\NeedsTeXFormat{LaTeX2e}[1995/12/01]
\ProvidesPackage{tablor}[02/12/2009 v4.06-d la machine a creer des tableaux de signes et variations]
\RequirePackage{filecontents}
\RequirePackage{ifthen}
\RequirePackage{fancyvrb}
\RequirePackage{ifpdf}
\fvset{gobble=0}
\newboolean{xcas}\setboolean{xcas}{false}
\DeclareOption{xcas}{\setboolean{xcas}{true}}
\newboolean{windows}\setboolean{windows}{false}
\DeclareOption{windows}{\setboolean{windows}{true}}
\ProcessOptions\relax
\IfFileExists{tablor.cfg}{\input{tablor.cfg}}
\ifthenelse{\boolean{windows}} {\newcommand{\rem}{DEL } \newcommand{\cat}{TYPE }
\newcommand{\cp}{COPY }} {\newcommand{\rem}{rm }\newcommand{\cat}{cat }
\newcommand{\cp}{cp }}
\ifpdf
\DeclareGraphicsRule{*}{mps}{*}{}
\fi
\AtEndDocument{\immediate\write18{\rem *.user XCas* Xcas* *.mpx}
}
\begin{VerbatimOut}{queue.mp}
end
\end{VerbatimOut}
\newcommand{\nettoyer}[1][\jobname]{\immediate\write18{\rem #1.Tab.log queue.mp enteteMP.cfg session.tex config.cxx}
}
\newcommand{\nomtravail}{\jobname}
\newcounter{TVn}
\newcommand{\tv}{\theTVn}
\newcounter{TVnbis}
\newcommand{\tvbis}{\theTVnbis}
\newcommand{\initablor}[1][\jobname]{\renewcommand{\nomtravail}{#1}\setcounter{TVn}{0}\ifthenelse{\boolean{xcas}}{\IfFileExists{\nomtravail_Tab.mp} {\immediate\write18{\rem \nomtravail_Tab.mp}} {} \immediate\write18{\cp enteteMP.cfg \nomtravail_Tab.mp}}
{\IfFileExists{\nomtravail_Tab.mp} {\immediate\write18{mpost -interaction=batchmode \nomtravail_Tab}}{\PackageWarning{tablor}{Pas de source metapost pour creer les tableaux.}} }}
\makeatletter
\newcommand{\executGiacmp}[1]{\ifthenelse{\boolean{windows}}{\immediate\write18{giac #1 }}{\immediate\write18{giac <#1 }}}
\makeatother
\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}
\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}
\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;"} }}}
if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0;
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(ksp==1){"plus;"}else{"moins;"}}else{
if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
if(ksp==1){"plus;"}else{"moins;"}
}}}};
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}
\begin{VerbatimOut}{XcasTVapp.cxx}
TVapp(L,F,nom,nomv,f,ftt,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(-100+k,k=0..200)]minus F;
for k in j do for(m:=-5;m<=5;m++){S:=S,fsolve(fp(x),x,k+m*0.1,newton_solver)};end_for}
else{if(L[0]==-infinity){j:=[seq(k,k=-100..floor(L[1]))] minus F;
for k in j do for(m:=-5;m<=5;m++){ S:=S,fsolve(fp(x),x,k+m*0.1,newton_solver)};end_for}
else{if(L[1]==+infinity){j:=[seq(k,k=floor(L[0])..100)] minus F;
for k in j do for(m:=-5;m<=5;m++){ S:=S,fsolve(fp(x),x,k+m*0.1,newton_solver)};end_for;}
else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;
for k in j do
for(m:=-5;m<=5;m++){S:=S,fsolve(fp(x),x,k+m*0.1,newton_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}
\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}
\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}
\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(-100+k,k=0..200)]minus F;
for k in j do for(m:=-5;m<=5;m++){S:=S,fsolve(fp(x),x,k+m*0.1,newton_solver)};end_for}
else{if(L[0]==-infinity){j:=[seq(k,k=-100..floor(L[1]))] minus F;
for k in j do for(m:=-5;m<=5;m++){ S:=S,fsolve(fp(x),x,k+m*0.1,newton_solver)};end_for}
else{if(L[1]==+infinity){j:=[seq(k,k=floor(L[0])..100)] minus F;
for k in j do for(m:=-5;m<=5;m++){ S:=S,fsolve(fp(x),x,k+m*0.1,newton_solver)};end_for;}
else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;
for k in j do
for(m:=-5;m<=5;m++){S:=S,fsolve(fp(x),x,k+m*0.1,newton_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}
\begin{VerbatimOut}{XcasTVP.cxx}
TVP(L,F,nom,nomv,ff,ftt,trigo,nmr):={
nl:=size(L);
fp:=[];
S:=[];
f:=[unapply(ff[0],x),unapply(ff[1],x)];
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}
\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}
\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}
\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}
%%$
\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}
%%$
\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}
%%$
\newcommand\echelle{1}
\newcommand\ech[1]{\renewcommand\echelle{#1}}
\newcommand{\dresse}[1]{\ifthenelse{\boolean{xcas}}{ \executGiacmp{XCas#1.giac} \immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab.mp}
\immediate\write18{\cat enteteMP.cfg >> \nomtravail_Tab#1.mp}
\immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab#1.mp}
\immediate\write18{\cat queue.mp >> \nomtravail_Tab#1.mp}
\immediate\write18{mpost -jobname=\nomtravail_Tab \nomtravail_Tab#1.mp}
\immediate\write18{\rem \nomtravail_Tab#1.mp}
} { \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}
}
\newcommand{\dressetoile}[1]{\IfFileExists{\nomtravail_Tab.\theTVn}{\immediate\write18{\cat TSav-\theTVn.mp >> \nomtravail_Tab.mp}}
{\executGiacmp{XCas#1.giac}\immediate\write18{\editeur XCasmpfc.mp }
\immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab.mp}
\immediate\write18{\cp XCasmpfc.mp TSav-\theTVn.mp} \immediate\write18{\cat enteteMP.cfg >> \nomtravail_Tab#1.mp}
\immediate\write18{\cat XCasmpfc.mp >> \nomtravail_Tab#1.mp}} \immediate\write18{\cat queue.mp >> \nomtravail_Tab#1.mp}
\immediate\write18{mpost -jobname=\nomtravail_Tab \nomtravail_Tab#1.mp} \immediate\write18{\rem \nomtravail_Tab#1.mp}
\begin{center}
\includegraphics[scale=\echelle]{\nomtravail_Tab.\theTVn}
\end{center}
\ech{1}
\setcounter{TVn}{\theTVnbis} }
\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{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{Q}}
\newenvironment{TSq*}[1]{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasQ.user}}
{\end{VerbatimOut}\dressetoile{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{L}}
\newenvironment{TS*}[1]
{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasL.user}}
{\end{VerbatimOut}\dressetoile{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{TSc}}
\newenvironment{TSc}{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTSc.user}}
{\end{VerbatimOut}\dresse{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{TV}}
\newenvironment{TV*}[1]{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTV.user}}{\end{VerbatimOut}\dressetoile{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{TVP}}
\newenvironment{TVP*}[1]{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVP.user}}{\end{VerbatimOut}\dressetoile{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{TVZ}}
\newenvironment{TVZ*}[1]{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVZ.user}}{\end{VerbatimOut}\dressetoile{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{TVapp}}
\newenvironment{TVapp*}[1]{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVapp.user}}{\end{VerbatimOut}\dressetoile{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{TVI}}
\newenvironment{TVI*}[1]{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVI.user}}{\end{VerbatimOut}\dressetoile{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{TVIex}}
\newenvironment{TVIex*}[1]{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIex.user}}{\end{VerbatimOut}\dressetoile{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{TVIapp}}
\newenvironment{TVIapp*}[1]{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIapp.user}}{\end{VerbatimOut}\dressetoile{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{TVPC}}
\newenvironment{TVPC*}[1]{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVPC.user}}{\end{VerbatimOut}\dressetoile{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{TVS}}
\newenvironment{TVS*}[1]{\setcounter{TVnbis}{\theTVn}
\setcounter{TVn}{#1}
\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVS.user}}{\end{VerbatimOut}\dressetoile{TVS}}
\AtEndDocument{\immediate\write18{\cat queue.mp >> \nomtravail_Tab.mp}
}