new package tablor, put into mathextra

git-svn-id: svn://tug.org/texlive/trunk@6313 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 726 insertions, 0 deletions

diff --git a/Master/texmf-dist/tex/latex/tablor/tablor.sty b/Master/texmf-dist/tex/latex/tablor/tablor.sty
new file mode 100644
index 00000000000..fa48fb7905c
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/tablor/tablor.sty
@@ -0,0 +1,726 @@
+
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+\ProvidesPackage{tablor}
+              [17/01/2008 v1.2
+ la machine à créer des tableaux de signes et variations]
+
+
+
+%% Crée 5 environnements :
+%% tableau de signes de 2 facteurs affines
+% \begin{TSa}
+% TSa(-2,3,-1,5,1);
+% \end{TSa}
+% %%%%%% Pour des tableaux de plus de 2 facteurs
+%
+% \begin{TS}
+% TS([-2*x+3,x^2-1,x^2+1,x-1,x^2-2],2);
+% \end{TS}
+%
+% pour les tableaux de signes avec quotient
+%\begin{TSq}
+%TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],3)
+%%\end{TSq}
+% un tableau de variation :
+%
+% \begin{TV}
+% TV([0,+infinity],[0],"h","x",ln(x)-(ln(x))^2,1,4)
+% \end{TV}
+%
+% tableau avec valeurs intermédiares
+%\begin{TVI}
+%TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,1)
+%\end{TVI}
+%%%
+
+
+
+\newcommand{\nettoyer}{
+\immediate\write18{rm XCasmp.mp* XCasmp.log XCasmp?.mp* XCasmp?.log XCasmpTV.mp* XCasmpTV.log *.out XCasmpTVI.mp* XCasmpTVI.log
+  *.in *.meta *mpx*}}
+
+\newcommand{\bouger}[1]{
+\immediate\write18{cp XCas* #1}}
+
+
+\newcommand{\recup}[2]{
+\immediate\write18{cp #1 #2}}
+
+
+
+\newcounter{TVn}
+
+
+\usepackage{fancyvrb}
+%\usepackage[upright]{fourier}
+
+\makeatletter
+\newcommand{\executGiacmp}[1]{
+\immediate\write18{giac  <#1 } }
+\makeatother
+
+
+\begin{VerbatimOut}{XcasTV.meta}
+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
+%&latex
+ \\documentclass{article}
+ \\usepackage[upright]{fourier}
+ \\usepackage{amsmath}
+ \\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
+ \\begin{document}
+ etex 
+
+"
+  
+
+MetaL:= 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.meta}
+
+
+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
+%&latex
+ \\documentclass{article}
+ \\usepackage[upright]{fourier}
+ \\usepackage{amsmath}
+ \\newcommand{\\Mathbold}[1]{\\mbox{\\boldmath$#1$\\unboldmath}}
+ \\begin{document}
+ etex 
+
+";
+  
+
+MetaL:= 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.meta}
+TS(L,nmr):={
+L:=apply(f->unapply(f,x),L)
+n:=size(L);
+Z:=NULL;
+
+
+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 
+                          Z:=Z,simplifier(S[j]);
+                      fpour;
+  fsi;
+fpour;
+Z:=sort(Z);
+nz:=size(Z);
+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:=" "; 
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);";fpour; 
+
+
+
+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(L[p](Z[0]-1.0)>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;"}}+ 
+                           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;"}
+    };  
+
+
+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
+%&latex
+ \\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);"+l0+"val(btex $+\\infty$ etex);"+
+                     li
+                     +
+    " newLigneSignes(btex $\\hbox{\\bf Signe du }\\atop{{\\bf produit}}$ etex);"+ 
+                         if(product(L[s](Z[0]-1.0),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"+
+                         lr+
+                         if(product(L[s](Z[nz-1]+1.0),s,0,n-1)>0){"plus;"}else{"moins;"}+"
+endTableau;
+end"
+;
+return(MetaL);
+ }:;
+\end{VerbatimOut}
+
+
+
+
+
+
+
+
+
+\begin{VerbatimOut}{XcasTabSignQ.meta}
+TSq(nomf,L,Fo,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;
+
+
+
+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 
+                          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 
+                          F:=F,simplifier(SF[j]);
+                      fpour;
+  fsi;
+fpour;
+
+
+
+Z:=sort(Z); // on classe les zéros dans l'ordre croissant 
+nz:=size(Z);
+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;
+nz:=size(Z);
+l0:=" ";li:=" ";lr:=" "; 
+pour m de 0 jusque nz-1 faire l0:=l0+"val(btex $"+latex(Z[m])+"$ etex);";fpour; 
+
+
+
+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(L[p](Z[0]-1.0)>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;"}}+ 
+                           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;
+                                                                    "}
+    };  
+
+
+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],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}                    
+                         fpour
+
+MetaL:=" input tableauVariation;
+           verbatimtex
+%&latex
+ \\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);"+l0+"val(btex $+\\infty$ etex);"+
+                     li
+                     +
+    " newLigneSignes(btex $\\hbox{\\bf Signe de }\\atop{\\bf "+nomf+"(x) }$ etex);"+ 
+                         if(product(L[s](Z[0]-1.0),s,0,n-1)>0){"plus;"}else{"moins;"}+if(member(Z[0],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+
+                         lr+                          
+                         if(product(L[s](Z[nz-1]+1.0),s,0,n-1)>0){"plus;"}else{"moins;"}+"
+endTableau;
+end"
+;
+return(MetaL);
+ }:;
+
+
+\end{VerbatimOut}
+
+\begin{VerbatimOut}{XcasTabSign.meta}
+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
+%&latex
+ \\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}{XCas.in}
+maple_mode(0);
+read("XcasTabSign.meta");
+Sortie:=fopen("XCasmp.mp");
+vect.xcas.out := read("XCas.out");
+vxo := vect.xcas.out;
+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}
+{\stepcounter{TVn}\VerbatimEnvironment\begin{VerbatimOut}{XCas.out}}
+{\end{VerbatimOut}
+           \executGiacmp{XCas.in}
+
+   \immediate\write18{mpost  XCasmp}
+
+\begin{center}
+  \includegraphics{XCasmp.\theTVn}
+\end{center}
+
+}
+
+
+\begin{VerbatimOut}{XCasQ.in}
+maple_mode(0);
+read("XcasTabSignQ.meta");
+Sortie:=fopen("XCasmpQ.mp");
+vect.xcas.out := read("XCasQ.out");
+vxo := vect.xcas.out;
+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}
+{\stepcounter{TVn}\VerbatimEnvironment\begin{VerbatimOut}{XCasQ.out}}
+{\end{VerbatimOut}
+           \executGiacmp{XCasQ.in}
+
+   \immediate\write18{mpost  XCasmpQ}
+
+\begin{center}
+  \includegraphics{XCasmpQ.\theTVn}
+\end{center}
+
+}
+
+
+
+\begin{VerbatimOut}{XCasL.in}
+maple_mode(0);
+read("XcasTabSignL.meta");
+Sortie:=fopen("XCasmpL.mp");
+vect.xcas.out := read("XCasL.out");
+vxo := vect.xcas.out;
+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}
+{\stepcounter{TVn}\VerbatimEnvironment\begin{VerbatimOut}{XCasL.out}}
+{\end{VerbatimOut}
+           \executGiacmp{XCasL.in}
+
+   \immediate\write18{mpost  XCasmpL}
+
+\begin{center}
+  \includegraphics{XCasmpL.\theTVn}
+\end{center}
+
+}
+
+
+
+
+
+
+\begin{VerbatimOut}{XCasTV.in}
+maple_mode(0);
+read("XcasTV.meta");
+Sortie:=fopen("XCasmpTV.mp");
+vect.xcas.out := read("XCasTV.out");
+vxo := vect.xcas.out;
+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}
+{\stepcounter{TVn}\VerbatimEnvironment\begin{VerbatimOut}{XCasTV.out}}
+{\end{VerbatimOut}
+           \executGiacmp{XCasTV.in}
+
+   \immediate\write18{mpost  XCasmpTV}
+
+\begin{center}
+  \includegraphics{XCasmpTV.\theTVn}
+\end{center}
+
+}
+
+
+
+
+\begin{VerbatimOut}{XCasTVI.in}
+maple_mode(0);
+read("XcasTVI.meta");
+Sortie:=fopen("XCasmpTVI.mp");
+vect.xcas.out := read("XCasTVI.out");
+vxo := vect.xcas.out;
+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}
+{\stepcounter{TVn}\VerbatimEnvironment\begin{VerbatimOut}{XCasTVI.out}}
+{\end{VerbatimOut}
+           \executGiacmp{XCasTVI.in}
+
+   \immediate\write18{mpost  XCasmpTVI}
+
+\begin{center}
+  \includegraphics{XCasmpTVI.\theTVn}
+\end{center}
+
+}
+
+
+
+
+
+
+%%
+%% Zi end