tablor 4.02c

git-svn-id: svn://tug.org/texlive/trunk@12009 c570f23f-e606-0410-a88d-b1316a301751

2 files changed, 215 insertions, 147 deletions

diff --git a/Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty b/Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty
index 9f689d30e2f..fc9b6e7a14c 100644
--- a/Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty
+++ b/Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty
@@ -1,5 +1,5 @@
 \NeedsTeXFormat{LaTeX2e}[1995/12/01]
-\ProvidesPackage{tablor-xetex}[24/11/2008 v4.02b  la machine a  creer des
+\ProvidesPackage{tablor-xetex}[29/01/2009 v4.02c  la machine a  creer des
 tableaux de signes et variations compatible xetex]
 
 % \copyleft Connan le Barbare (aka Guillaume Connan) \copyright
@@ -1149,31 +1149,38 @@ 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;
-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(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
+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}}};
+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;
+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(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}};
+}
 
-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);
-"};
+ 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);
+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(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(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(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "}; 
@@ -1181,28 +1188,33 @@ lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
 
 
 
- 
-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); 
+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:=(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;"}+
+                                          }}  
+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;"}+
+                                    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;"}
 
 
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;"}
 lm0:=limit(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);
+
+
+
+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,"}
@@ -1210,41 +1222,43 @@ TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))=
            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); 
+                     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(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
+                                            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:=(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); 
+};//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(TestS==0){if( TestL==1 ){lp:=lp}else{  lp:=lp+if(member(Z[rr],F)) {
+                   
+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(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
+                                            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;
-}// else testL==1
-}//testS==0
+}//  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(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+                                            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;
 
 
@@ -1254,7 +1268,10 @@ lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
     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;"}};    
-    
+
+
+
+
 
 
 
@@ -1308,6 +1325,10 @@ endTableau;
 
 
 
+
+
+
+
 sortie:=fopen("XCasmpfc.mp");
 fprint(sortie,Unquoted,MetaLfc);
 fclose(sortie);
@@ -1317,6 +1338,7 @@ fclose(sortie);
 
 
 
+
 \end{VerbatimOut}
 
 
@@ -1335,7 +1357,6 @@ fclose(sortie);
 
 \begin{VerbatimOut}{XcasTVIapp.cxx}
 
-
 TVIapp(L,F,nom,nomv,f,ftt,ao,nmr):={
 
 
@@ -1350,10 +1371,10 @@ nz:=size(z);
 
 
 S:=NULL;
-if(L==[-infinity,+infinity]){j:=[seq(-100+k,k=0..200)]minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
-else{if(L[0]==-infinity){j:=[seq(k,k=100..floor(L[1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
-else{if(L[1]==+infinity){j:=[seq(k,k=floor(L[0])..100)] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for;}
-else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for;  }}};
+if(L==[-infinity,+infinity]){j:=[seq(-100+k,k=0..200)]minus F;for k in j do S:=S,resoudre_numerique(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[0]==-infinity){j:=[seq(k,k=100..floor(L[1]))] minus F;for k in j do S:=S,resoudre_numerique(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[1]==+infinity){j:=[seq(k,k=floor(L[0])..100)] minus F;for k in j do S:=S,resoudre_numerique(fp(x),x,k/10,newton_solver);end_for;}
+else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;for k in j do S:=S,resoudre_numerique(fp(x),x,k/10,newton_solver);end_for;  }}};
 
 
 
@@ -1399,31 +1420,37 @@ 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;
-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(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
+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}}};
+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;
+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(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}};
+}
 
-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);
-"};
+ 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);
+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(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(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(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "}; 
@@ -1431,28 +1458,33 @@ lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
 
 
 
- 
-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); 
+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:=(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;"}+
+                                          }}  
+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;"}+
+                                    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;"}
 
 
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;"}
 lm0:=limit(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);
+
+
+
+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,"}
@@ -1460,43 +1492,44 @@ TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))=
            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); 
+                     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(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
+                                            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:=(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); 
+};//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(TestS==0){if( TestL==1 ){lp:=lp}else{  lp:=lp+if(member(Z[rr],F)) {
+                   
+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(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
+                                            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;
-}// else testL==1
-}//testS==0
+}//  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(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+                                            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;
 
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
 
 
 lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
@@ -1505,7 +1538,7 @@ lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
     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;"}};    
-    
+
 
 
 
@@ -1562,6 +1595,7 @@ endTableau;
 
 
 
+
 sortie:=fopen("XCasmpfc.mp");
 fprint(sortie,Unquoted,MetaLfc);
 fclose(sortie);
@@ -1571,6 +1605,7 @@ fclose(sortie);
 
 
 
+
 \end{VerbatimOut}
 
 
diff --git a/Master/texmf-dist/tex/latex/tablor/tablor.sty b/Master/texmf-dist/tex/latex/tablor/tablor.sty
index 60410882ba1..a8b81775251 100644
--- a/Master/texmf-dist/tex/latex/tablor/tablor.sty
+++ b/Master/texmf-dist/tex/latex/tablor/tablor.sty
@@ -1,5 +1,5 @@
 \NeedsTeXFormat{LaTeX2e}[1995/12/01]
-\ProvidesPackage{tablor}[24/11/2008 v4.02b la machine a creer des tableaux de signes et variations]
+\ProvidesPackage{tablor}[29/01/2009 v4.02c la machine a creer des tableaux de signes et variations]
 
 % \copyleft Connan le Barbare (aka Guillaume Connan) \copyright
 % This work may be distributed and/or mofified under the conditions
@@ -1112,31 +1112,38 @@ 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;
-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(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
+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}}};
+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;
+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(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}};
+}
 
-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);
-"};
+ 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);
+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(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(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(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "}; 
@@ -1144,28 +1151,33 @@ lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
 
 
 
- 
-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); 
+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:=(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;"}+
+                                          }}  
+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;"}+
+                                    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;"}
 
 
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;"}
 lm0:=limit(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);
+
+
+
+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,"}
@@ -1173,41 +1185,43 @@ TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))=
            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); 
+                     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(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
+                                            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:=(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); 
+};//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(TestS==0){if( TestL==1 ){lp:=lp}else{  lp:=lp+if(member(Z[rr],F)) {
+                   
+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(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
+                                            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;
-}// else testL==1
-}//testS==0
+}//  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(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+                                            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;
 
 
@@ -1217,7 +1231,10 @@ lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
     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;"}};    
-    
+
+
+
+
 
 
 
@@ -1271,6 +1288,10 @@ endTableau;
 
 
 
+
+
+
+
 sortie:=fopen("XCasmpfc.mp");
 fprint(sortie,Unquoted,MetaLfc);
 fclose(sortie);
@@ -1298,7 +1319,6 @@ fclose(sortie);
 
 \begin{VerbatimOut}{XcasTVIapp.cxx}
 
-
 TVIapp(L,F,nom,nomv,f,ftt,ao,nmr):={
 
 
@@ -1313,10 +1333,10 @@ nz:=size(z);
 
 
 S:=NULL;
-if(L==[-infinity,+infinity]){j:=[seq(-100+k,k=0..200)]minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
-else{if(L[0]==-infinity){j:=[seq(k,k=100..floor(L[1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for}
-else{if(L[1]==+infinity){j:=[seq(k,k=floor(L[0])..100)] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for;}
-else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;for k in j do S:=S,fsolve(fp(x),x,k/10,newton_solver);end_for;  }}};
+if(L==[-infinity,+infinity]){j:=[seq(-100+k,k=0..200)]minus F;for k in j do S:=S,resoudre_numerique(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[0]==-infinity){j:=[seq(k,k=100..floor(L[1]))] minus F;for k in j do S:=S,resoudre_numerique(fp(x),x,k/10,newton_solver);end_for}
+else{if(L[1]==+infinity){j:=[seq(k,k=floor(L[0])..100)] minus F;for k in j do S:=S,resoudre_numerique(fp(x),x,k/10,newton_solver);end_for;}
+else{ j:=[seq(k,k=floor(z[0])..floor(z[nz-1]))] minus F;for k in j do S:=S,resoudre_numerique(fp(x),x,k/10,newton_solver);end_for;  }}};
 
 
 
@@ -1362,31 +1382,37 @@ 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;
-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(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]};
+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}}};
+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;
+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(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}};
+}
 
-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);
-"};
+ 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);
+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(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(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(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "}; 
@@ -1394,28 +1420,33 @@ lsi:=lsic+nom+"'("+nomv+")}$ etex);"+
 
 
 
- 
-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); 
+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:=(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;"}+
+                                          }}  
+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;"}+
+                                    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;"}
 
 
 
-lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre;"}
 lm0:=limit(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);
+
+
+
+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,"}
@@ -1423,43 +1454,44 @@ TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))=
            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); 
+                     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(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
+                                            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:=(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); 
+};//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(TestS==0){if( TestL==1 ){lp:=lp}else{  lp:=lp+if(member(Z[rr],F)) {
+                   
+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(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex
+                                            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;
-}// else testL==1
-}//testS==0
+}//  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(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);
+                                            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;
 
+lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity;
 
 
 lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
@@ -1468,7 +1500,7 @@ lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+
     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;"}};    
-    
+
 
 
 
@@ -1525,6 +1557,7 @@ endTableau;
 
 
 
+
 sortie:=fopen("XCasmpfc.mp");
 fprint(sortie,Unquoted,MetaLfc);
 fclose(sortie);
@@ -1534,8 +1567,8 @@ fclose(sortie);
 
 
 
-\end{VerbatimOut}
 
+\end{VerbatimOut}