diff options
Diffstat (limited to 'Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty')
| -rw-r--r-- | Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty | 317 |
1 files changed, 314 insertions, 3 deletions
diff --git a/Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty b/Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty index 508315fb27a..482b6f7a360 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}[07/02/2009 v4.03 la machine a creer des +\ProvidesPackage{tablor-xetex}[07/03/2009 v4.04 la machine a creer des tableaux de signes et variations compatible xetex] % \copyleft Connan le Barbare (aka Guillaume Connan) \copyright @@ -50,6 +50,14 @@ tableaux de signes et variations compatible xetex] %TVI([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,\tv) %\end{TVI} %%% +%%% +% tableau avec valeurs intermediares et racines exactes +%\begin{TVIex} +%TVIex([-1,+infinity],[-1],"f","x",x2/sqrt(x+1)-1,1,2,n,\tv) +%\end{TVIex} +%%% +% +% % tableau de variations avec f' sans zero formel %\begin{TVapp} % TVapp([0,+infinity],[0],"g","x",ln(x)-x*exp(2-x),1,\tv) @@ -1149,7 +1157,11 @@ LI:=limit(f(x),x,Z[0],1); LF:=limit(f(x),x,Z[nz-1],-1); LP:=NULL; PB:=1; -if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])};if(member(Z[r],F)){PB:=PB,0,1}}}; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; NL:=size(LL); @@ -1342,6 +1354,280 @@ fclose(sortie); +%% +% +% +% +% Pour avoir les racines sous forme exacte.... quand c'est possible ! +% +% +% +%%%%%%%%% + + +\begin{VerbatimOut}{XcasTVIex.cxx} + + + +TVIex(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={ +nl:=size(L); +f:=unapply(f,x); +fp:=function_diff(f); +Z:=concat(L,F); +S:=[]; + +Sex:=NULL; +Zex:=solve(f(x)=ao); +Zex:=sort(Zex); +for(j:=0;j<size(Zex);j++){ +if((evalf(Zex[j])>=evalf(L[0])) and (evalf(Zex[j])<=evalf(L[nl-1]))){Sex:=Sex,Zex[j]}; +}; +Sex:=[Sex]; + + + + + + + + +if(trigo==t){ +all_trig_solutions:=1; +reset_solve_counter(-1,-1); +SS:=solve(factor(simplify(fp(x))),x); +ns:=size(SS); +for(k:=0;k<ns;k++){ +m:=0; +while(evalf(simplify(subst(SS[k],n_1=m)))<=evalf(L[nl-1])){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m+1; +};m:=-1; +while(evalf(subst(SS[k],n_1=m))>=L[0]){ +S:=concat(S,simplify(subst(SS[k],n_1=m)));m:=m-1; +} +} +}else{ +S:=solve(fp(x),x); +} + + si size(S)>0 alors pour j de 0 jusque size(S)-1 faire + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + if(kk==1){Z:=append(Z,simplify(S[j]))}; + fpour + fsi; + +Z:=sort(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:=limit(f(x),x,Z[0],1); +LF:=limit(f(x),x,Z[nz-1],-1); +LP:=NULL; +PB:=1; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; +if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; + +NL:=size(LL); +A:=NULL;aa:=0; +kk:=0; + + + +if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); +if(TestS==0){A:=A,aa;l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"+"val(btex $"+latex(simplify(Sex[aa]))+"$ etex);";aa:=aa+1;}else{l0:=l0+"val(btex $"+latex(Z[k])+"$ etex);"}} +l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);"}; +//chgmt NL->nz +if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); + +if(PB[k]==1){if(TestS==0){ + A:=A,aa;l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);"+"val(btex $"+latex(simplify(Sex[aa]))+"$ etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex $"+latex(Z[kk])+"$ etex);";kk:=kk+1}}; +} + + l0:=l0+"val(btex $"+latex(Z[nz-1])+"$ etex);" + + }; + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); + kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1)); + +lsi:=lsic+nom+"'("+nomv+")}$ etex);"+ + if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ + if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ + if(sign(fp((Z[0]+10^(-3))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ + if(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$ $ etex);"+ if(sign(fp(10^(-3)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "}; + + + + +if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + ksp:=evalf(fp(Z[r]+0.01))>0; + TestL:=(abs(LL[r])==abs(LL[r+1])); + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex $ $ etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; + }} +else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + + if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $ $ etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} + else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ + if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} +}}}}; + + + + + lsf:=if(member(Z[nz-1],F)==0){" "}else{"nonDefBarre;"} + + + +lm0:=limit(f(x),x=Z[0],1)==-infinity; + + + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); + + li:=lvic+nom+"}$ etex); +"+ if(member(Z[0],F)==0){"valPos(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"} + else{"nonDefBarre;limDroite(btex $"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$ etex,"}+ + if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex $ "+ao+" $ etex,0.5);"}else{" "}; + + + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1)); + krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ; + lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity; + lp:=lp+if(member(Z[r],F)) { + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[r])))+"$ + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + $ "+ao+" $ etex,0.5);" + }else{" "}; +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); + krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1)); + krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ; + lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + $ "+ao+" $ etex,0.5); + ";rr:=rr+1; +}// testS==0 +else{lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex $"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$ etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex $"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$ etex,"+if(krp==1){"1);"}else{"0);"}} + else{"valPos(btex $"+latex(simplify(f(Z[rr])))+"$ + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + "}}};rr:=rr+1; +}//else testS==0 +}//PB[r]==1 +}//for nz<NL +}// else nz<NL +//if nz=NL +};//if nz>2 + + + +lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; + + +lf:=if(member(Z[nz-1],F)==0){"valPos(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);"}else{"0);"}} + else{"limGauche(btex $"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$ etex,"+ + if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + + + + + + + +MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; + +";}else{ +"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+" +endTableau; + +"; +} +}else{ +if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ + l0+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +li+ +lf ++" +endTableau; +";}}else{ +if(nz>2){"beginTableau("+nmr+")"+ + l0+ +lsi+lsp+lsf+ +li+ +lp+ +lf ++" +endTableau; + +";}else{"beginTableau("+nmr+")"+ + l0+ +lsi+lsf+ +li+ +lf ++" +endTableau; + +";} +}}; + + + + + + +sortie:=fopen("XCasmpfc.mp"); +fprint(sortie,Unquoted,MetaLfc); +fclose(sortie); + + + }:; + + +\end{VerbatimOut} + + + + + @@ -1420,7 +1706,11 @@ LI:=limit(f(x),x,Z[0],1); LF:=limit(f(x),x,Z[nz-1],-1); LP:=NULL; PB:=1; -if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])};if(member(Z[r],F)){PB:=PB,0,1}}}; +if(nz>2){ for(r:=1; + r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}; +if(member(Z[r],F)){PB:=PB,0,1}else{PB:=PB,1}; +} +}; if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; NL:=size(LL); @@ -2818,6 +3108,27 @@ read("XCasTVI.user"); +\begin{VerbatimOut}{XCasTVIex.giac} +maple_mode(0); +read("config.cxx"); +read("XcasTVIex.cxx"); +read("XCasTVIex.user"); +\end{VerbatimOut} + +\newenvironment{TVIex}% +{\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIex.user}}% +{\end{VerbatimOut}\dresse{TVIex}} + + +\newenvironment{TVIex*}[1]% +{\setcounter{TVnbis}{\theTVn} +\setcounter{TVn}{#1} +\VerbatimEnvironment\begin{VerbatimOut}[commandchars=\\??]{XCasTVIex.user}}% +{\end{VerbatimOut}\dressetoile{TVIex}} + + + + \begin{VerbatimOut}{XCasTVIapp.giac} maple_mode(0); 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