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tablor.sty
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
\ProvidesPackage{tablor}[09/05/2010 v4.07 la machine a creer des tableaux de signes et variations]

% \copyleft Connan le Barbare (aka Guillaume Connan) \copyright
% This work may be distributed and/or mofified under the conditions
% or the LaTeX Project Public Licence, either v1.3 or (at your option)
% any later version. The latest version is in
%   http://www.latex-project.org/lppl/
% This work consists of the files tablor.sty, tablor-xetex.sty,  tablor.cfg, tablor.tex,
% tablor.pdf and tablor.html


%% Cree 16 environnements :
%% tableau de signes de 2 facteurs affines
% \begin{TSa}
% TSa(-2,3,-1,5,\tv);
% \end{TSa}
% %%%%%% Pour des tableaux de plus de 2 facteurs
%
% \begin{TS}
% TS("P",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[a,b],n,\tv);
% \end{TS}
%
% pour les tableaux de signes avec quotient
%\begin{TSq}
%TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],n,\tv)
%%\end{TSq}
% un tableau de variation :
%
% pour les tableaux de signes à une seule ligne
% \begin{TSc}
% TSc((x+10)/((x-5)*(x-2)),[-10,5],[2,5],n,0)
% \end{TSc}
%
%
% \begin{TV}
% TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,n,\tv)
% \end{TV}
%
% tableau de variation avec liste de valeurs
% \begin{TVS}
% TVS([1,2,3,4],[-1,-infinity,+infinity,2,9],[2],"f","x",\tv)
% \end{TVS}
%
%
% tableau de variation avec zones interdites
%
% \begin{TVZ}
%   TVZ([-infinity,+infinity],[],[[-1,1]],"f","x",sqrt(x^2-1),1,n,\tv)
% \end{TVZ}
%
%
% tableau avec valeurs intermediares
%\begin{TVI}
%TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,\tv)
%\end{TVI}
%%%
% tableau avec valeurs intermediares et racines exactes
%\begin{TVIex}
%TVIex([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,\tv)
%\end{TVIex}
%%%
%
%
% tableau de variations avec f' sans zero formel
%\begin{TVapp}
% TVapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,\tv)
% \end{TVapp}
%
%
% tableau de variations avec f' sans zero formel
%\begin{TVIapp}
% TVIapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,0,\tv)
% \end{TVIapp}
%
%
%%%
% et leurs pendants etoiles qui permettent l'affichage intermediaire du 
% fichier metapost pour le modifier
%
%
% Courbes parametrees
%  \begin{TVP}
%  TVP([-infinity,+infinity],[[-1,2],[-1]],["x","y"],"t",[t^2/((t+1)*(t-2)),t^2*(t+2)/(t+1)],1,n,\tv)
%  \end{TVP}
%
%
% \begin{TVP}
%  TVP([0,pi/2],[[],[]],["x","y"],"t",[2*cos(t),sin(2*t)],1,t,\tv)
%  \end{TVP}
% %

% Fonctions prolongeables par continuité
% TVP([intervalles d'étude],[valeurs prolongeables],[valeurs interdites pour f'],"g","t",e^(-1/x^2),1,n,\tv); 


% \begin{TVPC}
% TVPC([-infinity,+infinity],[0],[0],"g","t",e^(-1/x^2),1,n,\tv); 
% \end{TVPC}





%% extensions requises
%% Il faudra rajouter dans le preambule \usepackage{graphicx} si vous 
%% ne l'avez pas de base 


\RequirePackage{filecontents}
\RequirePackage{ifthen}
\RequirePackage{fancyvrb}
\RequirePackage{ifpdf}

\fvset{gobble=0}

% option xcas present 


\newboolean{xcas}\setboolean{xcas}{false}
\DeclareOption{xcas}{\setboolean{xcas}{true}}

%% Initialisation du choix d'OS
\newboolean{windows}\setboolean{windows}{false}
\DeclareOption{windows}{\setboolean{windows}{true}}

\ProcessOptions\relax



%% on configure  tablor  dans un fichier exterieur pour la plateforme
%% et l'editeur

\IfFileExists{tablor.cfg}{\input{tablor.cfg}}%\typeout{pas de fichier tablor.cfg}}


%% Definit des commandes disque selon l'OS utilise
\ifthenelse{\boolean{windows}}%
    {\newcommand{\rem}{DEL } \newcommand{\cat}{TYPE }
      \newcommand{\cp}{COPY } \newcommand{\echod}{ECHO }
         \newcommand{\echof}{ }}%
    {\newcommand{\rem}{rm }\newcommand{\cat}{cat }
      \newcommand{\cp}{cp } \newcommand{\echod}{echo "}
        \newcommand{\echof}{"}}







%% pour ceux compilant via pdflatex

\ifpdf
\DeclareGraphicsRule{*}{mps}{*}{}
\fi

%% pour nettoyer les fichiers auxiliaires

\AtEndDocument{\immediate\write18{\rem *.user XCas* Xcas* *.mpx}
                         }




%% Pour clore les fichiers metapost 


  \begin{VerbatimOut}{queue.mp}
  
  end

  \end{VerbatimOut}



%% Nettoie les fichiers log dont le nom depend du choix de l'utilisateur
%% Par defaut, c'est le nom du fichier tex courant (\jobname)
%% Clôt le fichier metapost contenant le recapitulatif de tous les tableaux



\newcommand{\nettoyer}[1][\jobname]%
{\immediate\write18{\rem #1.Tab.log  queue.mp enteteMP.cfg session.tex config.cxx}
}




%% Donne comme prefixe aux tableaux le prefixe courant
%% Peut-être modifie par \initablor

\newcommand{\nomtravail}{\jobname}

%% initialise les compteurs

\newcounter{TVn}
\newcommand{\tv}{\theTVn}

\newcounter{TVnbis}
\newcommand{\tvbis}{\theTVnbis}



%% permet de donner un prefixe aux tableaux produits (\jobname par defaut)
%% effectue quelques verifications :


\newcommand{\initablor}[1][\jobname]{%
\renewcommand{\nomtravail}{#1}%     Arret du nom des tableaux
\setcounter{TVn}{0}%     Initialisation du compteur de tableaux.
\ifthenelse{\boolean{xcas}}%    Avec l'option XCas
{\IfFileExists{\nomtravail_Tab.mp}%      Si Tableaux.mp est present...
        {\immediate\write18{\rem \nomtravail_Tab.mp}}%  le detruire
        {}%   
 \immediate\write18{\cp  enteteMP.cfg \nomtravail_Tab.mp}% Reconstituer l'entête de Tableaux.mp
} 
{\IfFileExists{\nomtravail_Tab.mp}%      Sans l'option XCas, si
                                %      Tableaux.mp existe
{\immediate\write18{mpost -interaction=batchmode \nomtravail_Tab}}% l'executer pour reconstituer les figures
{\PackageWarning{tablor}{Pas de source metapost pour creer les tableaux.}}% sinon message d'erreur
                                % (mais pas d'arret car les tableaux
                                % peuvent être presents )
}}%



%% commande pour lancer giac selon l'OS

\makeatletter
\newcommand{\executGiacmp}[1]{%
\ifthenelse{\boolean{windows}}%
{\immediate\write18{giac #1 }}%
{\immediate\write18{giac  <#1 }}}
\makeatother




%%%
%
%%% LES SCRIPTS GIAC/XCAS
%
%%%




%%
%% Code giac/Xcas pour les Tableaux de Variations
%%


\begin{VerbatimOut}{XcasTV.cxx}
TV(L,F,nom,nomv,f,ftt,trigo,nmr):={
nl:=size(L);
f:=unapply(f,x);
fp:=function_diff(f);
Z:=concat(L,F);
S:=[];


if(trigo==t){
all_trig_solutions:=1;
reset_solve_counter(-1,-1);
SS:=solve(factor(simplify(fp(x))),x);
ns:=size(SS);
for(k:=0;k<ns;k++){
m:=0;
while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
};m:=-1;
while(evalf(subst(SS[k],n_1=m))>=L[0]){
S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
}
}
}else{
S:=solve(factor(simplify(fp(x))),x);
}


  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire
                             qq:=member(simplify(S[j]),Z)==0;
                             kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                          if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}};
                          fpour
  fsi;
Z:=sort(Z);
nz:=size(Z);


 tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z);
     ftantque;







  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                             kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                          if(kk==1){Z:=append(Z,simplify(S[j]))};
                          fpour
  fsi;


Z:=sort([op(set[op(Z)])]);

nz:=size(Z);
l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";
pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
";fpour; 

       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                          
lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
     if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
                                                    if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
                                                         if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }}
 
if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.1))>0;                     
                                               lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                                if(ksp==1){"plus;"}else{"moins;"}
                                                  }; }

lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;
"}
lm0:=limit(f(x),x=Z[0],1)==-infinity;
     li:=lvic+nom+"}$ etex);"+
           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
           if(k0==1){"1"}else{"0"}+
                         ");";
            
                     if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                  lp:=lp+if(member(Z[r],F)){
                                    "limGauche(btex
                                    $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$
                                    etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
                                            etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
"}}}
                                                   }; }

lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
                          


lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
             if(kz==1){"1);"}else{"0);"}}
    else{"limGauche(btex $"+
         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
    




MetaLfc:=if(ftt==2){if(nz>2){"

beginTableau("+nmr+")"+
        l0+lsi+lsp+lsf+"
endTableau;

";}else{
"beginTableau("+nmr+")"+
        l0+
lsi+lsf+"
endTableau;

";
}
}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
        l0+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
li+
lf
+"
endTableau;

";}}else{
if(nz>2){"beginTableau("+nmr+")"+
        l0+
lsi+lsp+lsf+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
lsi+lsf+
li+
lf
+"
endTableau;

";}
}}


sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);


 }:;

\end{VerbatimOut}






%%%%


%
%
%  TVPC : pour les fonctions prolongeables par continuité.
%%
%%




\begin{VerbatimOut}{XcasTVPC.cxx}
TVPC(L,F,FP,nom,nomv,f,ftt,trigo,nmr):={
nl:=size(L);
f:=unapply(f,x);
fp:=function_diff(f);
Z:=concat(L,F);
Z:=concat(Z,FP);
S:=[];


if(trigo==t){
all_trig_solutions:=1;
reset_solve_counter(-1,-1);
SS:=solve(factor(simplify(fp(x))),x);
ns:=size(SS);
for(k:=0;k<ns;k++){
m:=0;
while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
};m:=-1;
while(evalf(subst(SS[k],n_1=m))>=L[0]){
S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
}
}
}else{
S:=solve(factor(simplify(fp(x))),x);
}


  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire
                             qq:=member(simplify(S[j]),Z)==0;
                             kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                          if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}};
                          fpour
  fsi;
Z:=sort(Z);
nz:=size(Z);


 tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z);
     ftantque;







  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                             kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                          if(kk==1){Z:=append(Z,simplify(S[j]))};
                          fpour
  fsi;


Z:=sort([op(set[op(Z)])]);

nz:=size(Z);
l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";
pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
";fpour; 

       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                          
lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
     if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],FP)==0){
                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
                                                    if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
                                                         if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }}
 
if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.1))>0;                     
                                               lsp:=lsp+if(member(Z[r],FP)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                                if(ksp==1){"plus;"}else{"moins;"}
                                                  }; }

lsf:=if(member(Z[nz-1],FP)==0){""}else{"nonDefBarre;
"}
lm0:=limit(f(x),x=Z[0],1)==-infinity;
     li:=lvic+nom+"}$ etex);"+
           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
             else{"limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
           if(k0==1){"1"}else{"0"}+
                         ");";
            
                     if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                  lp:=lp+if(member(Z[r],F)){ 
                                    "valPos(btex
                                    $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$
                                    etex,"+if(krm==1){"1);"}else{"0);"} }
                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
                                            etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
"}}}
                                                   }; }

lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
                          


lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
             if(kz==1){"1);"}else{"0);"}}
    else{"limGauche(btex $"+
         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
           if(kz==1){"1);"}else{"0);"}};    
    




MetaLfc:=if(ftt==2){if(nz>2){"

beginTableau("+nmr+")"+
        l0+lsi+lsp+lsf+"
endTableau;

";}else{
"beginTableau("+nmr+")"+
        l0+
lsi+lsf+"
endTableau;

";
}
}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
        l0+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
li+
lf
+"
endTableau;

";}}else{
if(nz>2){"beginTableau("+nmr+")"+
        l0+
lsi+lsp+lsf+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
lsi+lsf+
li+
lf
+"
endTableau;

";}
}}


sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);


 }:;

\end{VerbatimOut}












%%
%%
%% TV avec une zone interdite : on rajoute comme argument la liste des intervalles interdits
%% par exemple, pour sqrt(x^2-1) : TVZ([-infinity,100],[],[[-1,1]],"f","x",sqrt(x^2-1),1,1)
%%

\begin{VerbatimOut}{XcasTVZ.cxx}


TVZ(L,F,FF,nom,nomv,f,ftt,trigo,nmr):={
nl:=size(L);
nf:=size(FF);
 Ff:=NULL;IMIN:=NULL;IMAX:=NULL;
for(k:=0;k<nf;k++){
if(FF[k][0]>L[0]){Imin[k]:=FF[k][0];LL:=L}else{Imin[k]:=L[0];LL:=[L[1]]};
if(FF[k][1]<L[1]){Imax[k]:=FF[k][1];LL:=L}else{Imax[k]:=L[1];LL:=[L[0]]};
 Ff:=Ff,[Imin[k],Imax[k]];
 IMIN:=IMIN,Imin[k];
 IMAX:=IMAX,Imax[k];
 }
 FF:=[Ff];
 IMIN:=[IMIN];
 IMAX:=[IMAX];
 f:=unapply(f,x);
fp:=function_diff(f);
Z:=concat(LL,F);

for(k:=0;k<nf;k++){
Z:=concat(Z,FF[k]);
}

S:=[];


if(trigo==t){
all_trig_solutions:=1;
reset_solve_counter(-1,-1);
SS:=solve(factor(simplify(fp(x))),x);
ns:=size(SS);
for(k:=0;k<ns;k++){
m:=0;
while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
};m:=-1;
while(evalf(subst(SS[k],n_1=m))>=L[0]){
S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
}
}
}else{
S:=solve(factor(simplify(fp(x))),x);
}






  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                         for(k:=0;k<nf;k++){  
                           kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                             kK:=(evalf(S[j])<evalf(Imin[k])) or (evalf(S[j])>evalf(Imax[k]));
                             Kk:=(kk) and kK;
                          if(Kk==1){Z:=append(Z,simplify(S[j]))};
                          }
                        fpour
  fsi;


Z:=sort([op(set[op(Z)])]);

nz:=size(Z);

for(j:=0;j<nf;j++){
 for(k:=1;k<nz;k++){
   if ((Z[k]>Imin[j])and(Z[k]<Imax[j])){Z:=augment(Z[0..k-1],Z[k+1..nz-1]);nz:=nz-1;
   }
  }
}
nz:=size(Z);

l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";
pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
";fpour; 

       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                          
lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
if(member(Z[0],IMIN)!=0){if((member(Z[0],F)==0) and (fp(Z[0])!=undef)){"debutNonDef;"}else{"debutNonDefStrict;"}}else{if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
                                                    if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
                                                         if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }}}



// modif 3 avril 2010

if(nz>2){ for(r:=1; r<=nz-2;r++){ 
             lsp:=lsp+
              if(member(Z[r],IMIN)!=0){
                if((member(Z[r],F)==0) and (fp(Z[r])!=undef)){"debutNonDef;"}
                else{"debutNonDefStrict;"}}
              else{if(member(Z[r],IMAX)!=0){if((member(Z[r],F)==0) and (fp(Z[r])!=undef)){"finNonDef;"}
                                                else{"finNonDefStrict;"}+
                                                if(evalf(fp(Z[r]+0.01))>0){"plus;"}
                                                else{"moins;"}}
                    else{if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}
                          else{"nonDefBarre;"}+
                          if(evalf(fp(Z[r]+0.01))>0){"plus;"}
                          else{"moins;"}
                                                  }}
                            }}; 

// fin modif





lsf:=if(member(Z[nz-1],IMAX)!=0){if((member(Z[nz-1],F)==0) and (fp(Z[nz-1])!=undef)){"finNonDef;"}else{"finNonDefStrict;"}}else{if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;
"}}


lm0:=limit(f(x),x=Z[0],1)==-infinity;
     li:=lvic  +nom+"}$ etex);"+
           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
           if(k0==1){"1"}else{"0"}+
                         ");";
            
if(nz>2){ 
   for(r:=1; r<=nz-2;r++){ 
     krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
     krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
     lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;

     lp:=lp+if(member(Z[r],IMIN)!=0){"limGauche(btex $"+if(lmrm==1){
             "-\\infty"}else{
                latex(simplify(limit(f(x),x=Z[r],-1)))}
         +"$ etex,"+if(krm==1){
             "1);"}else{"0);"} 
         +if(member(Z[r],F)==0){"debutNonDef;"}else{"debutNonDefStrict;"}
       }//fsi Zr=Imin
      else{
        if (member(Z[r],IMAX)!=0){if(member(Z[r],F)==0){"finNonDef;"}else{"finNonDefStrict;"}+"limDroite(btex $"+if(lmrp==1){
             "-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}
         +"$ etex,"+if(krp==1){
             "1);"}else{"0);"}          
       }else{
          if(member(Z[r],F)){
         "limGauche(btex $"+if(lmrm==1){
             "-\\infty"}else{
                latex(simplify(limit(f(x),x=Z[r],-1)))}
         +"$ etex,"+if(krm==1){
             "1);"}else{"0);"}
         +"nonDefBarre;limDroite(btex $"+if(lmrp==1){
             "-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}
         +"$ etex,"+if(krp==1){
             "1);"}else{"0);"}
         }//fsi (member Zr F)
          else{"valPos(btex$"+latex(simplify(f(Z[r])))+"$etex,"+
             if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){
               "0.5);"}else{
                    if(krp==1){
                       "1);"}else{"0);"}//felse(krp)
                    }//felse(valpos)
               }//felse(member Zr F)
               } //felse(Zr=Imax)
              }//felse(Zr=Imin)
           };//ffor 
         }//fsi nz

lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;



lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
             if(kz==1){"1);"}else{"0);"}}
    else{"limGauche(btex $"+
         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
    


    

MetaLfc:=if(ftt==2){if(nz>2){"

beginTableau("+nmr+")"+
        l0+lsi+lsp+lsf+"
endTableau;

";}else{
"beginTableau("+nmr+")"+
        l0+
lsi+lsf+"
endTableau;

";
}
}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
        l0+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
li+
lf
+"
endTableau;

";}}else{
if(nz>2){"beginTableau("+nmr+")"+
        l0+
lsi+lsp+lsf+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
lsi+lsf+
li+
lf
+"
endTableau;

";}
}}


sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);

 }
:;


\end{VerbatimOut}


%%
%%
%% Quand les solutions formelles de f'(x)=0 ne sont pas calculables
%%



\begin{VerbatimOut}{XcasTVapp.cxx}


TVapp(L,F,nom,nomv,f,ftt,nmr):={
local  nl,fp,z0,z,nz,S,k,j,m,kk,kok,Z,l0,lp,lf,lsp,k0,kz,lsi,r,ksp,lsf,lm0,li,krm,krp,lmrm,lmrp,lnz;

nl:=size(L);
f:=unapply(f,x);
fp:=function_diff(f);
z0:=concat(L,F);z:=sort(z0);
nz:=size(z);



S:=NULL;



if(L==[-infinity,+infinity]){j:=[seq(-50+2*k,k=0..50)]minus F;
  for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for}
else{if(L[0]==-infinity){j:=[seq(2*k,k=-25..0.5*floor(L[1]))] minus F;
  for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for}
else{if(L[1]==+infinity){
j:=[seq(2*k,k=floor(0.5*L[0])..0.5*50)] minus F;
  for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for
}
else{ j:=[seq(2*k,k=0.5*floor(z[0])..0.5*floor(z[nz-1]))] minus F;
  for k in j do  for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for }
  }};




si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                             kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]);
                          if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}};
                          fpour;
fsi;


S:=NULL;
S:=S,z[0];
for(j:=1;j<size(z);j++){
 if(z[j]!=undef and (abs(z[j])>1e-15 or z[j]==0)){
   S:=S,z[j]};
}
z:=[S];

Z:=sort(z);
nz:=size(Z);

S:=NULL;
S:=S,Z[0];
for(j:=1;j<nz;j++){
 if(Z[j]!=S[size(S)-1]){
   S:=S,Z[j]};
}
Z:=[S]; 


nz:=size(Z);
l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";
pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
";fpour; 

       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                          
lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
     if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
                                                    if(evalf(sign(fp(Z[0]+10^(-5))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
                                                         if(evalf(sign(fp((Z[0]+10^(-5)))))==1.0){"plus;"}else{"moins;"} }}
 
if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp(Z[r]+0.01))>0;                     
                                               lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                                if(ksp==1){"plus;"}else{"moins;"}
                                                  }; }

lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;
"}
lm0:=limit(f(x),x=Z[0],1)==-infinity;
     li:=lvic+nom+"}$ etex);"+
           if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
           if(k0==1){"1"}else{"0"}+
                         ");";
            
                     if(nz>2){ for(r:=1; r<=nz-2;r++){  krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                  lp:=lp+if(member(Z[r],F)){
                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
                                            etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
"}}}
                                                   }; }

lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
 

lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
             if(kz==1){"1);"}else{"0);"}}
    else{"limGauche(btex $"+
         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
    


MetaLfc:=if(ftt==2){if(nz>2){"

beginTableau("+nmr+")"+
        l0+lsi+lsp+lsf+"
endTableau;

";}else{
"beginTableau("+nmr+")"+
        l0+
lsi+lsf+"
endTableau;

";
}
}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
        l0+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
li+
lf
+"
endTableau;

";}}else{
if(nz>2){"beginTableau("+nmr+")"+
        l0+
lsi+lsp+lsf+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
lsi+lsf+
li+
lf
+"
endTableau;

";}
}}


sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);


 }:;







\end{VerbatimOut}







%%
%% Code giac/Xcas pour les Tableaux de Variations avec 
%% Valeurs intermediaires
%%





\begin{VerbatimOut}{XcasTVI.cxx}


TVI(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={
nl:=size(L);
f:=unapply(f,x);
fp:=function_diff(f);
Z:=concat(L,F);
S:=[];


if(trigo==t){
all_trig_solutions:=1;
reset_solve_counter(-1,-1);
SS:=solve(factor(simplify(fp(x))),x);
ns:=size(SS);
for(k:=0;k<ns;k++){
m:=0;
while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
};m:=-1;
while(evalf(subst(SS[k],n_1=m))>=L[0]){
S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
}
}
}else{
S:=solve(factor(simplify(fp(x))),x);
}

  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                            kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                          if(kk==1){Z:=append(Z,simplify(S[j]))};
                          fpour
  fsi;


Z:=sort([op(set[op(Z)])]);



nz:=size(Z);
l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";



LI:=limit(f(x),x,Z[0],1);
LF:=limit(f(x),x,Z[nz-1],-1);
LP:=NULL;
PB:=1;
if(nz>2){                                                       for(r:=1;
  r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])};
if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1};
}
};
if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]};
      
NL:=size(LL);
A:=NULL;aa:=1;
kk:=0;



if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0);
if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}}
l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"};
//chgmt NL->nz
if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0);
  
if(PB[k]==1){if(TestS==0){
   A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;kk:=kk+1}
else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}};
}

 l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"

 };


TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0);
       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                          
lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
     if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1.0){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
                                                    if(evalf(sign(fp((Z[0]+10^(-3)))))==1.0){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
                                                         if(evalf(sign(fp(10^(-3)+Z[0])))==1.0){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$
                                                       $ etex);"+ 
if(evalf(sign(fp(10^(-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; 





if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); 
                                                 ksp:=evalf(fp(Z[r]+0.01))>0;  
                                                 TestL:=(abs(LL[r])==abs(LL[r+1]));
                                 lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                  if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $  $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "};
                                          }}  
else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0);
                                         
                      if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                  if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $  $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
                                    else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                  if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}        
}}}}; 




 lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"}



lm0:=limit(f(x),x=Z[0],1)==-infinity;




TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0);

     li:=lvic+nom+"}$ etex);
"+  if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
           if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; 
                         
            
                     if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); 
                                                 krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                  lp:=lp+if(member(Z[r],F)) {
                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
                                            etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
                                            $ "+ao+" $ etex,0.5);"
                                                           }else{" "}; 
};//for                
}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); 
                                                 krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1));
                                                 krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ;  
                         lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
                   
if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){
                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
                                            etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
                                            $ "+ao+" $ etex,0.5);
                                                                 ";rr:=rr+1;
}//  testS==0
else{lp:=lp+if(member(Z[rr],F)){
                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
                                            etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
                                                            "}}};rr:=rr+1;
}//else testS==0
}//PB[r]==1
}//for nz<NL
}// else nz<NL
//if nz=NL
};//if nz>2



lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;


lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
             if(kz==1){"1);"}else{"0);"}}
    else{"limGauche(btex $"+
         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    







MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+
        l0+lsi+lsp+lsf+"
endTableau;

";}else{
"beginTableau("+nmr+")"+
        l0+
lsi+lsf+"
endTableau;

";
}
}else{
if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
        l0+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
li+
lf
+"
endTableau;
";}}else{
if(nz>2){"beginTableau("+nmr+")"+
        l0+
lsi+lsp+lsf+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
lsi+lsf+
li+
lf
+"
endTableau;

";}
}};







sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);


 }:;



\end{VerbatimOut}



%%
%
%
%
% Pour avoir les racines sous forme exacte.... quand c'est possible !
%
%
%
%%%%%%%%%


\begin{VerbatimOut}{XcasTVIex.cxx}



TVIex(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={
nl:=size(L);
f:=unapply(f,x);
fp:=function_diff(f);
Z:=concat(L,F);
S:=[];

Sex:=NULL;
Zex:=solve(f(x)=ao);
Zex:=sort(Zex);
for(j:=0;j<size(Zex);j++){
if((evalf(Zex[j])>=evalf(L[0])) and (evalf(Zex[j])<=evalf(L[nl-1]))){Sex:=Sex,Zex[j]};
};
Sex:=[Sex];








if(trigo==t){
all_trig_solutions:=1;
reset_solve_counter(-1,-1);
SS:=solve(factor(simplify(fp(x))),x);
ns:=size(SS);
for(k:=0;k<ns;k++){
m:=0;
while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){
S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;
};m:=-1;
while(evalf(subst(SS[k],n_1=m))>=L[0]){
S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;
}
}
}else{
S:=solve(factor(simplify(fp(x))),x);
}

  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                            kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                          if(kk==1){Z:=append(Z,simplify(S[j]))};
                          fpour
  fsi;



 Z:=sort([op(set[op(Z)])]);


nz:=size(Z);
l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";



LI:=limit(f(x),x,Z[0],1);
LF:=limit(f(x),x,Z[nz-1],-1);
LP:=NULL;
PB:=1;
if(nz>2){                                                       for(r:=1;
  r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])};
if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1};
}
};
if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]};
      
NL:=size(LL);
A:=NULL;aa:=0;
kk:=0;



if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0);
if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $"+latex(simplify(Sex[aa]))+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}}
l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"};
//chgmt NL->nz
if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0);
  
if(PB[k]==1){if(TestS==0){
   A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $"+latex(simplify(Sex[aa]))+"$ etex);";aa:=aa+1;kk:=kk+1}
else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}};
}

 l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"

 };


TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0);
       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                          
lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
     if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
                                                    if(sign(fp((Z[0]+10^(-3))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
                                                         if(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$
                                                       $ etex);"+
if(evalf(sign(fp(10^(-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; 




if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); 
                                                 ksp:=evalf(fp(Z[r]+0.01))>0;  
                                                 TestL:=(abs(LL[r])==abs(LL[r+1]));
                                 lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                  if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $  $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "};
                                          }}  
else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0);
                                         
                      if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                  if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $  $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
                                    else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                  if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}        
}}}}; 




 lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"}



lm0:=limit(f(x),x=Z[0],1)==-infinity;




TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0);

     li:=lvic+nom+"}$ etex);
"+  if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
           if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; 
                         
            
                     if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); 
                                                 krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                  lp:=lp+if(member(Z[r],F)) {
                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
                                            etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
                                            $ "+ao+" $ etex,0.5);"
                                                           }else{" "}; 
};//for                
}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); 
                                                 krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1));
                                                 krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ;  
                         lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
                   
if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){
                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
                                            etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
                                            $ "+ao+" $ etex,0.5);
                                                                 ";rr:=rr+1;
}//  testS==0
else{lp:=lp+if(member(Z[rr],F)){
                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
                                            etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
                                                            "}}};rr:=rr+1;
}//else testS==0
}//PB[r]==1
}//for nz<NL
}// else nz<NL
//if nz=NL
};//if nz>2



lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;


lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
             if(kz==1){"1);"}else{"0);"}}
    else{"limGauche(btex $"+
         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    







MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+
        l0+lsi+lsp+lsf+"
endTableau;

";}else{
"beginTableau("+nmr+")"+
        l0+
lsi+lsf+"
endTableau;

";
}
}else{
if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
        l0+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
li+
lf
+"
endTableau;
";}}else{
if(nz>2){"beginTableau("+nmr+")"+
        l0+
lsi+lsp+lsf+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
lsi+lsf+
li+
lf
+"
endTableau;

";}
}};






sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);


 }:;


\end{VerbatimOut}







%%
%%
%% Quand les solutions de f'(x)=0 ne sont pas formellement calculables
%%




\begin{VerbatimOut}{XcasTVIapp.cxx}

TVIapp(L,F,nom,nomv,f,ftt,ao,nmr):={


nl:=size(L);
f:=unapply(f,x);
fp:=function_diff(f);
z0:=concat(L,F);z:=sort(z0);
nz:=size(z);







S:=op(fsolve(fp(x),x));




if(L==[-infinity,+infinity]){j:=[seq(-50+2*k,k=0..50)]minus F;
  for k in j do for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for}
else{if(L[0]==-infinity){j:=[seq(2*k,k=-25..0.5*floor(L[1]))] minus F;
  for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for}
else{if(L[1]==+infinity){
j:=[seq(2*k,k=floor(0.5*L[0])..0.5*50)] minus F;
  for k in j do for(m:=-5;m<=5;m++){ S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for
}
else{ j:=[seq(2*k,k=0.5*floor(z[0])..0.5*floor(z[nz-1]))] minus F;
  for k in j do  for(m:=-5;m<=5;m++){S:=S,resoudre_numerique(fp(y),y,k+m*0.1,k+(m+1)*0.1,bisection_solver)};end_for }
  }};













si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                             kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]);
                          if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}};
                          fpour;
fsi;


S:=NULL;
S:=S,z[0];
for(j:=1;j<size(z);j++){
 if(z[j]!=undef and (abs(z[j])>1e-15 or z[j]==0)){
   S:=S,z[j]};
}
z:=[S];



Z:=sort(z);
nz:=size(Z);

S:=NULL;
S:=S,Z[0];
for(j:=1;j<nz;j++){
 if(Z[j]!=S[size(S)-1]){
   S:=S,Z[j]};
}
Z:=[S]; 


nz:=size(Z);
l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";



LI:=limit(f(x),x,Z[0],1);
LF:=limit(f(x),x,Z[nz-1],-1);
LP:=NULL;
PB:=1;
if(nz>2){                                                       for(r:=1;
  r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])};
if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1};
}
};
if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]};
      
NL:=size(LL);
A:=NULL;aa:=1;
kk:=0;


if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0);
if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}}
l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"};
//chgmt NL->nz
if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0);
  
if(PB[k]==1){if(TestS==0){
   A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;kk:=kk+1}
else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}};
}

 l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"

 };


TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0);
       k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1));
       kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1));
                          
lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
     if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
                                                    if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+
                                                    if(sign(fp((Z[0]+10^(-3))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
                                                         if(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$
                                                       $ etex);"+

if(evalf(sign(fp(10^(-3)+ifte(Z[0]==-infinity,ifte(Z[1]==+infinity,ifte(member(0,F)==0,0,0.01),ifte(member(Z[1]-1,F)==0,Z[1]-1,Z[1]-1.1)),Z[0]))))==1.0){"plus;"}else{"moins;"}}else{" "}; 



if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); 
                                                 ksp:=evalf(fp(Z[r]+0.01))>0;  
                                                 TestL:=(abs(LL[r])==abs(LL[r+1]));
                                 lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                  if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $  $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "};
                                          }}  
else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0);
                                         
                      if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                  if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $  $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
                                    else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
                                  if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}        
}}}}; 




 lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"}



lm0:=limit(f(x),x=Z[0],1)==-infinity;




TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0);

     li:=lvic+nom+"}$ etex);
"+  if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}
             else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+                               
           if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; 
                         
            
                     if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); 
                                                 krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1));
                                                 krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ;  
                         lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity;
                                                  lp:=lp+if(member(Z[r],F)) {
                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f(Z[r])))+"$
                                            etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
                                            $ "+ao+" $ etex,0.5);"
                                                           }else{" "}; 
};//for                
}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); 
                                                 krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1));
                                                 krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ;  
                         lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
                   
if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){
                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
                                            etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
                                            $ "+ao+" $ etex,0.5);
                                                                 ";rr:=rr+1;
}//  testS==0
else{lp:=lp+if(member(Z[rr],F)){
                                    "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f(Z[rr])))+"$
                                            etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
                                                            "}}};rr:=rr+1;
}//else testS==0
}//PB[r]==1
}//for nz<NL
}// else nz<NL
//if nz=NL
};//if nz>2



lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;


lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
           if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+
             if(kz==1){"1);"}else{"0);"}}
    else{"limGauche(btex $"+
         if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ 
           if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    







MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+
        l0+lsi+lsp+lsf+"
endTableau;

";}else{
"beginTableau("+nmr+")"+
        l0+
lsi+lsf+"
endTableau;

";
}
}else{
if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
        l0+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
li+
lf
+"
endTableau;
";}}else{
if(nz>2){"beginTableau("+nmr+")"+
        l0+
lsi+lsp+lsf+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
lsi+lsf+
li+
lf
+"
endTableau;

";}
}};




sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);


 }:;




\end{VerbatimOut}







%%
%% Code giac/Xcas pour les Tableaux de variations de courbes parametrees
%%







\begin{VerbatimOut}{XcasTVP.cxx}
TVP(L,F,nom,nomv,ff,ftt,trigo,nmr):={

nl:=size(L);
fp:=[];
S:=[];
f:=[unapply(ff[0],t),unapply(ff[1],t)];
fp:=[function_diff(f[0]),function_diff(f[1])];
Z:=[];
LLL:=[];


all_trig_solutions:=1;
reset_solve_counter(-1,-1);

for(d:=0;d<=1;d++){
LLL:=concat(L,F[d]);
Z:=LLL union Z;
SS:=solve(factor(simplify(fp[d](t))),t);
ns:=size(SS);


for(k:=0;k<ns;k++){
if(trigo==t){
m:=0;
while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){

S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1;

};m:=-1;
while(evalf(subst(SS[k],n_1=m))>=L[0]){

S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1;

}
}else{
S:=concat(S,SS);
}
}


  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire
                             qq:=member(simplify(S[j]),Z)==0;
                             kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1]));
                          if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}};
                          fpour
  fsi;
Z:=sort(Z);
nz:=size(Z);


 tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z);
     ftantque;




nz:=size(Z);
u:=1;
 tantque (u<nz-2) and (nz>2) faire
     tantque evalf(Z[u])==evalf(Z[u+1]) faire
         Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=size(Z);
     ftantque;
  u:=u+1;
 ftantque;


 };

Z:=sort(Z);
nz:=size(Z);



 l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:="",""; lf:="","";lsp:="","";
pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
";fpour;

 lsi:="","";

FFF:=[[],[]];

for(d:=0;d<=1;d++){
FFF[d]:=concat(F[d],[-infinity,+infinity]);
       k0:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1));
       kz:=evalf(limit(f[d](x),x=Z[nz-1],-1))> evalf(limit(f[d](x),x=Z[nz-2],1));
//}
//$
 lsi[d]:=lsic+nom[d]+"'("+nomv+")}$ etex);"+if(member(Z[0],FFF[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[0])))+"$ etex);"}else{if(Z[0]==-infinity){" "}else{"nonDefBarre;
"}}+
     if(Z[0]==-infinity){if(sign(evalf(fp[d](if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F[d])==0){
                                                    if(sign(fp[d](Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{
                                                         if(sign(fp[d]((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}

if(nz>2){ for(r:=1; r<=nz-2;r++){      ksp:=evalf(fp[d](Z[r]+0.01))>0;
                                               lsp[d]:=lsp[d]+if(member(Z[r],F[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[r])))+"$ etex);"}else{"nonDefBarre;"}+
                                                if(ksp==1){"plus;"}else{"moins;"}
                                                  }; }

lsf[d]:=if(member(Z[nz-1],FFF[d])==0){"valBarre(btex $"+latex(simplify(fp[d](Z[nz-1])))+"$ etex);"}else{if(Z[nz-1]==+infinity){" "}else{"nonDefBarre;"}}




 }











 lm0:=1,2; li:=1,2; krm:=1,2; krp:=1,2; lmrm:=1,2; lmrp:=1,2; lp:="",""; lnz:=1,2; lf:=1,2; Kz:=1,2;K0:=1,2;


for(d:=0;d<=1;d++){
   K0[d]:= evalf(limit(f[d](x),x=Z[0],1))> evalf(limit(f[d](x),x=Z[1],-1));
  Kz[d]:=evalf(limit(f[d](x),x,Z[nz-1],-1))> evalf(limit(f[d](x),x,Z[nz-2],1));
//{
//$
lm0[d]:=limit(f[d](x),x,Z[0],1)==-infinity;
     li[d]:=lvic+nom[d]+"}$ etex);"+
           if(member(Z[0],F[d])==0){"valPos(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$ etex,"}
             else{"nonDefBarre;limDroite(btex $"+if(lm0[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[0],1)))}+"$ etex,"}+
           if(K0[d]==1){"1"}else{"0"}+
                         ");";

                     if(nz>2){ for(r:=1; r<=nz-2;r++){ krm[d]:=evalf(limit(f[d](x),x=Z[r-1],1))< evalf(limit(f[d](x),x=Z[r],-1));
                                                 krp[d]:=evalf(limit(f[d](x),x=Z[r],1))> evalf(limit(f[d](x),x,Z[r+1],-1)) ;
                         lmrm[d]:=limit(f[d](x),x,Z[r],-1)==-infinity;lmrp[d]:=limit(f[d](x),x,Z[r],1)==-infinity;
                                                  lp[d]:=lp[d]+if(member(Z[r],F[d])){
                                    "limGauche(btex
                                    $"+if(lmrm[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],-1)))}+"$
                                    etex,"+if(krm[d]==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x,Z[r],1)))}+"$ etex,"+if(krp[d]==1){"1);"}else{"0);"}}
                                          else{"valPos(btex          $"+latex(simplify(f[d](Z[r])))+"$
                                            etex,"+if(sign(evalf(fp[d](Z[r]-0.001)))==sign(evalf((fp[d](Z[r]+0.001))) )){"0.5);"}else{if(krp[d]==1){"1);"}else{"0);
"}}}
                                                   }; }

lnz[d]:=limit(f[d](x),x=Z[nz-1],-1)==-infinity;


lf[d]:=if(member(Z[nz-1],F[d])==0){"valPos(btex $"+
           if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$ etex,"+
             if(Kz[d]==1){"1);"}else{"0);"}}
    else{"limGauche(btex $"+
         if(lnz[d]==1){"-\\infty"}else{latex(simplify(limit(f[d](x),x=Z[nz-1],-1)))}+"$ etex,"+ 
           if(Kz[d]==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
    





}








MetaLfc:=if(ftt==2){if(nz>2){"

beginTableau("+nmr+")"+
        l0+lsi[0]+lsp[0]+lsf[0]+lsi[1]+lsp[1]+lsf[1]+"
endTableau;

";}else{
"beginTableau("+nmr+")"+
        l0+
lsi[0]+lsf[0]+lsi[1]+lsf[1]+"
endTableau;

";
}
}else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+
        l0+
li[0]+
lp[0]+
lf[0]+
li[1]+
lp[1]+
lf[1]
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
li[0]+
lf[0]+
li[1]+
lf[1]
+"
endTableau;

";}}else{
if(nz>2){"beginTableau("+nmr+")"+
        l0+
lsi[0]+lsp[0]+lsf[0]+
li[0]+
lp[0]+
lf[0]+
lsi[1]+lsp[1]+lsf[1]+
li[1]+
lp[1]+
lf[1]
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
lsi[0]+lsf[0]+
li[0]+
lf[0]+
lsi[1]+lsf[1]+
li[1]+
lf[1]
+"
endTableau;

";}
}
}

sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);

}:;
\end{VerbatimOut}




%%
%% Code giac/Xcas pour les Tableaux de signes de produits
%%




\begin{VerbatimOut}{XcasTabSignL.cxx}


TS(nomf,L,D,trigo,nmr):={
L:=apply(f->unapply(f,x),L)
n:=size(L);
Z:=NULL;
nl:=size(L);
S:=[];
mini:=D[0]; maxi:=D[1];

pour k de 0 jusque n-1 faire 




if(trigo==t){
all_trig_solutions:=1;
reset_solve_counter(-1,-1);
SS:=solve(factor(simplify(L[k](x))),x);
ns:=size(SS);
for(j:=0;j<ns;j++){
m:=0;
while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){
S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1;
};m:=-1;
while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){
S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1;
}
}

}else{
S:=solve(L[k](x),x);
}




  si size(S)>0 alors  pour j de 0 jusque size(S)-1 faire 
                          if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j]);}
                      fpour;
  fsi;
fpour;





Z:=sort(Z);
nz:=size(Z);


 Z:=sort([op(set[(Z)])]);


nz:=size(Z);

if(nz==0){li:="";l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
          for(p:=0;p<=n-1;p++){li:=li+lsic+latex(L[p](x))+"}$ etex);"+
if(mini!=-infinity and L[p](mini)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}+ 
if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}

}
           lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"};


MetaLfc:="    beginTableau("+nmr+")
newLigneVariables(btex $ {x}$ etex);
   "+l0+li+ lsic+nomf+"(x)}$ etex);"+
               if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}+  lf+
                               if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}+"
endTableau;
"
;

}else{

l0:="val(btex $"+latex(D[0])+"$ etex);";li:=" ";lr:=" "; 
pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
";fpour; 
l0:=l0+"val(btex $"+latex(D[1])+"$ etex);";


for(p:=0;p<=n-1;p++){lp:="";                                     
     li:=li+lsic+latex(L[p](x))+"}$ etex);"+
           if(mini!=-infinity and L[p](mini)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}+ 
           if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"};
                               
                           for(r:=0; r<=nz-2;r++){  
                             lp:=lp+if(simplify(L[p](Z[r]))==0){"
                                valBarre(btex 0 etex);"}else{"barre;
                              "}+ 
                             if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}};
 
                li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
                          if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins;
    "}+if(maxi!=+infinity and L[p](maxi)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}
    };  


pour t de 0 jusque nz-2 faire 
                           lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"                    
                         fpour

MetaLfc:="  beginTableau("+nmr+")
newLigneVariables(btex $ {x}$ etex);
   "+l0+
                     li
                     + lsic+nomf+"(x)}$ etex);"+
               if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}+  
                         if(product(L[s](Z[0]-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"+
                         lr+
                         if(product(L[s](Z[nz-1]+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+
                               if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}+"
endTableau;

 ";
}
sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);

 }:;

\end{VerbatimOut}




%%
%% Code giac/Xcas pour les Tableaux de signes de quotients
%%



\begin{VerbatimOut}{XcasTabSignQ.cxx}
TSq(nomf,L,Fo,D,trigo,nmr):={
L:=apply(f->unapply(f,x),L);
Fo:=apply(f->unapply(f,x),Fo);
L:=concat(L,Fo);
n:=size(L);
Z:=NULL;
m:=size(Fo);
F:=NULL;FF:=NULL;
mini:=D[0]; maxi:=D[1];
S:=[];
SF:=[];

pour k de 0 jusque n-1 faire 



if(trigo==t){
all_trig_solutions:=1;
reset_solve_counter(-1,-1);
SS:=solve(factor(simplify(L[k](x))),x);
ns:=size(SS);
for(j:=0;j<ns;j++){
mm:=0;
while(evalf(simplify(subst(SS[j],n_1=mm)))<=evalf(maxi)){
S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm+1;
};mm:=-1;
while(evalf(subst(SS[j],n_1=mm))>=evalf(mini)){
S:=concat(S,simplify(subst(SS[j],n_1=mm)));mm:=mm-1;
}
}

}else{
S:=concat(S,solve(L[k](x),x));
}





  si size(S)>0 alors   pour j de 0 jusque size(S)-1 faire 
                          if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j]);}
                      fpour;
  fsi;
fpour;


pour k de 0 jusque m-1 faire 



if(trigo==t){
all_trig_solutions:=1;
reset_solve_counter(-1,-1);
SSF:=solve(factor(simplify(Fo[k](x))),x);
nsf:=size(SSF);
for(j:=0;j<nsf;j++){
mm:=0;
while(evalf(simplify(subst(SSF[j],n_1=mm)))<=evalf(maxi)){
SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm+1;
};mm:=-1;
while(evalf(subst(SSF[j],n_1=mm))>=evalf(mini)){
SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm-1;
}
}

}else{
SF:=concat(SF,solve(Fo[k](x),x));
}

  si size(SF)>0 alors pour j de 0 jusque size(SF)-1 faire 
                          FF:=FF,simplify(SF[j]);
                          if(SF[j]>mini and SF[j]<maxi){F:=F,simplify(SF[j]);}
                      fpour;
  fsi;
fpour;



Z:=[Z,F];


Z:=sort([op(set[op(Z)])]);

nz:=size(Z);

if(nz==0){li:="";l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
          for(p:=0;p<=n-1;p++){li:=li+lsic+latex(L[p](x))+"}$ etex);"+
if(mini!=-infinity and L[p](mini)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}+ 
if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}

}
           lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"};




MetaLfc:=" 
beginTableau("+nmr+")
newLigneVariables(btex $ {x}$ etex);
   "+l0+li+
   lsic+nomf+"(x)}$ etex);"+
              if(member(mini,FF)==0){if((mini!=-infinity) and (product(L[s](mini),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+  lf+
              if(member(maxi,FF)==0){if((maxi!=+infinity) and (product(L[s](maxi),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+"
endTableau;

"
;




}else{


l0:="val(btex $"+latex(D[0])+"$ etex);";li:=" ";lr:=" "; 
pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
";fpour; 
l0:=l0+"val(btex $"+latex(D[1])+"$ etex);";


for(p:=0;p<=n-1;p++){lp:="";                                     
     li:=li+lsic+latex(L[p](x))+"}$ etex);"+
           if(mini!=-infinity and L[p](mini)==0){" valBarre(btex 0 etex);"}else{" "}+ 
           if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"};
                               
     for(r:=0; r<=nz-2;r++){lp:=lp+if(simplify(L[p](Z[r]))==0){" valBarre(btex 0 etex);"}else{"barre;"}+ 
                             if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}};
 
                li:=li+lp+ if(simplify(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ 
                          if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins;
    "}+if(maxi!=+infinity and L[p](maxi)==0){"valBarre(btex 0 etex);"}else{" "}
                              
    };  


pour t de 0 jusque nz-2 faire 
                           lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+
                                      if(member(Z[t+1],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"}                   
                         fpour




MetaLfc:="
beginTableau("+nmr+")
newLigneVariables(btex $ {x}$ etex);
   "+l0+
                     li
                     +
   lsic+nomf+"(x)}$ etex);"+
               if(member(mini,FF)==0){if((mini!=-infinity) and (product(L[s](mini),s,0,n-1)==0)){" valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+  
                         if(product(L[s](Z[0]-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+
                         if(member(Z[0],FF)==0){"valBarre(btex 0 etex);"}else{ "nonDefBarre;"}+
                         lr+
                         if(product(L[s](Z[nz-1]+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+
                         if(member(maxi,FF)==0){if((maxi!=+infinity) and (product(L[s](maxi),s,0,n-1)==0)){"valBarre(btex 0 etex);"}else{" "}}else{"nonDefBarre;"}+"
endTableau;

"


}




sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);





 }:;

\end{VerbatimOut}




%% Code giac/Xcas pour les Tableaux de signes du produit
%% de 2 facteurs affines
%%




\begin{VerbatimOut}{XcasTabSigna.cxx}
TSa(a,b,c,d,nmr):={
zA:=solve(a*x+b=0,x)[0];
zB:=solve(c*x+d=0,x)[0];
zmin:=min(zA,zB);
zmax:=max(zA,zB);
  Meta:= " 
          beginTableau("+nmr+")
   newLigneVariables(btex $ {x}$ etex);
   val(btex $-\\infty$ etex);val(btex $"+latex(zmin)+"$ etex);
val(btex $"+latex(zmax)+"$etex);
val(btex $+\\infty$ etex); 
  "+lsic+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+"}$ etex);"
        +   if(a>0){"moins;"}else{"plus;"}+
                                 if(zmin==zA){"valBarre(btex 0 etex);"}else{"barre;"}+
                                 if(zmin==zA){si a>0 alors "plus;"; sinon "moins;";fsi}
                                             else{si a>0 alors "moins;"; sinon "plus;"; fsi}+
                                 if(zmin==zA){"barre;"}else{"valBarre(btex 0 etex);"}+
                                 if(a>0){"plus;"}else{"moins;"}
     +lsic+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+"}$ etex);"
        +     if(c>0){"moins"}else{"plus"}+";"+
                                 if(zmin==zB){"valBarre(btex 0 etex);"}else{"barre;"}+
                                 if(zmin==zB){si c>0 alors "plus;"; sinon "moins;";fsi}
                                             else{si c>0 alors "moins;"; sinon "plus;"; fsi}+
                                 if(zmin==zB){"barre;"}else{"valBarre(btex 0 etex);"}+
                                 if(c>0){"plus;"}else{"moins;"}  
     
   +lsic+"{("+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+")("+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+")}}$ etex);"
        +   si a*c>0 alors plus; sinon moins;fsi+";"+
                                 "valBarre(btex 0 etex);"+
                                 si a*c>0 alors moins; sinon plus;fsi+";"+
                                 "valBarre(btex 0 etex);"+
                                 si a*c>0 alors plus; sinon moins;fsi+";"+"
endTableau;
"
;



sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,Meta);
fclose(sortie);


 }:;
\end{VerbatimOut}






%%$
%% Code giac/Xcas pour les Tableaux de Signes d'expression ne contenant 
%% qu'un seul terme




\begin{VerbatimOut}{XcasTSc.cxx}

TSc(g,D,F,trigo,nmr):={
f:=unapply(g,x);
mini:=D[0]; maxi:=D[1];lm:=" ";
Z:=mini,maxi;
S:=[];



if(trigo==t){
all_trig_solutions:=1;
reset_solve_counter(-1,-1);
SS:=solve(factor(simplify(f(x))),x);
ns:=size(SS);
for(j:=0;j<ns;j++){
m:=0;
while(evalf(simplify(subst(SS[j],n_1=m)))<=evalf(maxi)){
S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m+1;
};m:=-1;
while(evalf(subst(SS[j],n_1=m))>=evalf(mini)){
S:=concat(S,simplify(subst(SS[j],n_1=m)));m:=m-1;
}
}

}else{
S:=solve(f(x),x);
}





if(size(S)==0 and size(F)==0){
l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
li:=if(member(mini,F)!=0){"nonDefBarre;"}else{if(mini!=-infinity and f(mini)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}}+ 
if(mini!=-infinity or maxi!=+infinity){if(f((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}}else{if(f(0.3145274774464545777744)>0){"plus;"}else{"moins;"}};
lf:=if(member(maxi,F)!=0){"nonDefBarre;"}else{if(maxi!=+infinity and f(maxi)==0){"
                                valBarre(btex 0 etex);"}else{"
                              "}};
}else{
if(size(S!=0)){pour j de 0 jusque size(S)-1 faire 
                           if(S[j]>mini and S[j]<maxi){Z:=Z,simplify(S[j])};
                      fpour}

Z:=concat([Z],F);

 Z:=sort([op(set[op(Z)])]);


nz:=size(Z);
l0:=" ";li:=" ";lr:=" "; 
if(nz==2){l0:="val(btex $"+latex(D[0])+"$ etex);val(btex $"+latex(D[1])+"$ etex);";
li:=if(mini!=-infinity and f(mini)==0){"
                                valBarre(btex 0 etex);"}else{if(member(mini,F)==0){"
                              "}else{"nonDefBarre;"}}+ 
if(f((mini+maxi)*0.5)>0){"plus;"}else{"moins;"};
lf:=if(maxi!=+infinity and f(maxi)==0){"
                                valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){"
                              "}else{"nonDefBarre;"}
                              };

}else{
l0:="val(btex $"+latex(Z[0])+"$ etex);";li:=" ";
pour m de 1 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
";
fpour; 

                                     
li:= if(mini!=-infinity and f(mini)==0){"
                                valBarre(btex 0 etex);"}else{if(member(mini,F)==0){"
                              "}else{"nonDefBarre;"}
                              }                         

lm:=if(nz>2){for(r:=0; r<nz-2;r++){lm:=lm+if(Z[r]==-infinity){
if(f((Z[r+1]-1))>0){"plus;"}else{"moins;"}
}else{if(f((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}}
+
            if(member(Z[r+1],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"} 
                           }}else{" "}; 

lf:=if(f(Z[nz-2]+0.1)>0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}else{if(member(maxi,F)==0){"
                              "}else{"nonDefBarre;"}
                              };
}
};  




MetaLfc:="

beginTableau("+nmr+")
newLigneVariables(btex $\\displaystyle  {x}$ etex);
   "+l0+lsic+latex(f(x))+"}$ etex);"+
                     li+lm+lf
                     +"
endTableau;

"
;




sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);
 }:;

\end{VerbatimOut}







%%$






%%%%
%%%
%%% Pour des tableaux de variations simples sans fonctions
%%%
%%%



\begin{VerbatimOut}{XcasTVS.cxx}
TVS(La,Lo,F,nomf,nomv,nmr):={

na:=size(La);
f:=F;
if(member(La[0],F)){f:=f[1..size(f)-1]};
if(member(La[na-1],F)){f:=f[0..size(f)-2]};
Z:=sort(concat(La,f));
Zo:=sort([op(set[op(Z)])]);
nz:=size(Z);
nzo:=size(Zo);


k0:= evalf(Lo[0])> evalf(Lo[1]);
kz:=evalf(Lo[nz-1])> evalf(Lo[nz-2]);


l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";
  for(m:=0;m<=nzo-1;m++){l0:=l0+"val(btex $"+latex(Zo[m])+"$ etex);"}

li:=lvic+nomf+"}$ etex);"+
    if(member(Z[0],F)==0){"valPos(btex $"+latex(Lo[0])+"$ etex,"}
    else{"nonDefBarre;limDroite(btex $"+latex(Lo[0])+"$ etex,"}+                               
           if(k0==1){"1"}else{"0"}+
                         ");";
            
    if(nz>2){ for(r:=1; r<=nz-2;r++){ 
         krm:=evalf(Lo[r-1])< evalf(Lo[r]);
         krp:=evalf(Lo[r])> evalf(Lo[r+1]) ;  
         
      lp:=lp+if(Z[r]==Z[r+1]){
         "limGauche(btex$"+latex(Lo[r])+"$etex,"+
              if(krm==1){"1);"}
              else{"0);"}
             }// fin if zr=zr+1
             else{
              if(Z[r]==Z[r-1]){
         "nonDefBarre;limDroite(btex$"+latex(Lo[r])+"$etex,"+
              if(krp==1){"1);"}
              else{"0);"}
             }//fin if zr=zr-1
              else{
              "valPos(btex $"+latex(Lo[r])+"$etex,"+
              if(krp==1){"1);"}else{"0);"}
}//fin else zr=zr-1
}//fin else zr=zr+1
}//fin for 
}//fin de if nz>2
                                                                      


lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+latex(Lo[nz-1])+"$ etex,"+
             if(kz==1){"1);"}else{"0);"}}
    else{"limGauche(btex $"+latex(Lo[nz-1])+"$ etex,"+ 
             if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}};    
    

MetaLfc:=

 if(nz>2){"beginTableau("+nmr+")"+
        l0+
li+
lp+
lf
+"
endTableau;

";}else{"beginTableau("+nmr+")"+
        l0+
li+
lf
+"
endTableau;

";}

//return(MetaLfc);

sortie:=fopen("XCasmpfc.mp");
fprint(sortie,Unquoted,MetaLfc);
fclose(sortie);


}:;

\end{VerbatimOut}

%%$





















%%
%% traitement des fichiers produits par giac/xcas
%%
%%

% pour l'échelle des tableaux taper \ech{facteur de réduction}

\newcommand\echelle{1}
\newcommand\ech[1]{\renewcommand\echelle{#1}}


\newcommand\couleurtab{black}
\newcommand\coultab[1]{\renewcommand\couleurtab{#1}}


\newcommand{\dresse}[2]{%
\ifthenelse{\boolean{xcas}}{%        Avec l'option "XCas present"
         \executGiacmp{XCas#2.giac}% reconstituer le tableau
                                   % exporter le source mp
                                   % puis lancer metapost pour creer
                                   % l'image du tableau
         \immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab.mp}
         \immediate\write18{\cat enteteMP.cfg >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod def beginTableau(expr c) =\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod begingroup\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod charcode:=c;\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod clearxy; clearit; clearpen;\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod pickup defaultpen;\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod drawoptions(withcolor(#1));\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod initTableau;\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod enddef;\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab#2.mp}
         \immediate\write18{\cat queue.mp >> \nomtravail_Tab#2.mp}
         \immediate\write18{mpost   -jobname=\nomtravail_Tab \nomtravail_Tab#2.mp}
         \immediate\write18{\rem \nomtravail_Tab#2.mp}  
           }%
         {% sinon, si le tableau est absent, alerte.
         \IfFileExists{\nomtravail_Tab.\theTVn}{}{% 
         \PackageError{tablor}{Tableau absent non
         reconstituable.}{Pour compiler il faut, soit les fichiers de
         tableaux, soit le fichier \nomtravail_Tab.mp, soit disposer de
         XCas.}}}
                
\begin{center}
  \includegraphics[scale=\echelle]{\nomtravail_Tab.\theTVn}
\end{center}
\stepcounter{TVn}
}


%%
%% traitement des fichiers produits par giac/xcas avec possibilite
%% de modifier le fichier metapost (environnement etoile))
%%



\newcommand{\dressetoile}[2]{%
\IfFileExists{\nomtravail_Tab.\theTVn}{% Test sur l'existence du tableau
% Si oui, inclusion du fichier source de sauvegarde mp dans Tableaux
\immediate\write18{\cat TSav-\theTVn.mp >> \nomtravail_Tab.mp}}
% Si  non,  lancement des operations de fabrication 
{\executGiacmp{XCas#2.giac}%
\immediate\write18{\editeur  XCasmpfc.mp }

  % Modification avec l'editeur choisi
\immediate\write18{\cat  XCasmpfc.mp >> \nomtravail_Tab.mp} 
\immediate\write18{\cp  XCasmpfc.mp  TSav-\theTVn.mp}   % Sauvegarde du 
                                 % source mp sur le disque pour une
                                 % inclusion ulterieure dans Tableaux.mp. 
\immediate\write18{\cat enteteMP.cfg >> \nomtravail_Tab#2.mp}
 \immediate\write18{\echod def beginTableau(expr c) =\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod begingroup\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod charcode:=c;\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod clearxy; clearit; clearpen;\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod pickup defaultpen;\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod drawoptions(withcolor(#1));\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod initTableau;\echof >> \nomtravail_Tab#2.mp}
         \immediate\write18{\echod enddef;\echof >> \nomtravail_Tab#2.mp}
\immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab#2.mp}} % Inclusion du
                                                     % source dans le
                                                     % fichier
                                                     % Tableaux 
\immediate\write18{\cat queue.mp >> \nomtravail_Tab#2.mp}
\immediate\write18{mpost  -jobname=\nomtravail_Tab \nomtravail_Tab#2.mp}% Reconstitution des tableaux
                                % et creation du dernier. L'option
                                % pallie l'absence de end en fin de
                                % fichier 
\immediate\write18{\rem \nomtravail_Tab#2.mp}  

\begin{center}
  \includegraphics[scale=\echelle]{\nomtravail_Tab.\theTVn}
\end{center}
\ech{1}
\setcounter{TVn}{\theTVnbis}    % Restauration du compteur TVn
}







%%
%%
%%%
%%%
%%% les "giac" qui permettent d'executer la commande rentree dans le fichier tex
%%% suivis des environnements qui permettront la saisie du code giac/xcas
%%% Les versions etoilees permettent de modifier le code metapost produit initialement
%%%




\begin{VerbatimOut}{XCasa.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTabSigna.cxx");
read("XCasa.user");
\end{VerbatimOut}

\newenvironment{TSa}
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasa.user}}
{\end{VerbatimOut}
          \dresse{\couleurtab}{a}
}









\begin{VerbatimOut}{XCasQ.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTabSignQ.cxx");
read("XCasQ.user");
\end{VerbatimOut}

\newenvironment{TSq}%
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasQ.user}}
{\end{VerbatimOut}\dresse{\couleurtab}{Q}}



\newenvironment{TSq*}[1]%
{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasQ.user}}
{\end{VerbatimOut}\dressetoile{\couleurtab}{Q}}


\begin{VerbatimOut}{XCasL.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTabSignL.cxx");
read("XCasL.user");
\end{VerbatimOut}

\newenvironment{TS}%
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasL.user}}
{\end{VerbatimOut}\dresse{\couleurtab}{L}}


\newenvironment{TS*}[1]
{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasL.user}}
{\end{VerbatimOut}\dressetoile{\couleurtab}{L}}


\begin{VerbatimOut}{XCasTSc.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTSc.cxx");
read("XCasTSc.user");
\end{VerbatimOut}




\newenvironment{TSc*}[1]%
{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTSc.user}}
{\end{VerbatimOut}\dressetoile{\couleurtab}{TSc}}


\newenvironment{TSc}%
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTSc.user}}
{\end{VerbatimOut}\dresse{\couleurtab}{TSc}}


\begin{VerbatimOut}{XCasTV.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTV.cxx");
read("XCasTV.user");
\end{VerbatimOut}



\newenvironment{TV}{% 
\VerbatimEnvironment
\begin{VerbatimOut}[commandchars=\\??]{XCasTV.user}}%
{\end{VerbatimOut}
\dresse{\couleurtab}{TV}}

\newenvironment{TV*}[1]{%
\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTV.user}}%
{\end{VerbatimOut}\dressetoile{\couleurtab}{TV}}







\begin{VerbatimOut}{XCasTVP.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTVP.cxx");
read("XCasTVP.user");
\end{VerbatimOut}

\newenvironment{TVP}%
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVP.user}}%
{\end{VerbatimOut}
\dresse{\couleurtab}{TVP}}

\newenvironment{TVP*}[1]{%
\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVP.user}}%
{\end{VerbatimOut}\dressetoile{\couleurtab}{TVP}}










\begin{VerbatimOut}{XCasTVZ.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTVZ.cxx");
read("XCasTVZ.user");
\end{VerbatimOut}

\newenvironment{TVZ}%
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVZ.user}}%
{\end{VerbatimOut}
\dresse{\couleurtab}{TVZ}}

\newenvironment{TVZ*}[1]{%
\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVZ.user}}%
{\end{VerbatimOut}\dressetoile{\couleurtab}{TVZ}}








\begin{VerbatimOut}{XCasTVapp.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTVapp.cxx");
read("XCasTVapp.user");
\end{VerbatimOut}

\newenvironment{TVapp}%
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVapp.user}}%
{\end{VerbatimOut}
\dresse{\couleurtab}{TVapp}}

\newenvironment{TVapp*}[1]{%
\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVapp.user}}%
{\end{VerbatimOut}\dressetoile{\couleurtab}{TVapp}}











\begin{VerbatimOut}{XCasTVI.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTVI.cxx");
read("XCasTVI.user");
\end{VerbatimOut}

\newenvironment{TVI}%
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVI.user}}%
{\end{VerbatimOut}\dresse{\couleurtab}{TVI}}


\newenvironment{TVI*}[1]%
{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVI.user}}%
{\end{VerbatimOut}\dressetoile{\couleurtab}{TVI}}





\begin{VerbatimOut}{XCasTVIex.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTVIex.cxx");
read("XCasTVIex.user");
\end{VerbatimOut}

\newenvironment{TVIex}%
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIex.user}}%
{\end{VerbatimOut}\dresse{\couleurtab}{TVIex}}


\newenvironment{TVIex*}[1]%
{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIex.user}}%
{\end{VerbatimOut}\dressetoile{\couleurtab}{TVIex}}









\begin{VerbatimOut}{XCasTVIapp.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTVIapp.cxx");
read("XCasTVIapp.user");
\end{VerbatimOut}

\newenvironment{TVIapp}%
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIapp.user}}%
{\end{VerbatimOut}\dresse{\couleurtab}{TVIapp}}


\newenvironment{TVIapp*}[1]%
{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIapp.user}}%
{\end{VerbatimOut}\dressetoile{\couleurtab}{TVIapp}}





\begin{VerbatimOut}{XCasTVPC.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTVPC.cxx");
read("XCasTVPC.user");
\end{VerbatimOut}

\newenvironment{TVPC}%
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVPC.user}}%
{\end{VerbatimOut}
\dresse{\couleurtab}{TVPC}}

\newenvironment{TVPC*}[1]{%
\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVPC.user}}%
{\end{VerbatimOut}\dressetoile{\couleurtab}{TVPC}}












\begin{VerbatimOut}{XCasTVS.giac}
maple_mode(0);
approx_mode:=0;
read("config.cxx");
read("XcasTVS.cxx");
read("XCasTVS.user");
\end{VerbatimOut}

\newenvironment{TVS}%
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVS.user}}%
{\end{VerbatimOut}
\dresse{\couleurtab}{TVS}}

\newenvironment{TVS*}[1]{%
\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVS.user}}%
{\end{VerbatimOut}\dressetoile{\couleurtab}{TVS}}










%% pour nettoyer les fichiers auxiliaires

\AtEndDocument{\immediate\write18{\cat  queue.mp >> \nomtravail_Tab.mp}
                         }




%%
%% Zi end -> enjoy :)
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