 @@ keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,com
\author{Guillaume \textsc{Connan} \\ \href{http://gconnan.free.fr}{http://gconnan.free.fr}\\
avec l'efficace participation de Jean-Michel \textsc{Boucart}}
-\date{19 mars 2008 - Version 1.9}
+\date{24 mars 2008 - Version 2.01}
\begin{document}
@@ -312,7 +312,12 @@ ou bien, selon les cas~:
\end{lstlisting}
-\subsection{Tableaux des variations}
+
+
+
+\section{Tableaux des variations}
+
+\subsection{Tableau standard}
L'environnement s'appelle \texttt{TV}. On utilise une commande au format \texttt{XCAS}~:
@@ -470,6 +475,51 @@ TVI([-10,+infinity],[-1,1],"f","x",x^2/(x^2-1),1,-1,\tv)
+
+
+\subsection{Tableaux de variations avec approximation des zéros de la dérivée}
+
+Il n'est parfois pas possible d'obtenir une valeur formelle des zéros de la dérivée. On est donc
+amené à rechercher une approximation numérique de ces zéros. Cela est possible grâce à la commande
+\code{fsolve} de \Prog{XCAS} utilisée à bon escient. On appelera les environnements \code{TVapp} et
+\code{TVIapp} ainsi que leurs associés étoilés.
+
+Voyons sur un exemple.
+
+\paragraph*{Exemple}
+
+
+Soit $g$ la fonction $x\mapsto \ln(x)-x\E^{2-x} $.
+
+On étudie d'abord la fonction $x\mapsto g'(x)$~:
+
+\begin{lstlisting}
+\begin{TVIapp}
+ TVIapp([0,+infinity],[0],"g'","x",diff(ln(x)-x*exp(2-x),x),1,0,\tv)
+\end{TVIapp}
+\end{lstlisting}
+
+
+\begin{TVIapp}
+ TVIapp([0,+infinity],[0],"g'","x",diff(ln(x)-x*exp(2-x),x),1,0,\tv)
+ \end{TVIapp}
+
+On en déduit le tableau suivant~:
+
+
+\begin{lstlisting}
+\begin{TVapp*}{201}
+ TVapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,\tv)
+\end{TVapp*}
+\end{lstlisting}
+
+
+
+\begin{TVapp*}{201}
+TVapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,\tv)
+\end{TVapp*}
+
+
\subsection{Tableaux de signes}
@@ -491,7 +541,6 @@ TSa(-2,3,-1,5,\tv);
\end{TSa}
-
\subsubsection*{Cas du produit d'un nombre quelconque de facteurs quelconques sur un intervalle quelconque}
Certains cas pathologiques ne vont pas fonctionner, mais sinon, pour étudier le signe de
@@ -1050,7 +1099,39 @@ TSc((x-10)*(x+10),[-10,10],\tv)
+\begin{lstlisting}
+On considère la fonction $f$ définie sur $\bbr$ par $f(x)=\frac{1}{2}\bigl(x+(1-x)\E^{2x}\bigr)$
+
+Étudions sa dérivée~:
+
+
+\begin{TVIapp*}{202}
+ TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv)
+ \end{TVIapp*}
+
+On en déduit le tableau de variation de $f$
+
+
+\begin{TVapp*}{203}
+ TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv)
+ \end{TVapp*}
+\end{lstlisting}
+
+On considère la fonction $f$ définie sur $\bbr$ par $f(x)=\frac{1}{2}\bigl(x+(1-x)\E^{2x}\bigr)$
+
+Étudions sa dérivée~:
+
+
+\begin{TVIapp*}{202}
+ TVIapp([-infinity,+infinity],[],"f'","x",diff(1/2*(x+(1-x)*exp(2*x)),x),1,0,\tv)
+ \end{TVIapp*}
+
+On en déduit le tableau de variation de $f$
+
+\begin{TVapp*}{203}
+ TVapp([-infinity,+infinity],[],"f","x",1/2*(x+(1-x)*exp(2*x)),1,\tv)
+ \end{TVapp*}
diff --git a/Master/texmf-dist/tex/latex/tablor/tablor.sty b/Master/texmf-dist/tex/latex/tablor/tablor.sty
index 726ed6f45a5..4b5a9e57334 100644
--- a/Master/texmf-dist/tex/latex/tablor/tablor.sty
+++ b/Master/texmf-dist/tex/latex/tablor/tablor.sty
@@ -1,12 +1,12 @@
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
-\ProvidesPackage{tablor}[19/03/2008 v1.9 la machine à créer des tableaux de signes et variations]
+\ProvidesPackage{tablor}[24/03/2008 v2.01 la machine à créer des tableaux de signes et variations]
% \copyleft Connan le Barbare \copyright
% avec l'efficace participation de Jean-Michel Boucart
-%% Crée 10 environnements :
+%% Crée 14 environnements :
%% tableau de signes de 2 facteurs affines
% \begin{TSa}
% TSa(-2,3,-1,5,\tv);
@@ -32,7 +32,19 @@
%TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,\tv)
%\end{TVI}
%%%
+% tableau de variations avec f' sans zéro 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 zéro formel
+%\begin{TVIapp}
+% TVIapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,0,\tv)
+% \end{TVIapp}
+%
+%
+%%%
% et leurs pendants étoilés qui permet l'affichage intermédiaire du
% fichier metapost pour le modifier
%
@@ -375,6 +387,239 @@ return(MetaL);
+
+
+%%
+%%
+%% 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:=fonction_derivee(f);
+z0:=concat(L,F);z:=sort(z0);
+nz:=size(z);
+if(L==[-infinity,+infinity]){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..100);}
+else{if(L[0]==-infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..L[1]);}
+else{if(L[1]==+infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=L[0]..100);}
+else{S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=z[0]..z[nz-1])}}};
+si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
+ kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]);
+ if(kk==1){if(kok==1){z:=append(z,simplifier(S[j]))}};
+ 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(limite(f(x),x=Z[0],1))> evalf(limite(f(x),x=Z[1],-1));
+ kz:=evalf(limite(f(x),x=Z[nz-1],-1))> evalf(limite(f(x),x=Z[nz-2],1));
+
+lsi:="
+newLigneSignes(btex $\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$ etex);"+
+ if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
+ if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+ if(sign(fp(Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
+ if(sign(fp((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}
+
+if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0;
+ lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+ if(ksp==1){"plus;"}else{"moins;"}
+ }; }
+
+lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;
+"}
+lm0:=limite(f(x),x=Z[0],1)==-infinity;
+ li:="
+newLigneVariations(btex $\\hbox{\\bf Variations de }\\atop{\\displaystyle \\Mathbold{"+nom+"}}$ etex);"+
+ if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}
+ else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}+
+ if(k0==1){"1"}else{"0"}+
+ ");";
+
+ if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limite(f(x),x=Z[r-1],1))< evalf(limite(f(x),x=Z[r],-1));
+ krp:=evalf(limite(f(x),x=Z[r],1))> evalf(limite(f(x),x=Z[r+1],-1)) ;
+ lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+ lp:=lp+if(member(Z[r],F)){
+ "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+ else{"valPos(btex $"+latex(simplifier(f(Z[r])))+"$
+ etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+"}}}
+ }; }
+
+lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
+ lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}+
+ if(kz==1){"1);"}else{"0);
+"};
+
+
+intro:="input tableauVariation;
+ verbatimtex
+%&latex
+ \\documentclass{article}
+ \\usepackage[upright]{fourier}
+ \\usepackage{amsmath}
+ \\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
+ \\begin{document}
+ etex;
+
+"
+
+
+MetaL:=if(ftt==2){if(nz>2){intro+"beginTableau("+nmr+")"+
+ l0+lsi+lsp+lsf+"
+endTableau;
+end
+";}else{
+intro+"beginTableau("+nmr+")"+
+ l0+
+lsi+lsf+"
+endTableau;
+end";
+}
+}else{ if(ftt==0){if(nz>2){intro+"beginTableau("+nmr+")"+
+ l0+
+li+
+lp+
+lf
++"
+endTableau;
+end";}else{intro+"beginTableau("+nmr+")"+
+ l0+
+li+
+lf
++"
+endTableau;
+end";}}else{
+if(nz>2){intro+"beginTableau("+nmr+")"+
+ l0+
+lsi+lsp+lsf+
+li+
+lp+
+lf
++"
+endTableau;
+end";}else{intro+"beginTableau("+nmr+")"+
+ l0+
+lsi+lsf+
+li+
+lf
++"
+endTableau;
+end";}
+}}
+
+
+
+MetaLfc:=if(ftt==2){if(nz>2){"
+
+beginTableau("+nmr+")"+
+ l0+lsi+lsp+lsf+"
+endTableau;
+
+";}else{
+intro+"beginTableau("+nmr+")"+
+ l0+
+lsi+lsf+"
+endTableau;
+
+";
+}
+}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
+ l0+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+ l0+
+li+
+lf
++"
+endTableau;
+
+";}}else{
+if(nz>2){"beginTableau("+nmr+")"+
+ l0+
+lsi+lsp+lsf+
+li+
+lp+
+lf
++"
+endTableau;
+
+";}else{"beginTableau("+nmr+")"+
+ l0+
+lsi+lsf+
+li+
+lf
++"
+endTableau;
+
+";}
+}}
+
+
+sortie:=fopen("XCasmpfc.mp");
+fprint(sortie,Unquoted,MetaLfc);
+fclose(sortie);
+
+
+return(MetaL);
+ }:;
+
+
+
+
+
+
+
+\end{VerbatimOut}
+
+
+
+
+
+
+
%%
%% Code giac/Xcas pour les Tableaux de Variations avec
%% Valeurs intermédiaires
@@ -641,6 +886,306 @@ return(MetaL);
+
+
+
+
+%%
+%%
+%% 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:=fonction_derivee(f);
+z0:=concat(L,F);z:=sort(z0);
+nz:=size(z);
+if(L==[-infinity,+infinity]){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..100);}
+else{if(L[0]==-infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=-100..L[1]);}
+else{if(L[1]==+infinity){S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=L[0]..100);}
+else{S:=seq(fsolve(fp(x),x,k/10,newton_solver),k=z[0]..z[nz-1])}}};
+si size(S)>0 alors pour j de 0 jusque size(S)-1 faire
+ kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]);
+ if(kk==1){if(kok==1){z:=append(z,simplifier(S[j]))}};
+ 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:=limite(f(x),x,Z[0],1);
+LF:=limite(f(x),x,Z[nz-1],-1);
+LP:=NULL;
+if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limite(f(x),x,Z[r],-1),limite(f(x),x,Z[r],1)}else{f(Z[r])}}};
+if(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
+
+NL:=size(LL);
+A:=NULL;aa:=1;kk:=0;
+
+if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
+if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}}
+l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"};
+
+if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
+TestL:=(abs(LL[k])==abs(LL[k+1]));
+if(TestS==0){ if( TestL==1 ){l0:=l0}else{
+A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;kk:=kk+1}}else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}}
+l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);
+"};
+
+
+
+TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
+ k0:= evalf(limite(f(x),x=Z[0],1))> evalf(limite(f(x),x=Z[1],-1));
+ kz:=evalf(limite(f(x),x=Z[nz-1],-1))> evalf(limite(f(x),x=Z[nz-2],1));
+
+lsi:="
+newLigneSignes(btex $\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$ etex);"+
+ if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
+ if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
+ if(sign(fp((Z[0]+10^(-10))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
+ if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$ $ etex);"+ if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "};
+
+
+
+
+
+if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+ ksp:=evalf(fp(Z[r]+0.01))>0;
+ TestL:=(abs(LL[r])==abs(LL[r+1]));
+ lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+ if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $ $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "};
+ }}
+else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+ TestL:=(abs(LL[r])==abs(LL[r+1]));
+ if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+ if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $ $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
+ } else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+ if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
+}}
+ };
+
+
+
+lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;"}
+lm0:=limite(f(x),x=Z[0],1)==-infinity;
+
+TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
+
+ li:="
+newLigneVariations(btex $\\hbox{\\bf Variations de }\\atop{\\displaystyle \\Mathbold{"+nom+"}}$ etex);
+"+ if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}
+ else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}+
+ if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "};
+
+
+ if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+ krm:=evalf(limite(f(x),x=Z[r-1],1))< evalf(limite(f(x),x=Z[r],-1));
+ krp:=evalf(limite(f(x),x=Z[r],1))> evalf(limite(f(x),x=Z[r+1],-1)) ;
+ lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
+ lp:=lp+if(member(Z[r],F)) {
+ "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+ else{"valPos(btex $"+latex(simplifier(f(Z[r])))+"$
+ etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
+ $ "+ao+" $ etex,0.5);"
+ }else{" "};
+};//for
+}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
+ krm:=evalf(limite(f(x),x=Z[rr-1],1))< evalf(limite(f(x),x=Z[rr],-1));
+ krp:=evalf(limite(f(x),x=Z[rr],1))> evalf(limite(f(x),x=Z[rr+1],-1)) ;
+ lmrm:=limite(f(x),x=Z[rr],-1)==-infinity;lmrp:=limite(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
+if(TestS==0){if( TestL==1 ){lp:=lp}else{ lp:=lp+if(member(Z[rr],F)) {
+ "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+ else{"valPos(btex $"+latex(simplifier(f(Z[rr])))+"$
+ etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
+ $ "+ao+" $ etex,0.5);
+ ";rr:=rr+1;
+}// else testL==1
+}//testS==0
+else{lp:=lp+if(member(Z[rr],F)){
+ "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
+ else{"valPos(btex $"+latex(simplifier(f(Z[rr])))+"$
+ etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+ "}}};rr:=rr+1;
+}//else testS==0
+}//for nz<NL
+}// else nz<NL
+//if nz=NL
+};//if nz>2
+
+
+lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
+ lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}+
+ if(kz==1){"1);"}else{"0);"};
+
+
+
+intro:="
+input tableauVariation;
+verbatimtex
+%&latex
+ \\documentclass{article}
+ \\usepackage[upright]{fourier}
+ \\usepackage{amsmath}
+ \\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
+ \\begin{document}
+ etex;
+
+";
+
+
+MetaL:= if(ftt==2){if(nz>2){intro+"beginTableau("+nmr+")"+
+ l0+lsi+lsp+lsf+"
+endTableau;
+end";}else{
+intro+"beginTableau("+nmr+")"+
+ l0+
+lsi+lsf+"
+endTableau;
+end";
+}
+}else{
+if(ftt==0){if(nz>2){intro+"beginTableau("+nmr+")"+
+ l0+
+li+
+lp+
+lf
++"
+endTableau;
+end";}else{intro+"beginTableau("+nmr+")"+
+ l0+
+li+
+lf
++"
+endTableau;
+end";}}else{
+if(nz>2){intro+"beginTableau("+nmr+")"+
+ l0+
+lsi+lsp+lsf+
+li+
+lp+
+lf
++"
+endTableau;
+end";}else{intro+"beginTableau("+nmr+")"+
+ l0+
+lsi+lsf+
+li+
+lf
++"
+endTableau;
+end";}
+}};
+
+
+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);
+
+
+return(MetaL);
+ }:;
+
+
+
+\end{VerbatimOut}
+
+
+
+
+
+
+
+
+
+
+
+
+
%%
%% Code giac/Xcas pour les Tableaux de signes de produits
%%
@@ -986,7 +1531,7 @@ newLigneVariables(btex $\\Mathbold{x}$ etex);
li
+
"
- newLigneSignes(btex $\\hbox{\\bf Signe }\\atop{{\\bf de"+nomf+"(x)}}$ etex);"+
+ newLigneSignes(btex $\\hbox{\\bf Signe de}\\atop{{\\bf "+nomf+"(x)}}$ 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;"}+
@@ -1010,7 +1555,7 @@ newLigneVariables(btex $\\Mathbold{x}$ etex);
li
+
"
- newLigneSignes(btex $\\hbox{\\bf Signe }\\atop{{\\bf de"+nomf+"(x)}}$ etex);"+
+ newLigneSignes(btex $\\hbox{\\bf Signe de}\\atop{{\\bf "+nomf+"(x)}}$ 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;"}+
@@ -1284,6 +1829,7 @@ return(MetaL);
% source dans le
% fichier
% Tableaux
+
\immediate\write18{mpost -interaction=batchmode \Tableaux.Tab}% Reconstitution des tableaux
% et création du dernier. L'option
% pallie l'absence de end en fin de
@@ -1455,6 +2001,47 @@ fclose(Sortie);
{\end{VerbatimOut}\dressetoile{TV}}
+
+
+
+
+
+\begin{VerbatimOut}{XCasTVapp.giac}
+maple_mode(0);
+read("XcasTVapp.cxx");
+Sortie:=fopen("XCasmpTVapp.mp");
+vect.xcas.user := read("XCasTVapp.user");
+vxo := vect.xcas.user;
+dim.vxo := dim(vxo);
+nbr.line.vxo := dim.vxo;
+Resultat:=cat(" ");
+rslt := vxo[0]; RslT:=cat(rslt);
+Resultat:=cat(Resultat,RslT);
+fprint(Sortie,Unquoted,Resultat);
+fclose(Sortie);
+\end{VerbatimOut}
+
+\newenvironment{TVapp}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\£µ]{XCasTVapp.user}}%
+{\end{VerbatimOut}
+\dresse{TVapp}}
+
+\newenvironment{TVapp*}[1]{%
+\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\£µ]{XCasTVapp.user}}%
+{\end{VerbatimOut}\dressetoile{TVapp}}
+
+
+
+
+
+
+
+
+
+
+
\begin{VerbatimOut}{XCasTVI.giac}
maple_mode(0);
read("XcasTVI.cxx");
@@ -1486,6 +2073,35 @@ fclose(Sortie);
+\begin{VerbatimOut}{XCasTVIapp.giac}
+maple_mode(0);
+read("XcasTVIapp.cxx");
+Sortie:=fopen("XCasmpTVIapp.mp");
+vect.xcas.user := read("XCasTVIapp.user");
+vxo := vect.xcas.user;
+dim.vxo := dim(vxo);
+nbr.line.vxo := dim.vxo;
+Resultat:=cat(" ");
+rslt := vxo[0]; RslT:=cat(rslt);
+Resultat:=cat(Resultat,RslT);
+fprint(Sortie,Unquoted,Resultat);
+fclose(Sortie);
+\end{VerbatimOut}
+
+\newenvironment{TVIapp}%
+{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\£µ]{XCasTVIapp.user}}%
+{\end{VerbatimOut}\dresse{TVIapp}}
+
+
+\newenvironment{TVIapp*}[1]%
+{\setcounter{TVnbis}{\theTVn}
+\setcounter{TVn}{#1}
+\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\£µ]{XCasTVIapp.user}}%
+{\end{VerbatimOut}\dressetoile{TVIapp}}
+
+
+
+