diff options
| author | Karl Berry <karl@freefriends.org> | 2009-01-30 00:04:41 +0000 |
|---|---|---|
| committer | Karl Berry <karl@freefriends.org> | 2009-01-30 00:04:41 +0000 |
| commit | 308a0af8573a8c98d928c70da0ae23af2a9efc9c (patch) | |
| tree | 4286dabd335223f38e8680edd82f3d7f9f94e1aa | |
| parent | 57dc228a8a25fbb466bb7be4fe4ca0ba310c16f2 (diff) | |
tablor 4.02c
git-svn-id: svn://tug.org/texlive/trunk@12009 c570f23f-e606-0410-a88d-b1316a301751
| -rw-r--r-- | Master/texmf-dist/doc/latex/tablor/tablor.html | 426 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/tablor/tablor-xetex.sty | 181 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/tablor/tablor.sty | 181 |
3 files changed, 449 insertions, 339 deletions
diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.html b/Master/texmf-dist/doc/latex/tablor/tablor.html index fde38cb5681..7841bf6b493 100644 --- a/Master/texmf-dist/doc/latex/tablor/tablor.html +++ b/Master/texmf-dist/doc/latex/tablor/tablor.html @@ -22,7 +22,7 @@ } .constant { /* font-lock-constant-face */ - color: #68228b; + color: #9932cc; font-weight: bold; } .flyspell-duplicate { @@ -31,6 +31,12 @@ font-weight: bold; text-decoration: underline; } + .flyspell-incorrect { + /* flyspell-incorrect-face */ + color: #ff4500; + font-weight: bold; + text-decoration: underline; + } .font-latex-math { /* font-latex-math-face */ color: #436eee; @@ -54,11 +60,11 @@ } .function-name { /* font-lock-function-name-face */ - color: #6ca6cd; + color: #87ceeb; } .keyword { /* font-lock-keyword-face */ - color: #32cd32; + color: #6495ed; font-weight: bold; } .variable-name { @@ -81,10 +87,10 @@ <body> <pre> <span class="font-latex-sedate">\NeedsTeXFormat</span>{LaTeX2e}[1995/12/01] -<span class="font-latex-sedate">\ProvidesPackage</span>{<span class="flyspell-duplicate">tablor</span>}[24/11/2008 v4.02b la machine a creer des tableaux de signes et variations] +<span class="font-latex-sedate">\ProvidesPackage</span>{<span class="flyspell-duplicate">tablor</span>}[29/01/2009 v4.02c la machine a creer des tableaux de signes et variations] <span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\copyleft</span></span><span class="comment"> Connan le Barbare (aka Guillaume Connan) </span><span class="font-latex-sedate"><span class="comment">\copyright</span></span><span class="comment"> -</span><span class="comment-delimiter">% </span><span class="comment"><span class="flyspell-duplicate">This</span></span><span class="comment"> work may be distributed and/or mofified under the conditions +</span><span class="comment-delimiter">% </span><span class="comment">This work may be distributed and/or mofified under the conditions </span><span class="comment-delimiter">% </span><span class="comment">or the LaTeX Project Public Licence, either v1.3 or (at your option) </span><span class="comment-delimiter">% </span><span class="comment">any later version. The latest version is in </span><span class="comment-delimiter">% </span><span class="comment">http://www.latex-project.org/lppl/ @@ -105,7 +111,7 @@ </span><span class="comment-delimiter">%</span><span class="comment"> </span><span class="comment-delimiter">% </span><span class="comment">pour les tableaux de signes avec quotient </span><span class="comment-delimiter">%</span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TSq} -</span><span class="comment-delimiter">%</span><span class="comment"><span class="flyspell-duplicate">TSq</span></span><span class="comment">("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) +</span><span class="comment-delimiter">%</span><span class="comment">TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],[a,b],n,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">) </span><span class="comment-delimiter">%%</span><span class="font-latex-sedate"><span class="comment">\end</span></span><span class="comment">{TSq} </span><span class="comment-delimiter">% </span><span class="comment">un tableau de variation : </span><span class="comment-delimiter">%</span><span class="comment"> @@ -196,14 +202,14 @@ <span class="comment-delimiter">%% </span><span class="comment">Initialisation du choix d'OS -</span><span class="font-latex-sedate">\newboolean</span>{windows}<span class="font-latex-sedate">\setboolean</span>{windows}{false} +</span><span class="font-latex-sedate">\newboolean</span>{windows}<span class="font-latex-sedate">\setboolean</span>{windows}{<span class="flyspell-duplicate">false</span>} <span class="comment-delimiter">%% </span><span class="comment">on configure tablor dans un fichier exterieur pour la plateforme </span><span class="comment-delimiter">%% </span><span class="comment">et l'editeur </span> -<span class="font-latex-sedate">\IfFileExists</span>{tablor.cfg}{<span class="font-latex-sedate"><span class="keyword">\input</span></span><span class="constant">{tablor.cfg}</span>}<span class="comment">%</span><span class="font-latex-sedate"><span class="comment">\typeout</span></span><span class="comment">{pas de fichier tablor.cfg}} +<span class="font-latex-sedate">\IfFileExists</span>{tablor.cfg}{<span class="font-latex-sedate"><span class="keyword">\input</span></span><span class="constant">{tablor.cfg}</span>}<span class="comment">%</span><span class="font-latex-sedate"><span class="comment">\typeout</span></span><span class="comment">{pas de fichier tablor.</span><span class="comment"><span class="flyspell-duplicate">cfg</span></span><span class="comment">}} </span> <span class="comment-delimiter">%% </span><span class="comment">Definit des commandes disque selon l'OS utilise @@ -211,7 +217,7 @@ </span> {<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\rem</span></span><span class="function-name">}</span>{DEL } <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cat</span></span><span class="function-name">}</span>{TYPE } <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{COPY }}<span class="comment">% </span> {<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\rem</span></span><span class="function-name">}</span>{rm }<span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cat</span></span><span class="function-name">}</span>{cat } - <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{cp }} + <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\cp</span></span><span class="function-name">}</span>{<span class="flyspell-duplicate">cp</span> }} @@ -219,7 +225,7 @@ -<span class="comment-delimiter">%% </span><span class="comment">pour ceux compilant via pdflatex +<span class="comment-delimiter">%% </span><span class="comment">pour ceux compilant via </span><span class="comment"><span class="flyspell-incorrect">pdflatex</span></span><span class="comment"> </span> <span class="font-latex-sedate">\ifpdf</span> <span class="font-latex-sedate">\DeclareGraphicsRule</span>{*}{mps}{*}{} @@ -227,7 +233,7 @@ <span class="comment-delimiter">%% </span><span class="comment">pour nettoyer les fichiers auxiliaires </span> -<span class="font-latex-sedate">\AtEndDocument</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> *.user XCas* Xcas* *.mpx} +<span class="font-latex-sedate">\AtEndDocument</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> *.user XCas* Xcas* *.<span class="flyspell-incorrect">mpx</span>} } @@ -238,7 +244,7 @@ <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{queue.mp} - end + <span class="flyspell-duplicate">end</span> <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> @@ -251,7 +257,7 @@ <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\nettoyer</span></span><span class="function-name">}</span>[1][<span class="font-latex-sedate">\jobname</span>]<span class="comment">% -</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> #1.Tab.log queue.mp enteteMP.cfg session.tex config.cxx} +</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> #1.Tab.log queue.mp enteteMP.cfg session.tex config.<span class="flyspell-duplicate">cxx</span>} } @@ -267,30 +273,30 @@ <span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{TVn}</span> <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\tv</span></span><span class="function-name">}</span>{<span class="font-latex-sedate">\theTVn</span>} -<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{TVnbis}</span> +<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVnbis</span></span><span class="function-name">}</span> <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\tvbis</span></span><span class="function-name">}</span>{<span class="font-latex-sedate">\theTVnbis</span>} <span class="comment-delimiter">%% </span><span class="comment">permet de donner un prefixe aux tableaux produits (</span><span class="font-latex-sedate"><span class="comment">\jobname</span></span><span class="comment"> par defaut) -</span><span class="comment-delimiter">%% </span><span class="comment">effectue quelques verifications : +</span><span class="comment-delimiter">%% </span><span class="comment">effectue quelques </span><span class="comment"><span class="flyspell-incorrect">verifications</span></span><span class="comment"> : </span> <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\initablor</span></span><span class="function-name">}</span>[1][<span class="font-latex-sedate">\jobname</span>]{<span class="comment">% </span><span class="font-latex-sedate"><span class="keyword">\renewcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\nomtravail</span></span><span class="function-name">}</span>{#1}<span class="comment">% Arret du nom des tableaux </span><span class="font-latex-sedate"><span class="keyword">\setcounter</span></span><span class="variable-name">{TVn}{0}</span><span class="comment">% Initialisation du compteur de tableaux. -</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{xcas}}<span class="comment">% Avec l'option XCas +</span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{xcas}}<span class="comment">% Avec l'option </span><span class="comment"><span class="flyspell-duplicate">XCas</span></span><span class="comment"> </span>{<span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\nomtravail</span>.Tab.mp}<span class="comment">% Si Tableaux.mp est present... </span> {<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\rem</span> <span class="font-latex-sedate">\nomtravail</span>.Tab.mp}}<span class="comment">% le detruire </span> {}<span class="comment">% -</span> <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cp</span> enteteMP.cfg <span class="font-latex-sedate">\nomtravail</span>.Tab.mp}<span class="comment">% Reconstituer l'entête de Tableaux.mp +</span> <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="font-latex-sedate">\cp</span> enteteMP.cfg <span class="font-latex-sedate">\nomtravail</span>.Tab.mp}<span class="comment">% Reconstituer l'entête de Tableaux.</span><span class="comment"><span class="flyspell-duplicate">mp</span></span><span class="comment"> </span>} {<span class="font-latex-sedate">\IfFileExists</span>{<span class="font-latex-sedate">\nomtravail</span>.Tab.mp}<span class="comment">% Sans l'option XCas, si </span> <span class="comment">% Tableaux.mp existe </span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost -interaction=batchmode <span class="font-latex-sedate">\nomtravail</span>.Tab}}<span class="comment">% l'executer pour reconstituer les figures </span>{<span class="font-latex-sedate">\PackageWarning</span>{tablor}{Pas de source metapost pour creer les tableaux.}}<span class="comment">% sinon message d'erreur </span> <span class="comment">% (mais pas d'arret car les tableaux -</span> <span class="comment">% peuvent être presents ) +</span> <span class="comment">% peuvent être </span><span class="comment"><span class="flyspell-incorrect">presents</span></span><span class="comment"> ) </span>}}<span class="comment">% </span> @@ -300,7 +306,7 @@ <span class="font-latex-sedate">\makeatletter</span> <span class="font-latex-sedate"><span class="keyword">\newcommand</span></span><span class="function-name">{</span><span class="font-latex-sedate"><span class="function-name">\executGiacmp</span></span><span class="function-name">}</span>[1]{<span class="comment">% </span><span class="font-latex-sedate">\ifthenelse</span>{<span class="font-latex-sedate">\boolean</span>{windows}}<span class="comment">% -</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{giac #1 }}<span class="comment">% +</span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="flyspell-duplicate">giac</span> #1 }}<span class="comment">% </span>{<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{giac <#1 }}} <span class="font-latex-sedate">\makeatother</span> @@ -325,19 +331,19 @@ TV(L,F,nom,nomv,f,ftt,trigo,nmr):={ nl:=size(L); f:=unapply(f,x); -fp:=function_diff(f); +<span class="flyspell-duplicate">fp</span>:=function_diff(f); Z:=concat(L,F); S:=[]; if(trigo==t){ -all_trig_solutions:=1; +<span class="flyspell-duplicate">all</span>_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])){ +<span class="flyspell-duplicate">while</span>(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]){ @@ -353,14 +359,14 @@ S:=solve(fp(x),x); qq:=member(simplify(S[j]),Z)==0; kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); if(kk==1){if(qq==1){Z:=append(Z,simplify(S[j]))}}; - fpour + <span class="flyspell-duplicate">fpour</span> fsi; Z:=sort(Z); nz:=size(Z); tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); - ftantque; + <span class="flyspell-duplicate">ftantque</span>; @@ -376,7 +382,7 @@ nz:=size(Z); Z:=sort(Z); nz:=size(Z); - si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=nz-1; + si Z[0]==Z[1] alors Z:=augment(Z[0],Z[2..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-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; @@ -388,7 +394,7 @@ pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+ ";fpour; k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); - kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1)); + kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[<span class="flyspell-duplicate">nz</span>-2],1)); lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ @@ -426,12 +432,12 @@ lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; -lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ +<span class="flyspell-duplicate">lf</span>:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ if(kz==1){"1);"}else{"0);"}} else{"limGauche(btex <span class="font-latex-math">$"+ if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ - if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + if(kz==1){"1);nonDefBarre;"}else{"0);<span class="flyspell-duplicate">nonDefBarre</span>;"}}; @@ -441,30 +447,30 @@ MetaLfc:=if(ftt==2){if(nz>2){" beginTableau("+nmr+")"+ l0+lsi+lsp+lsf+" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";}else{ intro+"beginTableau("+nmr+")"+ l0+ lsi+lsf+" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; "; } }else{ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ l0+ li+ -lp+ +<span class="flyspell-duplicate">lp</span>+ lf +" endTableau; -";}else{"beginTableau("+nmr+")"+ +";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+ l0+ li+ lf +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";}}else{ if(nz>2){"beginTableau("+nmr+")"+ @@ -472,17 +478,17 @@ if(nz>2){"beginTableau("+nmr+")"+ lsi+lsp+lsf+ li+ lp+ -lf +<span class="flyspell-duplicate">lf</span> +" endTableau; ";}else{"beginTableau("+nmr+")"+ l0+ -lsi+lsf+ +<span class="flyspell-duplicate">lsi</span>+lsf+ li+ lf +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";} }} @@ -490,7 +496,7 @@ endTableau; sortie:=fopen("XCasmpfc.mp"); fprint(sortie,Unquoted,MetaLfc); -fclose(sortie); +<span class="flyspell-duplicate">fclose</span>(sortie); }:; @@ -507,7 +513,7 @@ fclose(sortie); <span class="comment-delimiter">%</span><span class="comment"> </span><span class="comment-delimiter">%</span><span class="comment"> -</span><span class="comment-delimiter">% </span><span class="comment">TVPC : pour les fonctions prolongeables par continuité. +</span><span class="comment-delimiter">% </span><span class="comment">TVPC : pour les fonctions prolongeables par </span><span class="comment"><span class="flyspell-duplicate">continuit</span></span><span class="comment">é. </span><span class="comment-delimiter">%%</span><span class="comment"> </span><span class="comment-delimiter">%%</span><span class="comment"> </span> @@ -526,7 +532,7 @@ S:=[]; if(trigo==t){ all_trig_solutions:=1; -reset_solve_counter(-1,-1); +<span class="flyspell-duplicate">reset</span>_solve_counter(-1,-1); SS:=solve(factor(simplify(fp(x))),x); ns:=size(SS); for(k:=0;k<ns;k++){ @@ -554,7 +560,7 @@ nz:=size(Z); tantque evalf(Z[0])==evalf(Z[1]) faire Z:=Z[1..nz-1];nz:=size(Z); - ftantque; + <span class="flyspell-duplicate">ftantque</span>; @@ -565,7 +571,7 @@ nz:=size(Z); 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 + <span class="flyspell-duplicate">fpour</span> fsi; Z:=sort(Z); @@ -584,7 +590,7 @@ pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+ 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+")}<span class="font-latex-math">$ etex);"+ +<span class="flyspell-duplicate">lsi</span>:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],FP)==0){ if(fp(Z[0])==0){"valBarre(btex 0 etex);"}else{" "}+ if(sign(fp(Z[0]+10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ @@ -595,7 +601,7 @@ if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.1))>0; if(ksp==1){"plus;"}else{"moins;"} }; } -lsf:=if(member(Z[nz-1],FP)==0){""}else{"nonDefBarre; +</span><span class="font-latex-math"><span class="flyspell-duplicate">lsf</span></span><span class="font-latex-math">:=if(member(Z[nz-1],FP)==0){""}else{"nonDefBarre; "} lm0:=limit(f(x),x=Z[0],1)==-infinity; li:=lvic+nom+"}$</span> etex);"+ @@ -616,16 +622,16 @@ lm0:=limit(f(x),x=Z[0],1)==-infinity; "}}} }; } -lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; +lnz:=limit(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>; lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ - if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ + if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"+ if(kz==1){"1);"}else{"0);"}} else{"limGauche(btex <span class="font-latex-math">$"+ if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ - if(kz==1){"1);"}else{"0);"}}; + if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}}; @@ -633,15 +639,15 @@ lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ MetaLfc:=if(ftt==2){if(nz>2){" -beginTableau("+nmr+")"+ +<span class="flyspell-duplicate">beginTableau</span>("+nmr+")"+ l0+lsi+lsp+lsf+" endTableau; ";}else{ -intro+"beginTableau("+nmr+")"+ +intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+ l0+ lsi+lsf+" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; "; } @@ -651,32 +657,32 @@ li+ lp+ lf +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";}else{"beginTableau("+nmr+")"+ l0+ li+ -lf +<span class="flyspell-duplicate">lf</span> +" endTableau; ";}}else{ if(nz>2){"beginTableau("+nmr+")"+ l0+ -lsi+lsp+lsf+ +<span class="flyspell-duplicate">lsi</span>+lsp+lsf+ li+ lp+ lf +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";}else{"beginTableau("+nmr+")"+ l0+ lsi+lsf+ li+ -lf +<span class="flyspell-duplicate">lf</span> +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";} }} @@ -708,7 +714,7 @@ fclose(sortie); </span><span class="comment-delimiter">%% </span><span class="comment">par exemple, pour sqrt(x^2-1) : TVZ([-infinity,100],[],[[-1,1]],"f","x",sqrt(x^2-1),1,1) </span><span class="comment-delimiter">%%</span><span class="comment"> </span> -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVZ.cxx} +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVZ.<span class="flyspell-duplicate">cxx</span>} TVZ(L,F,FF,nom,nomv,f,ftt,trigo,nmr):={ @@ -739,7 +745,7 @@ S:=[]; if(trigo==t){ all_trig_solutions:=1; reset_solve_counter(-1,-1); -SS:=solve(factor(simplify(fp(x))),x); +<span class="flyspell-duplicate">SS</span>:=solve(factor(simplify(fp(x))),x); ns:=size(SS); for(k:=0;k<ns;k++){ m:=0; @@ -761,12 +767,12 @@ S:=solve(fp(x),x); si size(S)>0 alors pour j de 0 jusque size(S)-1 faire for(k:=0;k<nf;k++){ - kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[<span class="flyspell-duplicate">nl</span>-1])); kK:=(evalf(S[j])<evalf(Imin[k])) or (evalf(S[j])>evalf(Imax[k])); Kk:=(kk) and kK; if(Kk==1){Z:=append(Z,simplify(S[j]))}; } - fpour + <span class="flyspell-duplicate">fpour</span> fsi; Z:=sort(Z); @@ -779,12 +785,12 @@ nz:=size(Z); 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; +<span class="flyspell-duplicate">fpour</span>; nz:=size(Z); for(j:=0;j<nf;j++){ for(k:=1;k<nz;k++){ - if ((Z[k]>Imin[j])and(Z[k]<Imax[j])){Z:=augment(Z[0..k-1],Z[k+1..nz-1]);nz:=nz-1; + if ((Z[k]>Imin[j])and(Z[k]<Imax[j])){Z:=augment(Z[0..k-1],Z[k+1..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1; } } } @@ -795,7 +801,7 @@ pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+ ";fpour; k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); - kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1)); + kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[<span class="flyspell-duplicate">nz</span>-2],1)); lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ if(member(Z[0],IMIN)!=0){"debutNonDef;"}else{if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ @@ -807,7 +813,7 @@ if(member(Z[0],IMIN)!=0){"debutNonDef;"}else{if(Z[0]==-infinity){if(sign(evalf(f if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0; lsp:=lsp+if(member(Z[r],IMIN)!=0){"debutNonDef;"}else{ - if(member(Z[r],IMAX)!=0){"finNonDef;"+ + if(member(Z[r],</span><span class="font-latex-math"><span class="flyspell-duplicate">IMAX</span></span><span class="font-latex-math">)!=0){"finNonDef;"+ if(ksp==1){"plus;"}else{"moins;"}}else{ if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ if(ksp==1){"plus;"}else{"moins;"} @@ -815,7 +821,7 @@ if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0; -lsf:=if(member(Z[0],IMAX)!=0){"finNonDef;"}else{if(member(Z[nz-1],F)==0){""}else{"nonDefBarre; +lsf:=if(member(Z[0],IMAX)!=0){"finNonDef;"}else{if(member(Z[nz-1],F)==0){""}</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{"nonDefBarre; "}} @@ -835,7 +841,7 @@ if(nz>2){ lp:=lp+if(member(Z[r],IMIN)!=0){"limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){ "-\\infty"}else{ latex(simplify(limit(f(x),x=Z[r],-1)))} - +"$</span> etex,"+if(krm==1){ + +"$</span> etex,"+if(<span class="flyspell-duplicate">krm</span>==1){ "1);"}else{"0);"} +"debutNonDef;" }//fsi Zr=Imin @@ -859,26 +865,26 @@ if(nz>2){ }//fsi (member Zr F) else{"valPos(btex<span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span>etex,"+ if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){ - "0.5);"}else{ + "0.5);"}<span class="flyspell-duplicate">else</span>{ if(krp==1){ "1);"}else{"0);"}//felse(krp) }//felse(valpos) }//felse(member Zr F) } //felse(Zr=Imax) - }//felse(Zr=Imin) + }//felse(Zr=<span class="flyspell-duplicate">Imin</span>) };//ffor }//fsi nz -lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; +lnz:=limit(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>; lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ if(kz==1){"1);"}else{"0);"}} - else{"limGauche(btex <span class="font-latex-math">$"+ + else{"limGauche(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$"+ if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ - if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; + if(kz==1){"1);nonDefBarre;"}else{"0);<span class="flyspell-duplicate">nonDefBarre</span>;"}}; @@ -888,13 +894,13 @@ MetaLfc:=if(ftt==2){if(nz>2){" beginTableau("+nmr+")"+ l0+lsi+lsp+lsf+" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";}else{ intro+"beginTableau("+nmr+")"+ l0+ lsi+lsf+" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; "; } @@ -904,39 +910,39 @@ li+ lp+ lf +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";}else{"beginTableau("+nmr+")"+ l0+ li+ lf +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";}}else{ if(nz>2){"beginTableau("+nmr+")"+ l0+ lsi+lsp+lsf+ li+ -lp+ +<span class="flyspell-duplicate">lp</span>+ lf +" endTableau; -";}else{"beginTableau("+nmr+")"+ +";}else{"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+ l0+ lsi+lsf+ li+ lf +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";} }} sortie:=fopen("XCasmpfc.mp"); -fprint(sortie,Unquoted,MetaLfc); +<span class="flyspell-duplicate">fprint</span>(sortie,Unquoted,MetaLfc); fclose(sortie); } @@ -953,7 +959,7 @@ fclose(sortie); </span> -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVapp.cxx} +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVapp.<span class="flyspell-duplicate">cxx</span>} @@ -966,7 +972,7 @@ TVapp(L,F,nom,nomv,f,ftt,nmr):={ nl:=size(L); f:=unapply(f,x); -fp:=function_diff(f); +<span class="flyspell-duplicate">fp</span>:=function_diff(f); z0:=concat(L,F);z:=sort(z0); nz:=size(z); @@ -977,7 +983,7 @@ 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} +<span class="flyspell-duplicate">else</span>{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; }}}; @@ -989,7 +995,7 @@ si size(S)>0 alors pour j de 0 jusque size(S)-1 faire kk:=(re(S[j])==S[j]);kok:=(evalf(S[j])>=L[0]) and (evalf(S[j])<=L[1]); if(kk==1){if(kok==1){z:=append(z,simplify(S[j]))}}; fpour; -fsi; +<span class="flyspell-duplicate">fsi</span>; S:=NULL; @@ -1014,7 +1020,7 @@ Z:=[S]; nz:=size(Z); l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" "; -pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex); +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> <span class="flyspell-duplicate">etex</span>); ";fpour; k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); @@ -1031,7 +1037,7 @@ if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0; if(ksp==1){"plus;"}else{"moins;"} }; } -lsf:=if(member(Z[nz-1],F)==0){""}else{"nonDefBarre; +lsf:=if(member(Z[nz-1],F)==0){""}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">; "} lm0:=limit(f(x),x=Z[0],1)==-infinity; li:=lvic+nom+"}$</span> etex);"+ @@ -1044,35 +1050,35 @@ lm0:=limit(f(x),x=Z[0],1)==-infinity; krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ; lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity; lp:=lp+if(member(Z[r],F)){ - "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span> etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); "}}} }; } -lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; +lnz:=limit(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>; lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ if(kz==1){"1);"}else{"0);"}} - else{"limGauche(btex <span class="font-latex-math">$"+ + else{"limGauche(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$"+ if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; -MetaLfc:=if(ftt==2){if(nz>2){" +<span class="flyspell-duplicate">MetaLfc</span>:=if(ftt==2){if(nz>2){" beginTableau("+nmr+")"+ l0+lsi+lsp+lsf+" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";}else{ intro+"beginTableau("+nmr+")"+ l0+ lsi+lsf+" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; "; } @@ -1080,7 +1086,7 @@ endTableau; l0+ li+ lp+ -lf +<span class="flyspell-duplicate">lf</span> +" endTableau; @@ -1097,7 +1103,7 @@ if(nz>2){"beginTableau("+nmr+")"+ lsi+lsp+lsf+ li+ lp+ -lf +<span class="flyspell-duplicate">lf</span> +" endTableau; @@ -1107,7 +1113,7 @@ lsi+lsf+ li+ lf +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";} }} @@ -1136,14 +1142,14 @@ fclose(sortie); <span class="comment-delimiter">%%</span><span class="comment"> </span><span class="comment-delimiter">%% </span><span class="comment">Code giac/Xcas pour les Tableaux de Variations avec -</span><span class="comment-delimiter">%% </span><span class="comment">Valeurs intermediaires +</span><span class="comment-delimiter">%% </span><span class="comment">Valeurs </span><span class="comment"><span class="flyspell-incorrect">intermediaires</span></span><span class="comment"> </span><span class="comment-delimiter">%%</span><span class="comment"> </span> -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVI.cxx} +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVI.<span class="flyspell-duplicate">cxx</span>} TVI(L,F,nom,nomv,f,ftt,ao,trigo,nmr):={ @@ -1194,31 +1200,38 @@ l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> ete 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 <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"}} l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> 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 <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=<span class="flyspell-duplicate">kk</span>+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 <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;kk:=kk+1}}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=kk+1}} -l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex); -"}; + l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> <span class="flyspell-duplicate">etex</span>);" + }; -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+")}<span class="font-latex-math">$ etex);"+ - if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ +<span class="flyspell-duplicate">lsi</span>:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ + if(Z[0]==-infinity){if(evalf(sign(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-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^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ if(sign(fp(10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$</span> <span class="font-latex-math">$ etex);"+ if(sign(fp(10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "}; @@ -1226,28 +1239,33 @@ lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ 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 $</span> <span class="font-latex-math">$ 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;"}+ + }} +</span><span class="font-latex-math"><span class="flyspell-duplicate">else</span></span><span class="font-latex-math">{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]-</span><span class="font-latex-math"><span class="flyspell-duplicate">ao</span></span><span class="font-latex-math">))==0.0); + + if(PB[r]==1){if(TestS==0){lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">;"}+ if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex $</span> <span class="font-latex-math">$ 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;} -}} - }; + else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">;"}+ + if(kspp==1){"plus;"}else{"moins;"};rr:=</span><span class="font-latex-math"><span class="flyspell-duplicate">rr</span></span><span class="font-latex-math">+1;} +}}}}; -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); + lsf:=if(member(Z[nz-1],F)==0){" "}else{"</span><span class="font-latex-math"><span class="flyspell-duplicate">nonDefBarre</span></span><span class="font-latex-math">;"} + + + +lm0:=limit(f(x),x=Z[0],1)==-</span><span class="font-latex-math"><span class="flyspell-duplicate">infinity</span></span><span class="font-latex-math">; + + + + +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-</span><span class="font-latex-math"><span class="flyspell-duplicate">ao</span></span><span class="font-latex-math">))==0.0); li:=lvic+nom+"}$</span> etex); "+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"} @@ -1255,63 +1273,68 @@ TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))= if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}else{" "}; - if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1)); krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ; lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity; lp:=lp+if(member(Z[r],F)) { "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span> - etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);" }else{" "}; -};//for -}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1)); krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ; lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); -if(TestS==0){if( TestL==1 ){lp:=lp}else{ lp:=lp+if(member(Z[rr],F)) { - "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span> - etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(<span class="flyspell-duplicate">btex</span> <span class="font-latex-math">$ "+ao+" $</span> etex,0.5); ";rr:=rr+1; -}// else testL==1 -}//testS==0 -else{lp:=lp+if(member(Z[rr],F)){ +}// testS==0 +<span class="flyspell-duplicate">else</span>{lp:=lp+if(member(Z[rr],F)){ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span> - etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + etex,"+if(evalf(sign(fp(Z[<span class="flyspell-duplicate">rr</span>]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); "}}};rr:=rr+1; }//else testS==0 +}//PB[r]==1 }//for nz<NL -}// else nz<NL +}// else nz<<span class="flyspell-duplicate">NL</span> //if nz=NL -};//if nz>2 +};//if <span class="flyspell-duplicate">nz</span>>2 -lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; + +lnz:=limit(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>; lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ - if(kz==1){"1);"}else{"0);"}} + if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}} else{"limGauche(btex <span class="font-latex-math">$"+ if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ - if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; - + if(kz==1){"1);nonDefBarre;"}else{"0);<span class="flyspell-duplicate">nonDefBarre</span>;"}}; -MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+nmr+")"+ + + + + +MetaLfc:= if(ftt==2){if(nz>2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+ l0+lsi+lsp+lsf+" endTableau; -";}else{ +";}<span class="flyspell-duplicate">else</span>{ "beginTableau("+nmr+")"+ l0+ -lsi+lsf+" -endTableau; +<span class="flyspell-duplicate">lsi</span>+lsf+" +<span class="flyspell-duplicate">endTableau</span>; "; } @@ -1320,41 +1343,45 @@ if(ftt==0){if(nz>2){"beginTableau("+nmr+")"+ l0+ li+ lp+ -lf +<span class="flyspell-duplicate">lf</span> +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";}else{"beginTableau("+nmr+")"+ l0+ li+ -lf +<span class="flyspell-duplicate">lf</span> +" endTableau; ";}}else{ -if(nz>2){"beginTableau("+nmr+")"+ +if(nz>2){"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+ l0+ lsi+lsp+lsf+ li+ lp+ lf +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";}else{"beginTableau("+nmr+")"+ l0+ lsi+lsf+ li+ -lf +<span class="flyspell-duplicate">lf</span> +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; ";} }}; + + + + sortie:=fopen("XCasmpfc.mp"); -fprint(sortie,Unquoted,MetaLfc); +<span class="flyspell-duplicate">fprint</span>(sortie,Unquoted,MetaLfc); fclose(sortie); @@ -1378,9 +1405,11 @@ fclose(sortie); -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVIapp.cxx} +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVIapp.<span class="flyspell-duplicate">cxx</span>} +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVIapp.cxx} + TVIapp(L,F,nom,nomv,f,ftt,ao,nmr):={ @@ -1395,10 +1424,10 @@ 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; }}}; @@ -1444,31 +1473,37 @@ l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> ete LI:=limit(f(x),x,Z[0],1); LF:=limit(f(x),x,Z[nz-1],-1); LP:=NULL; -if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])}}}; -if(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]}; +PB:=1; +if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limit(f(x),x,Z[r],-1),limit(f(x),x,Z[r],1)}else{f(Z[r])};if(member(Z[r],F)){PB:=PB,0,1}}}; +if(nz>2){ LL:=[LI,LP,LF]; PB:=[PB,1]}else{LL:=[LI,LF];PB:=[1,1]}; NL:=size(LL); -A:=NULL;aa:=1;kk:=0; +A:=NULL;aa:=1; +kk:=0; + -if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0); +if(NL==nz){for(k:=0;k<nz-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); if(TestS==0){A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[k])+"$</span> etex);"}} l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);"}; +//chgmt NL->nz +if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(evalf(sign(LL[k]-ao))==evalf(sign(LL[k+1]-ao))) or (evalf(sign(LL[k]-ao))==0.0)or (evalf(sign(LL[k+1]-ao))==0.0); + +if(PB[k]==1){if(TestS==0){ + A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;kk:=kk+1} +else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=kk+1}}; +} -if(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(LL[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0); -TestL:=(abs(LL[k])==abs(LL[k+1])); -if(TestS==0){ if( TestL==1 ){l0:=l0}else{ -A:=A,aa;l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);"+"val(btex <span class="font-latex-math">$\\alpha_</span><span class="font-latex-subscript"><span class="font-latex-math">"</span></span><span class="font-latex-math">+aa+"$</span> etex);";aa:=aa+1;kk:=kk+1}}else{l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[kk])+"$</span> etex);";kk:=kk+1}} -l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex); -"}; + l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> etex);" + }; -TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-ao))==0.0); +TestS:=(evalf(sign(LL[0]-ao))==evalf(sign(LL[1]-ao))) or (evalf(sign(LL[0]-ao))==0.0) or (evalf(sign(LL[1]-ao))==0.0); k0:= evalf(limit(f(x),x=Z[0],1))> evalf(limit(f(x),x=Z[1],-1)); kz:=evalf(limit(f(x),x=Z[nz-1],-1))> evalf(limit(f(x),x=Z[nz-2],1)); lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ etex);"+ - if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-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^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-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^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ if(sign(fp(10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex$</span> <span class="font-latex-math">$ etex);"+ if(sign(fp(10^</span><span class="font-latex-superscript"><span class="font-latex-math">(</span></span><span class="font-latex-math">-3)+Z[0]))==1){"plus;"}else{"moins;"}}else{" "}; @@ -1476,28 +1511,33 @@ lsi:=lsic+nom+"'("+nomv+")}<span class="font-latex-math">$ 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 $</span> <span class="font-latex-math">$ 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 $</span> <span class="font-latex-math">$ 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+"}$</span> etex); "+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[0],1)))}+"$</span> etex,"} @@ -1505,43 +1545,44 @@ TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))= if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}else{" "}; - if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); krm:=evalf(limit(f(x),x=Z[r-1],1))< evalf(limit(f(x),x=Z[r],-1)); krp:=evalf(limit(f(x),x=Z[r],1))> evalf(limit(f(x),x=Z[r+1],-1)) ; lmrm:=limit(f(x),x=Z[r],-1)==-infinity;lmrp:=limit(f(x),x=Z[r],1)==-infinity; lp:=lp+if(member(Z[r],F)) { "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[r])))+"$</span> - etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex + etex,"+if(evalf(sign(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);" }else{" "}; -};//for -}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); +};//for +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(evalf(sign(LL[r]-ao))==evalf(sign(LL[r+1]-ao))) or (evalf(sign(LL[r]-ao))==0.0)or (evalf(sign(LL[r+1]-ao))==0.0); krm:=evalf(limit(f(x),x=Z[rr-1],1))< evalf(limit(f(x),x=Z[rr],-1)); krp:=evalf(limit(f(x),x=Z[rr],1))> evalf(limit(f(x),x=Z[rr+1],-1)) ; lmrm:=limit(f(x),x=Z[rr],-1)==-infinity;lmrp:=limit(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); -if(TestS==0){if( TestL==1 ){lp:=lp}else{ lp:=lp+if(member(Z[rr],F)) { + +if(PB[r]==1){if(TestS==0){lp:=lp+if(member(Z[rr],F)){ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span> - etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5); ";rr:=rr+1; -}// else testL==1 -}//testS==0 +}// testS==0 else{lp:=lp+if(member(Z[rr],F)){ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],-1)))}+"$</span> etex,"+if(krm==1){"1);"}else{"0);"}+"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lmrp==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} else{"valPos(btex <span class="font-latex-math">$"+latex(simplify(f(Z[rr])))+"$</span> - etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + etex,"+if(evalf(sign(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); "}}};rr:=rr+1; }//else testS==0 +}//PB[r]==1 }//for nz<NL }// else nz<NL //if nz=NL };//if nz>2 -lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; +lnz:=limit(f(x),x=Z[nz-1],-1)==-infinity; lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ @@ -1550,7 +1591,7 @@ lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+ else{"limGauche(btex <span class="font-latex-math">$"+ if(lnz==1){"-\\infty"}else{latex(simplify(limit(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"+ if(kz==1){"1);nonDefBarre;"}else{"0);nonDefBarre;"}}; - + @@ -1607,6 +1648,7 @@ endTableau; + sortie:=fopen("XCasmpfc.mp"); fprint(sortie,Unquoted,MetaLfc); fclose(sortie); @@ -1616,8 +1658,8 @@ fclose(sortie); -<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> @@ -2038,7 +2080,7 @@ fclose(sortie); <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignQ.cxx} -<span class="flyspell-duplicate">TSq</span>(nomf,L,Fo,D,trigo,nmr):={ +TSq(nomf,L,Fo,D,trigo,nmr):={ L:=apply(f->unapply(f,x),L); Fo:=apply(f->unapply(f,x),Fo); L:=concat(L,Fo); @@ -2104,7 +2146,7 @@ SF:=concat(SF,simplify(subst(SSF[j],n_1=mm)));mm:=mm-1; } }else{ -SF:=solve(<span class="flyspell-duplicate">Fo</span>[k](x),x); +SF:=solve(Fo[k](x),x); } si size(SF)>0 alors pour j de 0 jusque size(SF)-1 faire 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} |