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 :)