\NeedsTeXFormat{LaTeX2e}[1995/12/01]
\ProvidesPackage{tablor}
[23/01/2008 v1.4
la machine à créer des tableaux de signes et variations]
\newcommand{\nettoyer}{
\immediate\write18{rm XCasmp.mp* XCasmp.log XCasmp?.mp* XCasmp?.log XCasmpTV.mp* XCasmpTV.log *.user XCasmpTVI.mp* XCasmpTVI.log
*.giac *.cxx *mpx* *~}}
\newcommand{\bouger}[1]{
\immediate\write18{cp XCas* #1}}
\newcommand{\recup}[2]{
\immediate\write18{cp #1 #2}}
\newcounter{TVn}
\newcommand{\tv}{\theTVn}
\usepackage{fancyvrb}
\makeatletter
\newcommand{\executGiacmp}[1]{
\immediate\write18{giac <#1 } }
\makeatother
\begin{VerbatimOut}{XcasTV.cxx}
TV(L,F,nom,nomv,f,ftt,nmr):={
nl:=size(L);
f:=unapply(f,x);
fp:=fonction_derivee(f);
Z:=concat(L,F);
S:=resoudre(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,simplifier(S[j]))};
fpour
fsi;
Z:=sort(Z);
nz:=size(Z);
si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1;
fsi;
pour u de 1 jusque nz-2 faire
si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1;
fsi;
fpour;
nz:=size(Z);
l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";
pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);
";fpour;
k0:= evalf(limite(f(x),x=Z[0],1))> evalf(limite(f(x),x=Z[1],-1));
kz:=evalf(limite(f(x),x=Z[nz-1],-1))> evalf(limite(f(x),x=Z[nz-2],1));
lsi:="
newLigneSignes(btex $\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$ etex);"+
if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
if(sign(fp(Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
if(sign(fp((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }}
if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0;
lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
if(ksp==1){"plus;"}else{"moins;"}
}; }
lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;
"}
lm0:=limite(f(x),x=Z[0],1)==-infinity;
li:="
newLigneVariations(btex $\\hbox{\\bf Variations de }\\atop{\\displaystyle \\Mathbold{"+nom+"}}$ etex);"+
if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}
else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}+
if(k0==1){"1"}else{"0"}+
");";
if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limite(f(x),x=Z[r-1],1))< evalf(limite(f(x),x=Z[r],-1));
krp:=evalf(limite(f(x),x=Z[r],1))> evalf(limite(f(x),x=Z[r+1],-1)) ;
lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
lp:=lp+if(member(Z[r],F)){
"limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
else{"valPos(btex $"+latex(simplifier(f(Z[r])))+"$
etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
"}}}
}; }
lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}+
if(kz==1){"1);"}else{"0);
"};
intro:="input tableauVariation;
verbatimtex
\\documentclass{article}
\\usepackage[upright]{fourier}
\\usepackage{amsmath}
\\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
\\begin{document}
etex
"
MetaL:=if(ftt==2){if(nz>2){intro+"beginTableau("+nmr+")"+
l0+lsi+lsp+lsf+"
endTableau;
end";}else{
intro+"beginTableau("+nmr+")"+
l0+
lsi+lsf+"
endTableau;
end";
}
}else{ if(ftt==0){if(nz>2){intro+"beginTableau("+nmr+")"+
l0+
li+
lp+
lf
+"
endTableau;
end";}else{intro+"beginTableau("+nmr+")"+
l0+
li+
lf
+"
endTableau;
end";}}else{
if(nz>2){intro+"beginTableau("+nmr+")"+
l0+
lsi+lsp+lsf+
li+
lp+
lf
+"
endTableau;
end";}else{intro+"beginTableau("+nmr+")"+
l0+
lsi+lsf+
li+
lf
+"
endTableau;
end";}
}}
return(MetaL);
}:;
\end{VerbatimOut}
\begin{VerbatimOut}{XcasTVI.cxx}
TVI(L,F,nom,nomv,f,ftt,ao,nmr):={
nl:=size(L);
f:=unapply(f,x);
fp:=fonction_derivee(f);
Z:=concat(L,F);
S:=resoudre(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,simplifier(S[j]))};
fpour
fsi;
Z:=sort(Z);
nz:=size(Z);
si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1;
fsi;
pour u de 1 jusque nz-2 faire
si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=nz-1;
fsi;
fpour;
nz:=size(Z);
l0:=" newLigneVariables(btex $"+nomv+"$ etex);";lp:=" "; lf:=" ";lsp:=" ";
LI:=limite(f(x),x,Z[0],1);
LF:=limite(f(x),x,Z[nz-1],-1);
LP:=NULL;
if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limite(f(x),x,Z[r],-1),limite(f(x),x,Z[r],1)}else{f(Z[r])}}};
if(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
NL:=size(LL);
A:=NULL;aa:=1;kk:=0;
if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}}
l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"};
if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0);
TestL:=(abs(LL[k])==abs(LL[k+1]));
if(TestS==0){ if( TestL==1 ){l0:=l0}else{
A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $\\alpha_"+aa+"$ etex);";aa:=aa+1;kk:=kk+1}}else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}}
l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);
"};
TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
k0:= evalf(limite(f(x),x=Z[0],1))> evalf(limite(f(x),x=Z[1],-1));
kz:=evalf(limite(f(x),x=Z[nz-1],-1))> evalf(limite(f(x),x=Z[nz-2],1));
lsi:="
newLigneSignes(btex $\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$ etex);"+
if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){
if(sign(fp((Z[0]+10^(-10))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+
if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$ $ etex);"+ if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "};
if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
ksp:=evalf(fp(Z[r]+0.01))>0;
TestL:=(abs(LL[r])==abs(LL[r+1]));
lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $ $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "};
}}
else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
TestL:=(abs(LL[r])==abs(LL[r+1]));
if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $ $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
} else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;}
}}
};
lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;"}
lm0:=limite(f(x),x=Z[0],1)==-infinity;
TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0);
li:="
newLigneVariations(btex $\\hbox{\\bf Variations de }\\atop{\\displaystyle \\Mathbold{"+nom+"}}$ etex);
"+ if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}
else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$ etex,"}+
if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "};
if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
krm:=evalf(limite(f(x),x=Z[r-1],1))< evalf(limite(f(x),x=Z[r],-1));
krp:=evalf(limite(f(x),x=Z[r],1))> evalf(limite(f(x),x=Z[r+1],-1)) ;
lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity;
lp:=lp+if(member(Z[r],F)) {
"limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
else{"valPos(btex $"+latex(simplifier(f(Z[r])))+"$
etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex
$ "+ao+" $ etex,0.5);"
}else{" "};
};//for
}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0);
krm:=evalf(limite(f(x),x=Z[rr-1],1))< evalf(limite(f(x),x=Z[rr],-1));
krp:=evalf(limite(f(x),x=Z[rr],1))> evalf(limite(f(x),x=Z[rr+1],-1)) ;
lmrm:=limite(f(x),x=Z[rr],-1)==-infinity;lmrp:=limite(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1]));
if(TestS==0){if( TestL==1 ){lp:=lp}else{ lp:=lp+if(member(Z[rr],F)) {
"limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
else{"valPos(btex $"+latex(simplifier(f(Z[rr])))+"$
etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
$ "+ao+" $ etex,0.5);
";rr:=rr+1;
}// else testL==1
}//testS==0
else{lp:=lp+if(member(Z[rr],F)){
"limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}}
else{"valPos(btex $"+latex(simplifier(f(Z[rr])))+"$
etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
"}}};rr:=rr+1;
}//else testS==0
}//for nz<NL
}// else nz<NL
//if nz=NL
};//if nz>2
lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity;
lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}else{"nonDefBarre;limGauche(btex $"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$ etex,"}+
if(kz==1){"1);"}else{"0);"};
intro:="
input tableauVariation;
verbatimtex
\\documentclass{article}
\\usepackage[upright]{fourier}
\\usepackage{amsmath}
\\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
\\begin{document}
etex
";
MetaL:= if(ftt==2){if(nz>2){intro+"beginTableau("+nmr+")"+
l0+lsi+lsp+lsf+"
endTableau;
end";}else{
intro+"beginTableau("+nmr+")"+
l0+
lsi+lsf+"
endTableau;
end";
}
}else{
if(ftt==0){if(nz>2){intro+"beginTableau("+nmr+")"+
l0+
li+
lp+
lf
+"
endTableau;
end";}else{intro+"beginTableau("+nmr+")"+
l0+
li+
lf
+"
endTableau;
end";}}else{
if(nz>2){intro+"beginTableau("+nmr+")"+
l0+
lsi+lsp+lsf+
li+
lp+
lf
+"
endTableau;
end";}else{intro+"beginTableau("+nmr+")"+
l0+
lsi+lsf+
li+
lf
+"
endTableau;
end";}
}};
return(MetaL);
}:;
\end{VerbatimOut}
\begin{VerbatimOut}{XcasTabSignL.cxx}
TS(L,D,nmr):={
L:=apply(f->unapply(f,x),L)
n:=size(L);
Z:=NULL;
mini:=D[0]; maxi:=D[1];
pour k de 0 jusque n-1 faire
S:=resoudre(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,simplifier(S[j]);}
fpour;
fsi;
fpour;
Z:=sort(Z);
nz:=size(Z);
if(nz>2){pour u de 1 jusque nz-2 faire
si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1;
fsi;
fpour;};
nz:=size(Z);
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+"
newLigneSignes(btex $\\hbox{\\bf Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$ 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;"};
MetaL:=" input tableauVariation;
verbatimtex
\\documentclass{article}
\\usepackage[upright]{fourier}
\\usepackage{amsmath}
\\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
\\begin{document}
etex
beginTableau("+nmr+")
newLigneVariables(btex $\\Mathbold{x}$ etex);
"+l0+li+
"
newLigneSignes(btex $\\hbox{\\bf Signe du }\\atop{{\\bf produit}}$ 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;
end"
;
}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+"
newLigneSignes(btex $\\hbox{\\bf Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$ 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(simplifier(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(simplifier(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
MetaL:=" input tableauVariation;
verbatimtex
\\documentclass{article}
\\usepackage[upright]{fourier}
\\usepackage{amsmath}
\\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
\\begin{document}
etex
beginTableau("+nmr+")
newLigneVariables(btex $\\Mathbold{x}$ etex);
"+l0+
li
+
"
newLigneSignes(btex $\\hbox{\\bf Signe du }\\atop{{\\bf produit}}$ 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;
end"
;}
return(MetaL);
}:;
\end{VerbatimOut}
\begin{VerbatimOut}{XcasTabSignQ.cxx}
TSq(nomf,L,Fo,D,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];
pour k de 0 jusque n-1 faire
S:=resoudre(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,simplifier(S[j]);}
fpour;
fsi;
fpour;
pour k de 0 jusque m-1 faire
SF:=resoudre(Fo[k](x),x);
si size(SF)>0 alors pour j de 0 jusque size(SF)-1 faire
FF:=FF,simplifier(SF[j]);
if(SF[j]>mini and SF[j]<maxi){F:=F,simplifier(SF[j]);}
fpour;
fsi;
fpour;
Z:=sort(Z); // on classe les zéros dans l'ordre croissant
nz:=size(Z);
if(nz>2){pour u de 1 jusque nz-2 faire
si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1; // pour les zéros en double
fsi;
fpour;}
Z:=sort(Z);
nz:=size(Z);
if(nz>2){pour u de 1 jusque nz-2 faire
si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1;
fsi;
fpour;};
nz:=size(Z);
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+"
newLigneSignes(btex $\\hbox{\\bf Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$ 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;"};
MetaL:=" input tableauVariation;
verbatimtex
\\documentclass{article}
\\usepackage[upright]{fourier}
\\usepackage{amsmath}
\\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
\\begin{document}
etex
beginTableau("+nmr+")
newLigneVariables(btex $\\Mathbold{x}$ etex);
"+l0+li+
"
newLigneSignes(btex $\\hbox{\\bf Signe }\\atop{{\\bf de "+nomf+"(x)}}$ 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;
end"
;
}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+"
newLigneSignes(btex $\\hbox{\\bf Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$ 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(simplifier(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(simplifier(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
MetaL:=" input tableauVariation;
verbatimtex
\\documentclass{article}
\\usepackage[upright]{fourier}
\\usepackage{amsmath}
\\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
\\begin{document}
etex
beginTableau("+nmr+")
newLigneVariables(btex $\\Mathbold{x}$ etex);
"+l0+
li
+
"
newLigneSignes(btex $\\hbox{\\bf Signe }\\atop{{\\bf de"+nomf+"(x)}}$ 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;
end"
;}
return(MetaL);
}:;
\end{VerbatimOut}
\begin{VerbatimOut}{XcasTabSign.cxx}
TSa(a,b,c,d,nmr):={
zA:=resoudre(a*x+b=0,x)[0];
zB:=resoudre(c*x+d=0,x)[0];
zmin:=min(zA,zB);
zmax:=max(zA,zB);
Meta:= " input tableauVariation;
verbatimtex
\\documentclass{article}
\\usepackage[upright]{fourier}
\\usepackage{amsmath}
\\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
\\begin{document}
etex
beginTableau("+nmr+")
newLigneVariables(btex $\\Mathbold{x}$ etex);
val(btex $-\\infty$ etex);val(btex $"+latex(zmin)+"$ etex);
val(btex $"+latex(zmax)+"$etex);
val(btex $+\\infty$ etex);
newLigneSignes(btex $\\hbox{\\bf Signe de }\\atop{\\displaystyle \\Mathbold{"+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+"}}$ 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;"}
+"
newLigneSignes(btex $\\hbox{\\bf Signe de }\\atop{\\displaystyle \\Mathbold{"+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+"}}$ 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;"}
+"
newLigneSignes(btex $\\hbox{\\bf Signe de }\\atop{\\displaystyle \\Mathbold{("+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+")("+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+")}}$ 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;
end"
;
return(Meta);
}:;
\end{VerbatimOut}
\begin{VerbatimOut}{XcasTSc.cxx}
TSc(g,D,nmr):={
f:=unapply(g,x);
Z:=NULL;
mini:=D[0]; maxi:=D[1];lm:=" ";
S:=resoudre(f(x),x);
if(size(S)==0){
li:=if(f(0)>0){"plus;"}else{"moins;"};
lm:=" ";lf:=" ";
}
else{pour j de 0 jusque size(S)-1 faire
if(S[j]>mini and S[j]<maxi){Z:=Z,simplifier(S[j])};
fpour;
Z:=sort(Z);
nz:=size(Z);
if(nz>2){pour u de 1 jusque nz-2 faire
si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1;
fsi;
fpour;}
nz:=size(Z);
l0:=" ";li:=" ";lr:=" ";
if(nz==0){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(f((mini+maxi)*0.5>0)){"plus;"}else{"moins;"};
lf:=if(maxi!=+infinity and f(maxi)==0){"
valBarre(btex 0 etex);"}else{"
"};
}else{
l0:="val(btex $"+latex(D[0])+"$ etex);";li:=" ";
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);";
li:= if(mini!=-infinity and f(mini)==0){"
valBarre(btex 0 etex);"}else{"
"}+
if(f(Z[0]-0.01)>0){"plus;"}else{"moins;"}+if(simplifier(f(Z[0]))==0){"valBarre(btex 0 etex);"}else{"barre;"};
lm:=if(nz>=2){for(r:=0; r<=nz-2;r++){if(f((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}+
if(simplifier(f(Z[r+1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}
}}else{" "};
lf:=if(f(Z[nz-1]+1.0)>0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}else{"
"};
}};
MetaL:=" input tableauVariation;
verbatimtex
\\documentclass{article}
\\usepackage[upright]{fourier}
\\usepackage{amsmath}
\\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
\\begin{document}
etex
beginTableau("+nmr+")
newLigneVariables(btex $\\Mathbold{x}$ etex);
"+l0+"
newLigneSignes(btex $\\hbox{\\bf Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(f(x))+"}}$ etex);"+
li+lm+lf
+"
endTableau;
end"
;
return(MetaL);
}:;
\end{VerbatimOut}
\begin{VerbatimOut}{XCas.giac}
maple_mode(0);
read("XcasTabSign.cxx");
Sortie:=fopen("XCasmp.mp");
vect.xcas.user := read("XCas.user");
vxo := vect.xcas.user;
dim.vxo := dim(vxo);
nbr.line.vxo := dim.vxo;
Resultat:=cat(" ");
rslt := vxo[0]; RslT:=cat(rslt);
Resultat:=cat(Resultat,RslT);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}
\newenvironment{TSa}
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\£µ]{XCas.user}}
{\end{VerbatimOut}
\executGiacmp{XCas.giac}
\immediate\write18{mpost XCasmp}
\begin{center}
\includegraphics{XCasmp.\theTVn}
\end{center}
\stepcounter{TVn}
}
\begin{VerbatimOut}{XCasQ.giac}
maple_mode(0);
read("XcasTabSignQ.cxx");
Sortie:=fopen("XCasmpQ.mp");
vect.xcas.user := read("XCasQ.user");
vxo := vect.xcas.user;
dim.vxo := dim(vxo);
nbr.line.vxo := dim.vxo;
Resultat:=cat(" ");
rslt := vxo[0]; RslT:=cat(rslt);
Resultat:=cat(Resultat,RslT);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}
\newenvironment{TSq}
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\£µ]{XCasQ.user}}
{\end{VerbatimOut}
\executGiacmp{XCasQ.giac}
\immediate\write18{mpost XCasmpQ}
\begin{center}
\includegraphics{XCasmpQ.\theTVn}
\end{center}
\stepcounter{TVn}
}
\begin{VerbatimOut}{XCasL.giac}
maple_mode(0);
read("XcasTabSignL.cxx");
Sortie:=fopen("XCasmpL.mp");
vect.xcas.user := read("XCasL.user");
vxo := vect.xcas.user;
dim.vxo := dim(vxo);
nbr.line.vxo := dim.vxo;
Resultat:=cat(" ");
rslt := vxo[0]; RslT:=cat(rslt);
Resultat:=cat(Resultat,RslT);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}
\newenvironment{TS}
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\£µ]{XCasL.user}}
{\end{VerbatimOut}
\executGiacmp{XCasL.giac}
\immediate\write18{mpost XCasmpL}
\begin{center}
\includegraphics{XCasmpL.\theTVn}
\end{center}
\stepcounter{TVn}
}
\begin{VerbatimOut}{XCasTSc.giac}
maple_mode(0);
read("XcasTSc.cxx");
Sortie:=fopen("XCasmpTSc.mp");
vect.xcas.user := read("XCasTSc.user");
vxo := vect.xcas.user;
dim.vxo := dim(vxo);
nbr.line.vxo := dim.vxo;
Resultat:=cat(" ");
rslt := vxo[0]; RslT:=cat(rslt);
Resultat:=cat(Resultat,RslT);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}
\newenvironment{TSc}
{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\£µ]{XCasTSc.user}}
{\end{VerbatimOut}
\executGiacmp{XCasTSc.giac}
\immediate\write18{mpost XCasmpTSc}
\begin{center}
\includegraphics{XCasmpTSc.\theTVn}
\end{center}
\stepcounter{TVn}
}
\begin{VerbatimOut}{XCasTV.giac}
maple_mode(0);
read("XcasTV.cxx");
Sortie:=fopen("XCasmpTV.mp");
vect.xcas.user := read("XCasTV.user");
vxo := vect.xcas.user;
dim.vxo := dim(vxo);
nbr.line.vxo := dim.vxo;
Resultat:=cat(" ");
rslt := vxo[0]; RslT:=cat(rslt);
Resultat:=cat(Resultat,RslT);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}
\newenvironment{TV}{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\£µ]{XCasTV.user}}{\end{VerbatimOut} \executGiacmp{XCasTV.giac}
\immediate\write18{mpost XCasmpTV}
\begin{center}
\includegraphics{XCasmpTV.\theTVn}
\end{center}
\stepcounter{TVn}
}
\begin{VerbatimOut}{XCasTVI.giac}
maple_mode(0);
read("XcasTVI.cxx");
Sortie:=fopen("XCasmpTVI.mp");
vect.xcas.user := read("XCasTVI.user");
vxo := vect.xcas.user;
dim.vxo := dim(vxo);
nbr.line.vxo := dim.vxo;
Resultat:=cat(" ");
rslt := vxo[0]; RslT:=cat(rslt);
Resultat:=cat(Resultat,RslT);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}
\newenvironment{TVI}{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\£µ]{XCasTVI.user}}{\end{VerbatimOut} \executGiacmp{XCasTVI.giac}
\immediate\write18{mpost XCasmpTVI}
\begin{center}
\includegraphics{XCasmpTVI.\theTVn}
\end{center}
\stepcounter{TVn}
}