diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex/tablor/tablor.html')
-rw-r--r-- | Master/texmf-dist/doc/latex/tablor/tablor.html | 802 |
1 files changed, 545 insertions, 257 deletions
diff --git a/Master/texmf-dist/doc/latex/tablor/tablor.html b/Master/texmf-dist/doc/latex/tablor/tablor.html index 9505cccb01f..3a8dd19054a 100644 --- a/Master/texmf-dist/doc/latex/tablor/tablor.html +++ b/Master/texmf-dist/doc/latex/tablor/tablor.html @@ -85,7 +85,7 @@ <span class="font-latex-sedate">\NeedsTeXFormat</span>{LaTeX2e}[1995/12/01] <span class="font-latex-sedate">\ProvidesPackage</span>{<span class="flyspell-incorrect">tablor</span>} - [21/01/2008 v1.3 + [23/01/2008 v1.4 la machine à créer des tableaux de signes et variations] @@ -93,17 +93,17 @@ <span class="comment-delimiter">%% </span><span class="comment">Crée 5 environnements : </span><span class="comment-delimiter">%% </span><span class="comment">tableau de signes de 2 facteurs affines </span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TSa} -</span><span class="comment-delimiter">% </span><span class="comment"><span class="flyspell-duplicate">TSa</span></span><span class="comment">(-2,3,-1,5,</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">); +</span><span class="comment-delimiter">% </span><span class="comment">TSa(-2,3,-1,5,</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">{TSa} </span><span class="comment-delimiter">% </span><span class="comment">%%%%%% Pour des tableaux de plus de 2 facteurs </span><span class="comment-delimiter">%</span><span class="comment"> </span><span class="comment-delimiter">% </span><span class="font-latex-sedate"><span class="comment">\begin</span></span><span class="comment">{TS} -</span><span class="comment-delimiter">% </span><span class="comment">TS([-2*x+3,x^2-1,x^2+1,x-1,x^2-2],</span><span class="font-latex-sedate"><span class="comment">\tv</span></span><span class="comment">); +</span><span class="comment-delimiter">% </span><span class="comment">TS([-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[a,b],</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">{TS} </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">TSq("Q",[-2*x+3,-4*x+5],[x^2-16,x-2],</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],</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"> @@ -120,11 +120,11 @@ <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>{ -<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{rm XCasmp.mp* XCasmp.log XCasmp?.mp* XCasmp?.log XCasmpTV.mp* XCasmpTV.log *.out XCasmpTVI.mp* XCasmpTVI.log - *.in *.meta *<span class="flyspell-incorrect">mpx</span>* *~}} +<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{rm XCasmp.mp* XCasmp.log XCasmp?.mp* XCasmp?.log XCasmpTV.mp* XCasmpTV.log *.user XCasmpTVI.mp* XCasmpTVI.log + *.giac *.cxx *<span class="flyspell-incorrect">mpx</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">\bouger</span></span><span class="function-name">}</span>[1]{ -<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{cp <span class="flyspell-duplicate">XCas</span>* #1}} +<span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{cp XCas* #1}} <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">\recup</span></span><span class="function-name">}</span>[2]{ @@ -132,7 +132,7 @@ -<span class="font-latex-sedate"><span class="keyword">\newcounter</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVn</span></span><span class="function-name">}</span> +<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>} @@ -145,7 +145,7 @@ <span class="font-latex-sedate">\makeatother</span> -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTV.meta} +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTV.cxx} TV(L,F,nom,nomv,f,ftt,nmr):={ nl:=size(L); f:=unapply(f,x); @@ -153,9 +153,9 @@ fp:=fonction_derivee(f); Z:=concat(L,F); S:=resoudre(fp(x),x); si size(S)>0 alors pour j de 0 jusque size(S)-1 faire - kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=<span class="flyspell-duplicate">evalf</span>(L[<span class="flyspell-duplicate">nl</span>-1])); + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[<span class="flyspell-duplicate">nl</span>-1])); if(kk==1){Z:=append(Z,simplifier(S[j]))}; - <span class="flyspell-duplicate">fpour</span> + fpour fsi; Z:=sort(Z); @@ -175,8 +175,8 @@ pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+ kz:=evalf(limite(f(x),x=Z[nz-1],-1))> evalf(limite(f(x),x=Z[nz-2],1)); lsi:=" -newLigneSignes(btex <span class="font-latex-math">$\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$</span> <span class="flyspell-duplicate">etex</span>);"+ - if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ +newLigneSignes(btex <span class="font-latex-math">$\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$</span> etex);"+ + if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}<span class="flyspell-duplicate">else</span>{"moins;"}}else{if(member(Z[0],F)==0){ if(sign(fp(Z[0]+10^(-5)))==1){"plus;"}else{"moins;"}}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"+ if(sign(fp((Z[0]+10^(-5))))==1){"plus;"}else{"moins;"} }} @@ -185,19 +185,19 @@ if(nz>2){ for(r:=1; r<=nz-2;r++){ ksp:=evalf(fp(Z[r]+0.01))>0; if(ksp==1){"plus;"}else{"moins;"} }; } -lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre; +<span class="flyspell-duplicate">lsf</span>:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre; "} -lm0:=limite(f(x),x=Z[0],1)==-<span class="flyspell-duplicate">infinity</span>; +lm0:=limite(f(x),x=Z[0],1)==-infinity; li:=" newLigneVariations(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Variations de }\\atop{\\displaystyle \\Mathbold{"+nom+"}}$</span> <span class="flyspell-duplicate">etex</span>);"+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"} else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}+ - if(k0==1){"1"}else{"0"}+ + if(k0==1){"1"}<span class="flyspell-duplicate">else</span>{"0"}+ ");"; if(nz>2){ for(r:=1; r<=nz-2;r++){ krm:=evalf(limite(f(x),x=Z[r-1],1))< evalf(limite(f(x),x=Z[r],-1)); krp:=evalf(limite(f(x),x=Z[r],1))> evalf(limite(f(x),x=Z[r+1],-1)) ; - lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity; + lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-<span class="flyspell-duplicate">infinity</span>; lp:=lp+if(member(Z[r],F)){ "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(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(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span> @@ -205,13 +205,13 @@ newLigneVariations(btex <span class="font-latex-math">$\\hbox{\</span><span clas "}}} }; } -lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity; - lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+ +lnz:=limite(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">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+ if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0); "}; -intro:="input tableauVariation; +intro:="input <span class="flyspell-duplicate">tableauVariation</span>; verbatimtex <span class="comment-delimiter">%</span><span class="comment">&latex </span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span> @@ -224,58 +224,68 @@ intro:="input tableauVariation; " -MetaL:= if(ftt==0){if(nz>2){intro+"beginTableau("+nmr+")"+ +<span class="flyspell-duplicate">MetaL</span>:=if(ftt==2){if(nz>2){intro+"beginTableau("+nmr+")"+ + l0+lsi+lsp+lsf+" +endTableau; +end";}else{ +intro+"beginTableau("+nmr+")"+ + l0+ +<span class="flyspell-duplicate">lsi</span>+lsf+" +endTableau; +end"; +} +}<span class="flyspell-duplicate">else</span>{ if(ftt==0){if(nz>2){intro+"beginTableau("+nmr+")"+ l0+ li+ lp+ <span class="flyspell-duplicate">lf</span> +" -endTableau; -end";}else{intro+"beginTableau("+nmr+")"+ +<span class="flyspell-duplicate">endTableau</span>; +end";}else{intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+ l0+ li+ <span class="flyspell-duplicate">lf</span> +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; end";}}else{ if(nz>2){intro+"beginTableau("+nmr+")"+ l0+ <span class="flyspell-duplicate">lsi</span>+lsp+lsf+ li+ lp+ -lf +<span class="flyspell-duplicate">lf</span> +" endTableau; <span class="flyspell-duplicate">end</span>";}else{intro+"beginTableau("+nmr+")"+ l0+ lsi+lsf+ li+ -lf +<span class="flyspell-duplicate">lf</span> +" <span class="flyspell-duplicate">endTableau</span>; -end";} -} +<span class="flyspell-duplicate">end</span>";} +}} -return(<span class="flyspell-duplicate">MetaL</span>); +<span class="flyspell-duplicate">return</span>(<span class="flyspell-duplicate">MetaL</span>); }:; <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">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTVI.<span class="flyspell-duplicate">meta</span>} +<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,nmr):={ +<span class="flyspell-duplicate">TVI</span>(L,F,nom,nomv,f,ftt,ao,nmr):={ nl:=size(L); f:=unapply(f,x); -fp:=fonction_derivee(f); +<span class="flyspell-duplicate">fp</span>:=fonction_derivee(f); Z:=concat(L,F); S:=resoudre(fp(x),x); si size(S)>0 alors pour j de 0 jusque size(S)-1 faire - kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[nl-1])); + kk:=(evalf(S[j])>=evalf(L[0])) and (evalf(S[j])<=evalf(L[<span class="flyspell-duplicate">nl</span>-1])); if(kk==1){Z:=append(Z,simplifier(S[j]))}; - fpour + <span class="flyspell-duplicate">fpour</span> fsi; Z:=sort(Z); @@ -283,60 +293,60 @@ nz:=size(Z); 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; + si Z[u]==Z[u+1] alors Z:=augment(Z[0..u-1],Z[u+1..nz-1]);nz:=<span class="flyspell-duplicate">nz</span>-1; fsi; fpour; -nz:=size(Z); -l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";lsp:=" "; +<span class="flyspell-duplicate">nz</span>:=size(Z); +l0:=" newLigneVariables(btex <span class="font-latex-math">$"+nomv+"$</span> etex);";lp:=" "; lf:=" ";<span class="flyspell-duplicate">lsp</span>:=" "; LI:=limite(f(x),x,Z[0],1); -LF:=limite(f(x),x,Z[nz-1],-1); +<span class="flyspell-duplicate">LF</span>:=limite(f(x),x,Z[nz-1],-1); <span class="flyspell-duplicate">LP</span>:=NULL; if(nz>2){ for(r:=1; r<=nz-2;r++){LP:=LP,if(member(Z[r],F)){limite(f(x),x,Z[r],-1),limite(f(x),x,Z[r],1)}else{f(Z[r])}}}; -if(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,LF]}; +if(nz>2){ LL:=[LI,LP,LF]}else{LL:=[LI,<span class="flyspell-duplicate">LF</span>]}; NL:=size(LL); -A:=NULL;aa:=1;kk:=0; +A:=NULL;aa:=1;<span class="flyspell-duplicate">kk</span>:=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:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(<span class="flyspell-duplicate">LL</span>[k]-ao))==0.0)or (sign(evalf(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);"}; +l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[nz-1])+"$</span> <span class="flyspell-duplicate">etex</span>);"}; -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(NL>nz){for(k:=0;k<NL-1;k++){TestS:=(sign(evalf(LL[k]-ao))==sign(evalf(LL[k+1]-ao))) or (sign(evalf(<span class="flyspell-duplicate">LL</span>[k]-ao))==0.0)or (sign(evalf(LL[k+1]-ao))==0.0); +<span class="flyspell-duplicate">TestL</span>:=(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}} +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}} 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); +<span class="flyspell-duplicate">TestS</span>:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(<span class="flyspell-duplicate">LL</span>[1]-<span class="flyspell-duplicate">ao</span>))==0.0); k0:= evalf(limite(f(x),x=Z[0],1))> evalf(limite(f(x),x=Z[1],-1)); kz:=evalf(limite(f(x),x=Z[nz-1],-1))> evalf(limite(f(x),x=Z[<span class="flyspell-duplicate">nz</span>-2],1)); -lsi:=" -newLigneSignes(btex <span class="font-latex-math">$\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$</span> etex);"+ - if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}else{"moins;"}}else{if(member(Z[0],F)==0){ - if(sign(fp((Z[0]+10^(-10))))==1){"plus;"}else{"moins;"}}else{"nonDefBarre;"+ - if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex<span class="font-latex-math">$ $</span> etex);"+ if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"}}<span class="flyspell-duplicate">else</span>{" "}; +<span class="flyspell-duplicate">lsi</span>:=" +<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\hbox{ Signe de }\\atop{\\displaystyle "+nom+"'("+nomv+")}$</span> <span class="flyspell-duplicate">etex</span>);"+ + if(Z[0]==-infinity){if(sign(evalf(fp(if(Z[1]==+infinity){0}else{Z[1]-10^(-5)})))==1){"plus;"}<span class="flyspell-duplicate">else</span>{"moins;"}}else{if(member(Z[0],F)==0){ + if(sign(fp((Z[0]+10^(-10))))==1){"plus;"}else{"moins;"}}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"+ + if(sign(fp(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"} }}+if(TestS==0){"valBarre(btex<span class="font-latex-math">$ $</span> etex);"+ if(sign(<span class="flyspell-duplicate">fp</span>(10^(-10)+Z[0]))==1){"plus;"}else{"moins;"}}<span class="flyspell-duplicate">else</span>{" "}; -if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); +if(nz>2){rr:=1; if(nz==NL){for(r:=1; r<=NL-2;r++){ TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-<span class="flyspell-duplicate">ao</span>))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-<span class="flyspell-duplicate">ao</span>))==0.0); ksp:=evalf(fp(Z[r]+0.01))>0; TestL:=(abs(LL[r])==abs(LL[r+1])); - lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ - if(ksp==1){"plus;"}else{"moins;"}+if(<span class="flyspell-duplicate">TestS</span>==0){"valBarre(btex <span class="font-latex-math">$ $</span> etex);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; + lsp:=lsp+if(member(Z[r],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+ + if(ksp==1){"plus;"}else{"moins;"}+if(TestS==0){"valBarre(btex <span class="font-latex-math">$ $</span> <span class="flyspell-duplicate">etex</span>);"}else{" "}+if(TestS==0){if(ksp==1){"plus;"}else{"moins;"}}else{" "}; }} -else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); +<span class="flyspell-duplicate">else</span>{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); TestL:=(abs(LL[r])==abs(LL[r+1])); - if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ - if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex <span class="font-latex-math">$ $</span> etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=rr+1;} + if(TestS==0){if( TestL==1 ){lsp:=lsp}else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+ + if(kspp==1){"plus;"}else{"moins;"}+"valBarre(btex <span class="font-latex-math">$ $</span> etex);"+if(kspp==1){"plus;"}else{"moins;"};rr:=<span class="flyspell-duplicate">rr</span>+1;} } else{lsp:=lsp+if(member(Z[rr],F)==0){"valBarre(btex 0 etex);"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+ if(kspp==1){"plus;"}else{"moins;"};rr:=<span class="flyspell-duplicate">rr</span>+1;} }} @@ -344,104 +354,115 @@ else{for(r:=1; r<=NL-2;r++){kspp:=evalf(fp(Z[rr]+0.01))>0;TestS:=(sign(eva -lsf:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;"} +<span class="flyspell-duplicate">lsf</span>:=if(member(Z[nz-1],F)==0){""}else{"nomDefBarre;"} lm0:=limite(f(x),x=Z[0],1)==-infinity; -TestS:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(LL[1]-<span class="flyspell-duplicate">ao</span>))==0.0); +<span class="flyspell-duplicate">TestS</span>:=(sign(evalf(LL[0]-ao))==sign(evalf(LL[1]-ao))) or (sign(evalf(LL[0]-ao))==0.0) or (sign(evalf(<span class="flyspell-duplicate">LL</span>[1]-<span class="flyspell-duplicate">ao</span>))==0.0); li:=" -newLigneVariations(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Variations de }\\atop{\\displaystyle \\Mathbold{"+nom+"}}$</span> etex); +<span class="flyspell-duplicate">newLigneVariations</span>(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Variations de }\\atop{\\displaystyle \\Mathbold{"+nom+"}}$</span> etex); "+ if(member(Z[0],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"} - else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> etex,"}+ + else{"nonDefBarre;limDroite(btex <span class="font-latex-math">$"+if(lm0==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[0],1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"}+ if(k0==1){"1);"}else{"0);"}+if(TestS==0){"valPos(btex <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);"}<span class="flyspell-duplicate">else</span>{" "}; - if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); + if(nz>2){if(nz==NL){for(r:=1; r<=nz-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(<span class="flyspell-duplicate">evalf</span>(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-ao))==0.0); krm:=evalf(limite(f(x),x=Z[r-1],1))< evalf(limite(f(x),x=Z[r],-1)); krp:=evalf(limite(f(x),x=Z[r],1))> evalf(limite(f(x),x=Z[r+1],-1)) ; - lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-infinity; + lmrm:=limite(f(x),x=Z[r],-1)==-infinity;lmrp:=limite(f(x),x=Z[r],1)==-<span class="flyspell-duplicate">infinity</span>; lp:=lp+if(member(Z[r],F)) { - "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[r],-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(simplifier(limite(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"}else{latex(simplifier(limite(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(simplifier(limite(f(x),x=Z[r],1)))}+"$</span> etex,"+if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}} else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[r])))+"$</span> - etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(<span class="flyspell-duplicate">TestS</span>==0){"valPos(btex - <span class="font-latex-math">$ "+ao+" $</span> etex,0.5);" + etex,"+if(sign(evalf(fp(Z[r]-0.01)))==sign(fp(Z[r]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+if(TestS==0){"<span class="flyspell-duplicate">valPos</span>(<span class="flyspell-duplicate">btex</span> + <span class="font-latex-math">$ "+ao+" $</span> <span class="flyspell-duplicate">etex</span>,0.5);" }else{" "}; };//for -}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(evalf(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-<span class="flyspell-duplicate">ao</span>))==0.0); - krm:=evalf(limite(f(x),x=Z[rr-1],1))< evalf(limite(f(x),x=Z[rr],-1)); - krp:=evalf(limite(f(x),x=Z[rr],1))> evalf(limite(f(x),x=Z[rr+1],-1)) ; - lmrm:=limite(f(x),x=Z[rr],-1)==-infinity;lmrp:=limite(f(x),x=Z[rr],1)==-infinity; TestL:=(abs(LL[r])==abs(LL[r+1])); +}else{rr:=1;for(r:=1; r<=NL-2;r++){TestS:=(sign(evalf(LL[r]-ao))==sign(evalf(LL[r+1]-ao))) or (sign(<span class="flyspell-duplicate">evalf</span>(LL[r]-ao))==0.0)or (sign(evalf(LL[r+1]-<span class="flyspell-duplicate">ao</span>))==0.0); + krm:=evalf(limite(f(x),x=Z[rr-1],1))< evalf(limite(f(x),x=Z[<span class="flyspell-duplicate">rr</span>],-1)); + krp:=evalf(limite(f(x),x=Z[rr],1))> evalf(limite(f(x),x=Z[<span class="flyspell-duplicate">rr</span>+1],-1)) ; + lmrm:=limite(f(x),x=Z[rr],-1)==-infinity;lmrp:=limite(f(x),x=Z[rr],1)==-<span class="flyspell-duplicate">infinity</span>; TestL:=(abs(LL[r])==abs(LL[r+1])); if(TestS==0){if( TestL==1 ){lp:=lp}else{ lp:=lp+if(member(Z[rr],F)) { - "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(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(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(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(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}} else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[rr])))+"$</span> - etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(btex - <span class="font-latex-math">$ "+ao+" $</span> etex,0.5); - ";rr:=<span class="flyspell-duplicate">rr</span>+1; -}// else testL==1 + etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0);"}}}+"valPos(<span class="flyspell-duplicate">btex</span> + <span class="font-latex-math">$ "+ao+" $</span> <span class="flyspell-duplicate">etex</span>,0.5); + ";rr:=rr+1; +}// else <span class="flyspell-incorrect">testL</span>==1 }//testS==0 -else{lp:=lp+if(member(Z[rr],F)){ - "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(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(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}else{"0);"}} +<span class="flyspell-duplicate">else</span>{lp:=lp+if(member(Z[rr],F)){ + "limGauche(btex <span class="font-latex-math">$"+if(lmrm==1){"-\\infty"}else{latex(simplifier(limite(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(simplifier(limite(f(x),x=Z[rr],1)))}+"$</span> etex,"+if(krp==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}} else{"valPos(btex <span class="font-latex-math">$"+latex(simplifier(f(Z[rr])))+"$</span> - etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[rr]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); + etex,"+if(sign(evalf(fp(Z[rr]-0.01)))==sign(fp(Z[<span class="flyspell-duplicate">rr</span>]+0.01))){"0.5);"}else{if(krp==1){"1);"}else{"0); "}}};rr:=<span class="flyspell-duplicate">rr</span>+1; -}//else testS==0 -}//for nz<NL -}// else nz<NL -//if nz=NL +}//else <span class="flyspell-duplicate">testS</span>==0 +}//for nz<<span class="flyspell-duplicate">NL</span> +}// else nz<<span class="flyspell-duplicate">NL</span> +//if nz=<span class="flyspell-duplicate">NL</span> };//if <span class="flyspell-duplicate">nz</span>>2 -lnz:=limite(f(x),x=Z[nz-1],-1)==-infinity; - lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"nonDefBarre;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> <span class="flyspell-duplicate">etex</span>,"}+ - if(kz==1){"1);"}else{"0);"}; +<span class="flyspell-duplicate">lnz</span>:=limite(f(x),x=Z[nz-1],-1)==-<span class="flyspell-duplicate">infinity</span>; + lf:=if(member(Z[nz-1],F)==0){"valPos(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}else{"<span class="flyspell-duplicate">nonDefBarre</span>;limGauche(btex <span class="font-latex-math">$"+if(lnz==1){"-\\infty"}else{latex(simplifier(limite(f(x),x=Z[nz-1],-1)))}+"$</span> etex,"}+ + if(kz==1){"1);"}<span class="flyspell-duplicate">else</span>{"0);"}; -intro:=" +<span class="flyspell-duplicate">intro</span>:=" input tableauVariation; -<span class="flyspell-duplicate">verbatimtex</span> +verbatimtex <span class="comment-delimiter">%</span><span class="comment">&latex </span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>} <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span> - etex + <span class="flyspell-duplicate">etex</span> "; -<span class="flyspell-duplicate">MetaL</span>:= if(ftt==0){if(nz>2){intro+"beginTableau("+nmr+")"+ +MetaL:= if(<span class="flyspell-duplicate">ftt</span>==2){if(nz>2){intro+"beginTableau("+nmr+")"+ + l0+lsi+lsp+<span class="flyspell-duplicate">lsf</span>+" +<span class="flyspell-duplicate">endTableau</span>; +<span class="flyspell-duplicate">end</span>";}<span class="flyspell-duplicate">else</span>{ +<span class="flyspell-duplicate">intro</span>+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+ + l0+ +lsi+<span class="flyspell-duplicate">lsf</span>+" +endTableau; +<span class="flyspell-duplicate">end</span>"; +} +}<span class="flyspell-duplicate">else</span>{ +if(ftt==0){if(nz>2){intro+"beginTableau("+nmr+")"+ l0+ li+ -lp+ -lf +<span class="flyspell-duplicate">lp</span>+ +<span class="flyspell-duplicate">lf</span> +" <span class="flyspell-duplicate">endTableau</span>; end";}else{intro+"beginTableau("+nmr+")"+ l0+ li+ -lf +<span class="flyspell-duplicate">lf</span> +" <span class="flyspell-duplicate">endTableau</span>; end";}}else{ -if(nz>2){intro+"beginTableau("+nmr+")"+ +if(nz>2){intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+ l0+ -lsi+lsp+lsf+ +<span class="flyspell-duplicate">lsi</span>+lsp+<span class="flyspell-duplicate">lsf</span>+ li+ <span class="flyspell-duplicate">lp</span>+ lf +" -endTableau; -end";}else{intro+"beginTableau("+nmr+")"+ +<span class="flyspell-duplicate">endTableau</span>; +<span class="flyspell-duplicate">end</span>";}else{intro+"beginTableau("+<span class="flyspell-duplicate">nmr</span>+")"+ l0+ -<span class="flyspell-duplicate">lsi</span>+lsf+ +<span class="flyspell-duplicate">lsi</span>+<span class="flyspell-duplicate">lsf</span>+ li+ -lf +<span class="flyspell-duplicate">lf</span> +" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; <span class="flyspell-duplicate">end</span>";} -}; +}}; return(<span class="flyspell-duplicate">MetaL</span>); }:; @@ -459,72 +480,136 @@ return(<span class="flyspell-duplicate">MetaL</span>); -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignL.meta} -TS(L,nmr):={ +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignL<span class="flyspell-duplicate">.cxx</span>} + + +<span class="flyspell-duplicate">TS</span>(L,D,nmr):={ L:=apply(f->unapply(f,x),L) n:=size(L); -Z:=<span class="flyspell-duplicate">NULL</span>; +Z:=NULL; +mini:=D[0]; maxi:=D[1]; pour k de 0 jusque n-1 faire S:=resoudre(L[k](x),x); si size(S)>0 alors pour j de 0 jusque size(S)-1 faire - Z:=Z,simplifier(S[j]); + if(S[j]>mini and S[j]<maxi){Z:=Z,simplifier(S[j]);} <span class="flyspell-duplicate">fpour</span>; fsi; -fpour; +<span class="flyspell-duplicate">fpour</span>; Z:=sort(Z); -nz:=size(Z); -pour u de 1 jusque nz-2 faire +<span class="flyspell-duplicate">nz</span>:=size(Z); +if(nz>2){pour u de 1 jusque nz-2 faire si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=<span class="flyspell-duplicate">nz</span>-1; fsi; -fpour; -nz:=size(Z); -l0:=" ";li:=" ";lr:=" "; -pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex); -";<span class="flyspell-duplicate">fpour</span>; +<span class="flyspell-duplicate">fpour</span>;}; +<span class="flyspell-duplicate">nz</span>:=size(Z); + +if(<span class="flyspell-duplicate">nz</span>==0){li:="";l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> <span class="flyspell-duplicate">etex</span>);"; + for(p:=0;p<=n-1;p++){li:=li+" +<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$</span> etex);"+ +if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}+ +if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](maxi)==0){" + valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"}<span class="flyspell-duplicate">else</span>{" + "} + +} + lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"}; + +MetaL:=" input <span class="flyspell-duplicate">tableauVariation</span>; + <span class="flyspell-duplicate">verbatimtex</span> +<span class="comment-delimiter">%</span><span class="comment">&latex +</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span> + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span> + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span> + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>} + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span> + <span class="flyspell-duplicate">etex</span> + <span class="flyspell-duplicate">beginTableau</span>("+nmr+") +<span class="flyspell-duplicate">newLigneVariables</span>(btex <span class="font-latex-math">$\\Mathbold{x}$</span> <span class="flyspell-duplicate">etex</span>); + "+l0+li+ + " + newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe du }\\atop{{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> produit}}$</span> <span class="flyspell-duplicate">etex</span>);"+ + if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}+ <span class="flyspell-duplicate">lf</span>+ + if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}+" +<span class="flyspell-duplicate">endTableau</span>; +<span class="flyspell-duplicate">end</span>" +; +}<span class="flyspell-duplicate">else</span>{ + + -for(p:=0;p<=n-1;p++){lp:=" "; - li:=li+"newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$</span> <span class="flyspell-duplicate">etex</span>);"+ - if(L[p](Z[0]-1.0)>0){"plus;"}else{"moins;"}+ +l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);";li:=" ";<span class="flyspell-duplicate">lr</span>:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> <span class="flyspell-duplicate">etex</span>); +";fpour; +l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> <span class="flyspell-duplicate">etex</span>);"; + + +for(p:=0;p<=n-1;p++){lp:=""; + li:=li+" +<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$</span> <span class="flyspell-duplicate">etex</span>);"+ + if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}+ + if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"}; + for(r:=0; r<=nz-2;r++){ - lp:=lp+if(simplifier(L[p](Z[r]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ - if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}}+ - if(simplifier(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ + lp:=lp+if(simplifier(L[p](Z[r]))==0){" + valBarre(btex 0 etex);"}else{"barre; + "}+ + if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}}; + + li:=li+lp+ if(simplifier(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins; - "} + "}+if(maxi!=+infinity and L[p](<span class="flyspell-duplicate">maxi</span>)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "} }; pour t de 0 jusque nz-2 faire - lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);" - <span class="flyspell-duplicate">fpour</span> + lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);" + fpour -MetaL:=" input tableauVariation; - verbatimtex +<span class="flyspell-duplicate">MetaL</span>:=" input <span class="flyspell-duplicate">tableauVariation</span>; + <span class="flyspell-duplicate">verbatimtex</span> <span class="comment-delimiter">%</span><span class="comment">&latex </span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>} <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span> - etex + <span class="flyspell-duplicate">etex</span> beginTableau("+nmr+") -newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> <span class="flyspell-duplicate">etex</span>); - val(btex <span class="font-latex-math">$-\\infty$</span> etex);"+l0+"val(btex <span class="font-latex-math">$+\\infty$</span> etex);"+ +<span class="flyspell-duplicate">newLigneVariables</span>(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex); + "+l0+ li + - " newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe du }\\atop{{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> produit}}$</span> etex);"+ - if(product(L[s](Z[0]-1.0),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 etex);"+ - lr+ - if(product(L[s](Z[nz-1]+1.0),s,0,n-1)>0){"plus;"}else{"moins;"}+" -endTableau; + " + newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe du }\\atop{{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> produit}}$</span> <span class="flyspell-duplicate">etex</span>);"+ + if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}+ + if(product(L[s](Z[0]-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"+ + <span class="flyspell-duplicate">lr</span>+ + if(product(L[s](Z[nz-1]+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}+" +<span class="flyspell-duplicate">endTableau</span>; <span class="flyspell-duplicate">end</span>" -; -return(MetaL); +;} +<span class="flyspell-duplicate">return</span>(<span class="flyspell-duplicate">MetaL</span>); }:; + <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> @@ -535,102 +620,167 @@ return(MetaL); -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignQ.meta} -TSq(nomf,L,Fo,nmr):={ +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSignQ<span class="flyspell-duplicate">.cxx</span>} +<span class="flyspell-duplicate">TSq</span>(nomf,L,Fo,D,nmr):={ L:=apply(f->unapply(f,x),L); -Fo:=apply(f->unapply(f,x),Fo); +<span class="flyspell-duplicate">Fo</span>:=<span class="flyspell-duplicate">apply</span>(f->unapply(f,x),Fo); L:=concat(L,Fo); n:=size(L); Z:=NULL; -m:=size(Fo); -F:=<span class="flyspell-duplicate">NULL</span>; - +m:=size(<span class="flyspell-duplicate">Fo</span>); +F:=<span class="flyspell-duplicate">NULL</span>;<span class="flyspell-duplicate">FF</span>:=NULL; +mini:=D[0]; maxi:=D[1]; pour k de 0 jusque n-1 faire S:=resoudre(L[k](x),x); si size(S)>0 alors pour j de 0 jusque size(S)-1 faire - Z:=Z,simplifier(S[j]); + if(S[j]>mini and S[j]<maxi){Z:=Z,simplifier(S[j]);} <span class="flyspell-duplicate">fpour</span>; fsi; -fpour; +<span class="flyspell-duplicate">fpour</span>; pour k de 0 jusque m-1 faire SF:=resoudre(Fo[k](x),x); si size(SF)>0 alors pour j de 0 jusque size(SF)-1 faire - F:=F,simplifier(SF[j]); - fpour; + FF:=FF,simplifier(SF[j]); + if(SF[j]>mini and SF[j]<maxi){F:=F,simplifier(SF[j]);} + <span class="flyspell-duplicate">fpour</span>; fsi; <span class="flyspell-duplicate">fpour</span>; Z:=sort(Z); // on classe les zéros dans l'ordre croissant -nz:=size(Z); -pour u de 1 jusque nz-2 faire +<span class="flyspell-duplicate">nz</span>:=size(Z); +if(nz>2){pour u de 1 jusque nz-2 faire si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=nz-1; // pour les zéros en double fsi; -fpour; -nz:=size(Z); -l0:=" ";li:=" ";lr:=" "; +<span class="flyspell-duplicate">fpour</span>;} + + +Z:=sort(Z); +<span class="flyspell-duplicate">nz</span>:=size(Z); +if(nz>2){pour u de 1 jusque nz-2 faire + si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=<span class="flyspell-duplicate">nz</span>-1; + fsi; +<span class="flyspell-duplicate">fpour</span>;}; +<span class="flyspell-duplicate">nz</span>:=size(Z); + +if(nz==0){li:="";l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> <span class="flyspell-duplicate">etex</span>);"; + for(p:=0;p<=n-1;p++){li:=li+" +<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$</span> etex);"+ +if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}+ +if(L[p]((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}+if(maxi!=+infinity and L[p](<span class="flyspell-duplicate">maxi</span>)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "} + +} + lf:=if(product(L[s]((mini+maxi)*.5),s,0,n-1)>0){"plus;"}else{"moins;"}; + +<span class="flyspell-duplicate">MetaL</span>:=" input <span class="flyspell-duplicate">tableauVariation</span>; + <span class="flyspell-duplicate">verbatimtex</span> +<span class="comment-delimiter">%</span><span class="comment">&latex +</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span> + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span> + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span> + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>} + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span> + <span class="flyspell-duplicate">etex</span> + +<span class="flyspell-duplicate">beginTableau</span>("+nmr+") +<span class="flyspell-duplicate">newLigneVariables</span>(btex <span class="font-latex-math">$\\Mathbold{x}$</span> <span class="flyspell-duplicate">etex</span>); + "+l0+li+ + " + newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe }\\atop{{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> de "+nomf+"(x)}}$</span> <span class="flyspell-duplicate">etex</span>);"+ + if(member(mini,FF)==0){if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}}else{"nonDefBarre;"}+ <span class="flyspell-duplicate">lf</span>+ + if(member(maxi,FF)==0){if(maxi!=+infinity and product(L[s](maxi),s,0,n-1)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}}else{"nonDefBarre;"}+" +<span class="flyspell-duplicate">endTableau</span>; +<span class="flyspell-duplicate">end</span>" +; +}<span class="flyspell-duplicate">else</span>{ + + +l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);";li:=" ";lr:=" "; pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> <span class="flyspell-duplicate">etex</span>); ";fpour; +l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> <span class="flyspell-duplicate">etex</span>);"; - -for(p:=0;p<=n-1;p++){lp:=" "; +for(p:=0;p<=n-1;p++){<span class="flyspell-duplicate">lp</span>:=""; li:=li+" -<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$</span> etex);"+ - if(L[p](Z[0]-1.0)>0){"plus;"}else{"moins;"}+ +<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(L[p](x))+"}}$</span> <span class="flyspell-duplicate">etex</span>);"+ + if(mini!=-infinity and L[p](mini)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}+ + if(L[p](Z[0]-0.01)>0){"plus;"}else{"moins;"}; + for(r:=0; r<=nz-2;r++){ lp:=lp+if(simplifier(L[p](Z[r]))==0){" - valBarre(btex 0 etex);"}else{"barre;"}+ - if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}}+ - if(simplifier(L[p](Z[nz-1]))==0){"valBarre(btex 0 etex);"}else{"barre;"}+ - if(L[p](Z[nz-1]+1.0)>0){"plus;"}else{"moins; - "} + valBarre(btex 0 etex);"}else{"barre; + "}+ + if(L[p]((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}}; + + li:=li+lp+ if(simplifier(L[p](Z[<span class="flyspell-duplicate">nz</span>-1]))==0){"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"}else{"barre;"}+ + if(L[p](Z[<span class="flyspell-duplicate">nz</span>-1]+1.0)>0){"plus;"}<span class="flyspell-duplicate">else</span>{"moins; + "}+if(maxi!=+infinity and L[p](<span class="flyspell-duplicate">maxi</span>)==0){" + <span class="flyspell-duplicate">valBarre</span>(<span class="flyspell-duplicate">btex</span> 0 <span class="flyspell-duplicate">etex</span>);"}<span class="flyspell-duplicate">else</span>{" "} + }; pour t de 0 jusque nz-2 faire - lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+if(member(Z[t+1],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"} - fpour + lr:=lr+if(product(L[s]((Z[t]+Z[t+1])*.5),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(Z[t+1],<span class="flyspell-duplicate">FF</span>)==0){"valBarre(btex 0 etex);"}else{ "<span class="flyspell-duplicate">nonDefBarre</span>;"} + <span class="flyspell-duplicate">fpour</span> -MetaL:=" input tableauVariation; - <span class="flyspell-duplicate">verbatimtex</span> +<span class="flyspell-duplicate">MetaL</span>:=" input <span class="flyspell-duplicate">tableauVariation</span>; +<span class="flyspell-duplicate">verbatimtex</span> <span class="comment-delimiter">%</span><span class="comment">&latex </span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>} <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span> - etex - beginTableau("+nmr+") -newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex); - val(btex <span class="font-latex-math">$-\\infty$</span> etex);"+l0+"val(btex <span class="font-latex-math">$+\\infty$</span> etex);"+ + <span class="flyspell-duplicate">etex</span> + beginTableau("+<span class="flyspell-duplicate">nmr</span>+") +<span class="flyspell-duplicate">newLigneVariables</span>(btex <span class="font-latex-math">$\\Mathbold{x}$</span> <span class="flyspell-duplicate">etex</span>); + "+l0+ li + - " newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> "+nomf+"(x) }$</span> etex);"+ - if(product(L[s](Z[0]-1.0),s,0,n-1)>0){"plus;"}else{"moins;"}+if(member(Z[0],F)==0){"valBarre(btex 0 etex);"}else{"nonDefBarre;"}+ - lr+ - if(product(L[s](Z[nz-1]+1.0),s,0,n-1)>0){"plus;"}else{"moins;"}+" -endTableau; -end" -; -return(<span class="flyspell-duplicate">MetaL</span>); + " + newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe }\\atop{{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> de"+nomf+"(x)}}$</span> <span class="flyspell-duplicate">etex</span>);"+ + if(member(mini,<span class="flyspell-duplicate">FF</span>)==0){if(mini!=-infinity and product(L[s](mini),s,0,n-1)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}}else{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+ + if(product(L[s](Z[0]-0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(Z[0],FF)==0){"valBarre(btex 0 etex);"}else{ "<span class="flyspell-duplicate">nonDefBarre</span>;"}+ + <span class="flyspell-duplicate">lr</span>+ + if(product(L[s](Z[nz-1]+0.01),s,0,n-1)>0){"plus;"}else{"moins;"}+ + if(member(maxi,<span class="flyspell-duplicate">FF</span>)==0){if(<span class="flyspell-duplicate">maxi</span>!=+<span class="flyspell-duplicate">infinity</span> and product(L[s](maxi),s,0,n-1)==0){" + <span class="flyspell-duplicate">valBarre</span>(btex 0 <span class="flyspell-duplicate">etex</span>);"}<span class="flyspell-duplicate">else</span>{" "}}<span class="flyspell-duplicate">else</span>{"<span class="flyspell-duplicate">nonDefBarre</span>;"}+" +<span class="flyspell-duplicate">endTableau</span>; +<span class="flyspell-duplicate">end</span>" +;} +<span class="flyspell-duplicate">return</span>(<span class="flyspell-duplicate">MetaL</span>); }:; - <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">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XcasTabSign.meta} -TSa(a,b,c,d,nmr):={ +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{<span class="flyspell-duplicate">XcasTabSign.cxx</span>} +<span class="flyspell-duplicate">TSa</span>(a,b,c,d,<span class="flyspell-duplicate">nmr</span>):={ <span class="flyspell-duplicate">zA</span>:=resoudre(a*x+b=0,x)[0]; -zB:=resoudre(c*x+d=0,x)[0]; -zmin:=min(zA,zB); -zmax:=max(zA,zB); - Meta:= " input tableauVariation; +<span class="flyspell-duplicate">zB</span>:=resoudre(c*x+d=0,x)[0]; +<span class="flyspell-duplicate">zmin</span>:=min(zA,<span class="flyspell-duplicate">zB</span>); +<span class="flyspell-duplicate">zmax</span>:=max(zA,<span class="flyspell-duplicate">zB</span>); + Meta:= " input <span class="flyspell-duplicate">tableauVariation</span>; <span class="flyspell-duplicate">verbatimtex</span> <span class="comment-delimiter">%</span><span class="comment">&latex </span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span> @@ -639,63 +789,173 @@ zmax:=max(zA,zB); <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>} <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span> etex - beginTableau("+nmr+") - newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex); + beginTableau("+<span class="flyspell-duplicate">nmr</span>+") + newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> <span class="flyspell-duplicate">etex</span>); val(btex <span class="font-latex-math">$-\\infty$</span> etex);val(btex <span class="font-latex-math">$"+latex(zmin)+"$</span> etex); val(btex <span class="font-latex-math">$"+latex(zmax)+"$</span>etex); val(btex <span class="font-latex-math">$+\\infty$</span> <span class="flyspell-duplicate">etex</span>); newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+"}}$</span> etex);" + if(a>0){"moins;"}else{"plus;"}+ if(zmin==zA){"valBarre(btex 0 etex);"}else{"barre;"}+ - if(zmin==zA){si a>0 alors "plus;"; sinon "moins;";fsi} - else{si a>0 alors "moins;"; sinon "plus;"; fsi}+ - if(zmin==zA){"barre;"}else{"valBarre(btex 0 etex);"}+ + if(zmin==zA){si a>0 alors "plus;"; sinon "moins;";<span class="flyspell-duplicate">fsi</span>} + else{si a>0 alors "moins;"; sinon "plus;"; <span class="flyspell-duplicate">fsi</span>}+ + if(zmin==zA){"barre;"}else{"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"}+ if(a>0){"plus;"}else{"moins;"} +" -newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+"}}$</span> etex);" +<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+"}}$</span> <span class="flyspell-duplicate">etex</span>);" + if(c>0){"moins"}else{"plus"}+";"+ if(zmin==zB){"valBarre(btex 0 etex);"}else{"barre;"}+ - if(zmin==zB){si c>0 alors "plus;"; sinon "moins;";fsi} + if(zmin==zB){si c>0 alors "plus;"; sinon "moins;";<span class="flyspell-duplicate">fsi</span>} else{si c>0 alors "moins;"; sinon "plus;"; fsi}+ if(zmin==zB){"barre;"}else{"valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"}+ if(c>0){"plus;"}else{"moins;"} +" -newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{("+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+")("+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+")}}$</span> <span class="flyspell-duplicate">etex</span>);" - + si a*c>0 alors plus; sinon moins;fsi+";"+ - "valBarre(btex 0 etex);"+ - si a*c>0 alors moins; sinon plus;fsi+";"+ - "valBarre(btex 0 etex);"+ +<span class="flyspell-duplicate">newLigneSignes</span>(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{("+if(a==1){"x+"}else{if(a==-1){"-x+"}else{a+"x+"}}+b+")("+if(c==1){"x+"}else{if(c==-1){"-x+"}else{c+"x+"}}+d+")}}$</span> etex);" + + si a*c>0 alors plus; sinon moins;<span class="flyspell-duplicate">fsi</span>+";"+ + "valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"+ + si a*c>0 alors moins; sinon plus;<span class="flyspell-duplicate">fsi</span>+";"+ + "valBarre(btex 0 <span class="flyspell-duplicate">etex</span>);"+ si a*c>0 alors plus; sinon moins;fsi+";"+" -endTableau; +<span class="flyspell-duplicate">endTableau</span>; <span class="flyspell-duplicate">end</span>" ; -return(Meta); +<span class="flyspell-duplicate">return</span>(<span class="flyspell-duplicate">Meta</span>); }:; <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCas.in} -maple_mode(0); -read("XcasTabSign.meta"); + + + + + + + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{<span class="flyspell-incorrect">XcasTSc</span>.<span class="flyspell-duplicate">cxx</span>} +<span class="flyspell-duplicate">TSc</span>(g,D,nmr):={ +f:=unapply(g,x); +Z:=NULL; +mini:=D[0]; maxi:=D[1];<span class="flyspell-duplicate">lm</span>:=" "; +S:=resoudre(f(x),x); +if(size(S)==0){ +li:=if(f(0)>0){"plus;"}<span class="flyspell-duplicate">else</span>{"moins;"}; +<span class="flyspell-duplicate">lm</span>:=" ";<span class="flyspell-duplicate">lf</span>:=" "; +} +else{pour j de 0 jusque size(S)-1 faire + if(S[j]>mini and S[j]<maxi){Z:=Z,simplifier(S[j])}; + <span class="flyspell-duplicate">fpour</span>; + + +Z:=sort(Z); +nz:=size(Z); +if(nz>2){pour u de 1 jusque nz-2 faire + si Z[u]==Z[u+1] alors Z:=Z[0..u-1],Z[u+1..nz-1];nz:=<span class="flyspell-duplicate">nz</span>-1; + fsi; +<span class="flyspell-duplicate">fpour</span>;} +nz:=size(Z); +l0:=" ";li:=" ";lr:=" "; +if(nz==0){l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> etex);"; +li:=if(mini!=-infinity and f(mini)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}+ +if(f((mini+maxi)*0.5>0)){"plus;"}else{"moins;"}; +lf:=if(maxi!=+infinity and f(maxi)==0){" + valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}; + +}else{ +l0:="val(btex <span class="font-latex-math">$"+latex(D[0])+"$</span> etex);";li:=" "; +pour m de 0 jusque nz-1 faire l0:=l0+"val(btex <span class="font-latex-math">$"+latex(Z[m])+"$</span> etex); +"; +<span class="flyspell-duplicate">fpour</span>; +l0:=l0+"val(btex <span class="font-latex-math">$"+latex(D[1])+"$</span> <span class="flyspell-duplicate">etex</span>);"; + +li:= if(mini!=-infinity and f(mini)==0){" + <span class="flyspell-duplicate">valBarre</span>(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}+ +if(f(Z[0]-0.01)>0){"plus;"}<span class="flyspell-duplicate">else</span>{"moins;"}+if(simplifier(f(Z[0]))==0){"<span class="flyspell-duplicate">valBarre</span>(<span class="flyspell-duplicate">btex</span> 0 <span class="flyspell-duplicate">etex</span>);"}<span class="flyspell-duplicate">else</span>{"barre;"}; + +<span class="flyspell-duplicate">lm</span>:=if(<span class="flyspell-duplicate">nz</span>>=2){for(r:=0; r<=nz-2;r++){if(f((Z[r]+Z[r+1])*.5)>0){"plus;"}else{"moins;"}+ + if(simplifier(f(Z[r+1]))==0){"valBarre(btex 0 etex);"}else{"barre;"} + }}<span class="flyspell-duplicate">else</span>{" "}; + +<span class="flyspell-duplicate">lf</span>:=if(f(Z[nz-1]+1.0)>0){"plus;"}else{"moins;"}+if(maxi!=+infinity and f(maxi)==0){"valBarre(btex 0 etex);"}<span class="flyspell-duplicate">else</span>{" + "}; +}}; + + +MetaL:=" input <span class="flyspell-duplicate">tableauVariation</span>; + <span class="flyspell-duplicate">verbatimtex</span> +<span class="comment-delimiter">%</span><span class="comment">&latex +</span> <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">documentclass</span><span class="function-name">{article}</span> + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="variable-name">[upright]</span><span class="function-name">{fourier}</span> + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">usepackage</span><span class="function-name">{amsmath}</span> + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">newcommand</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">Mathbold}</span>[1]{<span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">mbox</span><span class="function-name">{</span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">boldmath</span><span class="function-name"><span class="font-latex-math">$#1$</span></span><span class="function-name"><span class="font-latex-warning">\\</span></span><span class="function-name">unboldmath}</span>} + <span class="font-latex-warning">\</span><span class="keyword"><span class="font-latex-warning">\</span></span><span class="keyword">begin</span><span class="function-name">{document}</span> + etex +<span class="flyspell-duplicate">beginTableau</span>("+nmr+") +newLigneVariables(btex <span class="font-latex-math">$\\Mathbold{x}$</span> etex); + "+l0+" +newLigneSignes(btex <span class="font-latex-math">$\\hbox{\</span><span class="font-latex-bold"><span class="font-latex-math">\bf</span></span><span class="font-latex-math"> Signe de }\\atop{\\displaystyle \\Mathbold{"+latex(f(x))+"}}$</span> <span class="flyspell-duplicate">etex</span>);"+ + li+<span class="flyspell-duplicate">lm</span>+lf + +" +<span class="flyspell-duplicate">endTableau</span>; +end" +; +return(<span class="flyspell-duplicate">MetaL</span>); + }:; +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + + + + + + + + + +<span class="comment-delimiter">%%% </span><span class="comment">les "</span><span class="comment"><span class="flyspell-duplicate">giac</span></span><span class="comment">" +</span> + + + + + + + + + + + + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCas.giac} +<span class="flyspell-duplicate">maple</span>_mode(0); +<span class="flyspell-duplicate">read</span>("XcasTabSign.cxx"); Sortie:=fopen("XCasmp.mp"); -vect.xcas.out := read("XCas.out"); -vxo := vect.xcas.out; -dim.vxo := dim(vxo); -nbr.line.vxo := dim.vxo; -Resultat:=cat(" "); -<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt); +<span class="flyspell-duplicate">vect</span>.xcas.user := read("XCas.user"); +vxo := vect.xcas.user; +<span class="flyspell-duplicate">dim</span>.vxo := dim(vxo); +<span class="flyspell-duplicate">nbr</span>.line.vxo := dim.vxo; +<span class="flyspell-duplicate">Resultat</span>:=cat(" "); +rslt := vxo[0]; RslT:=cat(<span class="flyspell-duplicate">rslt</span>); <span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,RslT); -<span class="flyspell-duplicate">fprint</span>(Sortie,Unquoted,Resultat); -fclose(Sortie); +fprint(Sortie,Unquoted,Resultat); +<span class="flyspell-duplicate">fclose</span>(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">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TSa</span></span><span class="function-name">}</span> -{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>£µ]{XCas.out}} +{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>£µ]{XCas.user}} {<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> - <span class="font-latex-sedate">\executGiacmp</span>{XCas.in} + <span class="font-latex-sedate">\executGiacmp</span>{XCas.giac} <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost <span class="flyspell-duplicate">XCasmp</span>} @@ -706,25 +966,25 @@ fclose(Sortie); } -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasQ.in} -maple_mode(0); -read("XcasTabSignQ.meta"); +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasQ.giac} +<span class="flyspell-duplicate">maple</span>_mode(0); +<span class="flyspell-duplicate">read</span>("XcasTabSignQ.cxx"); Sortie:=fopen("XCasmpQ.mp"); -<span class="flyspell-duplicate">vect</span>.xcas.out := read("XCasQ.out"); -<span class="flyspell-duplicate">vxo</span> := vect.xcas.out; -<span class="flyspell-duplicate">dim</span>.vxo := dim(vxo); +vect.xcas.user := read("XCasQ.user"); +<span class="flyspell-duplicate">vxo</span> := vect.xcas.user; +dim.vxo := dim(vxo); nbr.line.vxo := dim.vxo; -Resultat:=cat(" "); -rslt := vxo[0]; RslT:=cat(rslt); -<span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,RslT); +<span class="flyspell-duplicate">Resultat</span>:=cat(" "); +<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt); +Resultat:=cat(Resultat,RslT); <span class="flyspell-duplicate">fprint</span>(Sortie,Unquoted,Resultat); -<span class="flyspell-duplicate">fclose</span>(Sortie); +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">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TSq</span></span><span class="function-name">}</span> -{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>£µ]{XCasQ.out}} +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TSq}</span> +{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>£µ]{XCasQ.user}} {<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> - <span class="font-latex-sedate">\executGiacmp</span>{XCasQ.in} + <span class="font-latex-sedate">\executGiacmp</span>{XCasQ.giac} <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost <span class="flyspell-duplicate">XCasmpQ</span>} @@ -736,25 +996,25 @@ rslt := vxo[0]; RslT:=cat(rslt); -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasL.in} +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasL.giac} maple_mode(0); -read("XcasTabSignL.meta"); +<span class="flyspell-duplicate">read</span>("XcasTabSignL.cxx"); Sortie:=fopen("XCasmpL.mp"); -<span class="flyspell-duplicate">vect</span>.xcas.out := read("XCasL.out"); -<span class="flyspell-duplicate">vxo</span> := vect.xcas.out; -<span class="flyspell-duplicate">dim</span>.vxo := dim(vxo); +<span class="flyspell-duplicate">vect</span>.xcas.user := read("XCasL.user"); +<span class="flyspell-duplicate">vxo</span> := vect.xcas.user; +dim.vxo := dim(vxo); nbr.line.vxo := dim.vxo; -Resultat:=cat(" "); -rslt := vxo[0]; RslT:=cat(rslt); +<span class="flyspell-duplicate">Resultat</span>:=cat(" "); +<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt); <span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,RslT); <span class="flyspell-duplicate">fprint</span>(Sortie,Unquoted,Resultat); -<span class="flyspell-duplicate">fclose</span>(Sortie); +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">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TS</span></span><span class="function-name">}</span> -{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>£µ]{XCasL.out}} +{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>£µ]{XCasL.user}} {<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> - <span class="font-latex-sedate">\executGiacmp</span>{XCasL.in} + <span class="font-latex-sedate">\executGiacmp</span>{XCasL.giac} <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost <span class="flyspell-duplicate">XCasmpL</span>} @@ -764,31 +1024,59 @@ rslt := vxo[0]; RslT:=cat(rslt); <span class="font-latex-sedate">\stepcounter</span>{<span class="flyspell-duplicate">TVn</span>} } +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{<span class="flyspell-duplicate">XCasTSc</span>.giac} +<span class="flyspell-duplicate">maple</span>_mode(0); +read("<span class="flyspell-duplicate">XcasTSc.cxx</span>"); +Sortie:=<span class="flyspell-duplicate">fopen</span>("<span class="flyspell-duplicate">XCasmpTSc</span>.<span class="flyspell-duplicate">mp</span>"); +<span class="flyspell-duplicate">vect</span>.xcas.user := read("<span class="flyspell-duplicate">XCasTSc</span>.user"); +vxo := vect.xcas.user; +dim.vxo := dim(<span class="flyspell-duplicate">vxo</span>); +<span class="flyspell-duplicate">nbr</span>.line.vxo := dim.<span class="flyspell-duplicate">vxo</span>; +Resultat:=<span class="flyspell-duplicate">cat</span>(" "); +rslt := vxo[0]; RslT:=cat(rslt); +<span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,RslT); +fprint(Sortie,Unquoted,Resultat); +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">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TSc</span></span><span class="function-name">}</span> +{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[<span class="flyspell-duplicate">commandchars</span>=<span class="font-latex-warning">\\</span>£µ]{<span class="flyspell-incorrect">XCasTSc</span>.user}} +{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span> + <span class="font-latex-sedate">\executGiacmp</span>{<span class="flyspell-duplicate">XCasTSc</span>.<span class="flyspell-duplicate">giac</span>} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="flyspell-duplicate">mpost</span> <span class="flyspell-duplicate">XCasmpTSc</span>} +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span> + <span class="font-latex-sedate">\includegraphics</span>{<span class="flyspell-duplicate">XCasmpTSc</span>.<span class="font-latex-sedate">\theTVn</span>} +<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span> +<span class="font-latex-sedate">\stepcounter</span>{<span class="flyspell-duplicate">TVn</span>} +} -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTV.in} + + + +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTV.giac} <span class="flyspell-duplicate">maple</span>_mode(0); -<span class="flyspell-duplicate">read</span>("XcasTV.meta"); +read("XcasTV.cxx"); Sortie:=fopen("XCasmpTV.mp"); -vect.xcas.out := read("XCasTV.out"); -vxo := vect.xcas.out; -dim.vxo := dim(vxo); +vect.xcas.user := read("XCasTV.user"); +vxo := vect.xcas.user; +<span class="flyspell-duplicate">dim</span>.vxo := dim(vxo); <span class="flyspell-duplicate">nbr</span>.line.vxo := dim.vxo; -<span class="flyspell-duplicate">Resultat</span>:=cat(" "); -<span class="flyspell-duplicate">rslt</span> := vxo[0]; RslT:=cat(rslt); +Resultat:=cat(" "); +rslt := vxo[0]; RslT:=cat(rslt); Resultat:=cat(Resultat,RslT); fprint(Sortie,Unquoted,Resultat); -fclose(Sortie); +<span class="flyspell-duplicate">fclose</span>(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">\newenvironment</span></span><span class="function-name">{TV}</span><span class="comment">% -</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>£µ]{XCasTV.out}}<span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>£µ]{XCasTV.user}}<span class="comment">% </span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="comment">% -</span> <span class="font-latex-sedate">\executGiacmp</span>{XCasTV.in} - <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost <span class="flyspell-duplicate">XCasmpTV</span>} +</span> <span class="font-latex-sedate">\executGiacmp</span>{XCasTV.giac} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost XCasmpTV} <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span> <span class="font-latex-sedate">\includegraphics</span>{XCasmpTV.<span class="font-latex-sedate">\theTVn</span>} <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span> @@ -798,26 +1086,26 @@ fclose(Sortie); -<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVI.in} -maple_mode(0); -<span class="flyspell-duplicate">read</span>("XcasTVI.meta"); +<span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>{XCasTVI.giac} +<span class="flyspell-duplicate">maple</span>_mode(0); +read("XcasTVI.<span class="flyspell-duplicate">cxx</span>"); Sortie:=fopen("XCasmpTVI.mp"); -<span class="flyspell-duplicate">vect</span>.xcas.out := read("XCasTVI.out"); -vxo := vect.xcas.out; -dim.vxo := dim(<span class="flyspell-duplicate">vxo</span>); -nbr.line.vxo := dim.<span class="flyspell-duplicate">vxo</span>; -Resultat:=<span class="flyspell-duplicate">cat</span>(" "); +<span class="flyspell-duplicate">vect</span>.xcas.user := read("XCasTVI.user"); +vxo := vect.xcas.user; +dim.vxo := dim(vxo); +<span class="flyspell-duplicate">nbr</span>.line.vxo := dim.vxo; +Resultat:=cat(" "); rslt := vxo[0]; RslT:=cat(rslt); -<span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,<span class="flyspell-duplicate">RslT</span>); -fprint(Sortie,Unquoted,<span class="flyspell-duplicate">Resultat</span>); -<span class="flyspell-duplicate">fclose</span>(Sortie); +<span class="flyspell-duplicate">Resultat</span>:=cat(Resultat,RslT); +fprint(Sortie,Unquoted,Resultat); +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">\newenvironment</span></span><span class="function-name">{</span><span class="function-name"><span class="flyspell-duplicate">TVI</span></span><span class="function-name">}</span><span class="comment">% -</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[<span class="flyspell-duplicate">commandchars</span>=<span class="font-latex-warning">\\</span>£µ]{XCasTVI.out}}<span class="comment">% +<span class="font-latex-sedate"><span class="keyword">\newenvironment</span></span><span class="function-name">{TVI}</span><span class="comment">% +</span>{<span class="font-latex-sedate">\VerbatimEnvironment</span><span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{VerbatimOut}</span>[commandchars=<span class="font-latex-warning">\\</span>£µ]{XCasTVI.user}}<span class="comment">% </span>{<span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{VerbatimOut}</span><span class="comment">% -</span> <span class="font-latex-sedate">\executGiacmp</span>{XCasTVI.in} - <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{<span class="flyspell-duplicate">mpost</span> XCasmpTVI} +</span> <span class="font-latex-sedate">\executGiacmp</span>{XCasTVI.<span class="flyspell-duplicate">giac</span>} + <span class="font-latex-sedate">\immediate</span><span class="font-latex-sedate">\write</span>18{mpost XCasmpTVI} <span class="font-latex-sedate"><span class="keyword">\begin</span></span><span class="function-name">{center}</span> <span class="font-latex-sedate">\includegraphics</span>{XCasmpTVI.<span class="font-latex-sedate">\theTVn</span>} <span class="font-latex-sedate"><span class="keyword">\end</span></span><span class="function-name">{center}</span> @@ -832,7 +1120,7 @@ fprint(Sortie,Unquoted,<span class="flyspell-duplicate">Resultat</span>); <span class="comment-delimiter">%%</span><span class="comment"> -</span><span class="comment-delimiter">%% </span><span class="comment">Zi </span><span class="comment"><span class="flyspell-duplicate">end</span></span><span class="comment"> +</span><span class="comment-delimiter">%% </span><span class="comment">Zi end </span></pre> </body> </html> |