From ebdd82171b15452eaab47d1063eae03bd546f19a Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Sun, 14 Mar 2021 23:20:35 +0000 Subject: profcollege (14mar21) (branch) git-svn-id: svn://tug.org/texlive/branches/branch2020.0@58365 c570f23f-e606-0410-a88d-b1316a301751 --- .../doc/latex/profcollege/ProfCollege-doc.pdf | Bin 1702509 -> 2573778 bytes .../doc/latex/profcollege/ProfCollege-doc.zip | Bin 1216103 -> 1672987 bytes .../metapost/profcollege/PfC-Afficheur.mp | 182 + .../metapost/profcollege/PfC-Calculatrice.mp | 11 +- .../metapost/profcollege/PfC-Constantes.mp | 3 - .../texmf-dist/metapost/profcollege/PfC-LaTeX.mp | 7 +- .../metapost/profcollege/PfC-Svgnames.mp | 3 - .../latex/profcollege/PfC-EquationComposition1.tex | 277 - .../latex/profcollege/PfC-EquationComposition2.tex | 275 + .../profcollege/PfC-EquationSoustraction1.tex | 332 -- .../profcollege/PfC-EquationSoustraction2.tex | 345 ++ .../tex/latex/profcollege/ProfCollege.sty | 5976 +++++++++++++------- 12 files changed, 4769 insertions(+), 2642 deletions(-) create mode 100644 Master/texmf-dist/metapost/profcollege/PfC-Afficheur.mp delete mode 100644 Master/texmf-dist/tex/latex/profcollege/PfC-EquationComposition1.tex create mode 100644 Master/texmf-dist/tex/latex/profcollege/PfC-EquationComposition2.tex delete mode 100644 Master/texmf-dist/tex/latex/profcollege/PfC-EquationSoustraction1.tex create mode 100644 Master/texmf-dist/tex/latex/profcollege/PfC-EquationSoustraction2.tex (limited to 'Master') diff --git a/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.pdf b/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.pdf index 941ccd943fc..0238567ab07 100644 Binary files a/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.pdf and b/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.pdf differ diff --git a/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.zip b/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.zip index b11824f7d50..300ef54b56a 100644 Binary files a/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.zip and b/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.zip differ diff --git a/Master/texmf-dist/metapost/profcollege/PfC-Afficheur.mp b/Master/texmf-dist/metapost/profcollege/PfC-Afficheur.mp new file mode 100644 index 00000000000..166cd229792 --- /dev/null +++ b/Master/texmf-dist/metapost/profcollege/PfC-Afficheur.mp @@ -0,0 +1,182 @@ +u:=1cm; + +vardef Afficheur(expr nb,creux)= + pair Aa[]; + Aa1=u*(-0.5,-1); + Aa2-Aa1=u*(1,0); + Aa4-Aa2=u*(0,2); + Aa3=1/2[Aa2,Aa4]; + Aa5-Aa4=Aa1-Aa2; + Aa6-Aa3=Aa1-Aa2; + pair Bb[]; + Bb1=Aa1 xscaled0.7 yscaled 0.85; + Bb2=Aa2 xscaled0.7 yscaled 0.85; + Bb4=Aa4 xscaled0.7 yscaled 0.85; + Bb5=Aa5 xscaled0.7 yscaled 0.85; + Bb3=1/2[Bb2,Bb4]; + Bb6=1/2[Bb1,Bb5]; + Bb7=1/2[Bb6,Bb3]+(0,4); + Bb8=1/2[Bb6,Bb3]-(0,6); + pair Cc[]; + Cc1=u*(0.4,-0.85)+(0,-1); + ecarth:=1.5; + ecartv:=0.05; + path ASegment[]; + ASegment[1]=1/10[Bb1,Bb2]--9/10[Bb1,Bb2]; + ASegment[2]=1/10[Bb2,Bb3]--9/10[Bb2,Bb3]; + ASegment[3]=1/10[Bb3,Bb4]--9/10[Bb3,Bb4]; + ASegment[4]=1/10[Bb4,Bb5]--9/10[Bb4,Bb5]; + ASegment[5]=1/10[Bb5,Bb6]--9/10[Bb5,Bb6]; + ASegment[6]=1/10[Bb6,Bb1]--9/10[Bb6,Bb1]; + ASegment[7]=1/10[Bb6,Bb3]--9/10[Bb6,Bb3]; + color fondsegment; + fondsegment=0.2[LightSteelBlue,white]; + save $; + picture $; + $=image( + fill Aa1--Aa2--Aa4--Aa5--cycle withcolor LightSteelBlue; + draw Aa1--Aa2--Aa4--Aa5--cycle withcolor LightSteelBlue; + if creux=0: + fill (unitsquare scaled 2) shifted Cc1 withcolor fondsegment; + else: + fill (unitsquare scaled 2) shifted Cc1 withcolor Crimson; + fi; + if nb=1: + drawoptions(withpen pensquare scaled2 withcolor Crimson); + draw ASegment[2]; + draw ASegment[3]; + drawoptions(withpen pensquare scaled2 withcolor fondsegment); + draw ASegment[1]; + draw ASegment[4]; + draw ASegment[5]; + draw ASegment[6]; + draw ASegment[7]; + drawoptions(); + fi; + if nb=2: + drawoptions(withpen pensquare scaled2 withcolor Crimson); + draw ASegment[1]; + draw ASegment[3]; + draw ASegment[4]; + draw ASegment[6]; + draw ASegment[7]; + drawoptions(withpen pensquare scaled2 withcolor fondsegment); + draw ASegment[2]; + draw ASegment[5]; + drawoptions(); + fi; + if nb=3: + drawoptions(withpen pensquare scaled2 withcolor Crimson); + draw ASegment[1]; + draw ASegment[2]; + draw ASegment[3]; + draw ASegment[4]; + draw ASegment[7]; + drawoptions(withpen pensquare scaled2 withcolor fondsegment); + draw ASegment[5]; + draw ASegment[6]; + drawoptions(); + fi; + if nb=4: + drawoptions(withpen pensquare scaled2 withcolor Crimson); + draw ASegment[2]; + draw ASegment[3]; + draw ASegment[5]; + draw ASegment[7]; + drawoptions(withpen pensquare scaled2 withcolor fondsegment); + draw ASegment[1]; + draw ASegment[4]; + draw ASegment[6]; + drawoptions(); + fi; + if nb=5: + drawoptions(withpen pensquare scaled2 withcolor Crimson); + draw ASegment[1]; + draw ASegment[2]; + draw ASegment[4]; + draw ASegment[5]; + draw ASegment[7]; + drawoptions(withpen pensquare scaled2 withcolor fondsegment); + draw ASegment[3]; + draw ASegment[6]; + drawoptions(); + fi; + if nb=6: + drawoptions(withpen pensquare scaled2 withcolor Crimson); + draw ASegment[1]; + draw ASegment[2]; + draw ASegment[4]; + draw ASegment[5]; + draw ASegment[6]; + draw ASegment[7]; + drawoptions(withpen pensquare scaled2 withcolor fondsegment); + draw ASegment[3]; + drawoptions(); + fi; + if nb=7: + drawoptions(withpen pensquare scaled2 withcolor Crimson); + draw ASegment[2]; + draw ASegment[3]; + draw ASegment[4]; + drawoptions(withpen pensquare scaled2 withcolor fondsegment); + draw ASegment[1]; + draw ASegment[5]; + draw ASegment[6]; + draw ASegment[7]; + drawoptions(); + fi; + if nb=8: + drawoptions(withpen pensquare scaled2 withcolor Crimson); + draw ASegment[1]; + draw ASegment[2]; + draw ASegment[3]; + draw ASegment[4]; + draw ASegment[5]; + draw ASegment[6]; + draw ASegment[7]; + drawoptions(); + fi; + if nb=9: + drawoptions(withpen pensquare scaled2 withcolor Crimson); + draw ASegment[1]; + draw ASegment[2]; + draw ASegment[3]; + draw ASegment[4]; + draw ASegment[5]; + draw ASegment[7]; + drawoptions(withpen pensquare scaled2 withcolor fondsegment); + draw ASegment[6]; + drawoptions(); + fi; + if nb=0: + drawoptions(withpen pensquare scaled2 withcolor Crimson); + draw ASegment[1]; + draw ASegment[2]; + draw ASegment[3]; + draw ASegment[4]; + draw ASegment[5]; + draw ASegment[6]; + drawoptions(withpen pensquare scaled2 withcolor fondsegment); + draw ASegment[7]; + drawoptions(); + fi; + if nb=10: + drawoptions(withpen pensquare scaled2 withcolor Crimson); + fill (unitsquare scaled 2) shifted Bb7 withcolor Crimson; + fill (unitsquare scaled 2) shifted Bb8 withcolor Crimson; + drawoptions(withpen pensquare scaled2 withcolor fondsegment); + draw ASegment[1]; + draw ASegment[2]; + draw ASegment[3]; + draw ASegment[4]; + draw ASegment[5]; + draw ASegment[6]; + draw ASegment[7]; + drawoptions(); + fi; + ); + $ +enddef; + +endinput; + diff --git a/Master/texmf-dist/metapost/profcollege/PfC-Calculatrice.mp b/Master/texmf-dist/metapost/profcollege/PfC-Calculatrice.mp index a6326e19258..92d4d3057d6 100644 --- a/Master/texmf-dist/metapost/profcollege/PfC-Calculatrice.mp +++ b/Master/texmf-dist/metapost/profcollege/PfC-Calculatrice.mp @@ -1,6 +1,3 @@ -%Author : Christophe Poulain -%Licence : Released under the LaTeX Project Public License v1.3c -% or later, see http://www.latex-project.org/lppl.txtf prologues:=3; path carre[]; @@ -174,7 +171,7 @@ vardef Test(expr cptk,cptnt)= fi; enddef; -vardef LCD(text nt)(text rep)= +vardef LCD(text nt)(text rep)(expr NB)= decahoriz:=0; nblignes:=nblignes+1; path Ecran; @@ -185,6 +182,12 @@ vardef LCD(text nt)(text rep)= BlocAffichage; Test(k,nt); endfor; + for k=1 upto NB: + nblignes:=nblignes+1; + Ecran:=(u*(0,-1)--u*(120,-1)--u*(120,7)--u*(0,7)--cycle) shifted(u*(0,-8*(nblignes-1))); + fill Ecran withcolor if print=true:0.8white else:CouleurEcran fi; + draw Ecran withcolor if print=true:0.8white else:CouleurEcran fi; + endfor; nblignes:=nblignes+1; Ecran:=(u*(0,-1)--u*(120,-1)--u*(120,7)--u*(0,7)--cycle) shifted(u*(0,-8*(nblignes-1))); fill Ecran withcolor if print=true:0.8white else:CouleurEcran fi; diff --git a/Master/texmf-dist/metapost/profcollege/PfC-Constantes.mp b/Master/texmf-dist/metapost/profcollege/PfC-Constantes.mp index b97bd8a4c0a..02895dcf8c4 100644 --- a/Master/texmf-dist/metapost/profcollege/PfC-Constantes.mp +++ b/Master/texmf-dist/metapost/profcollege/PfC-Constantes.mp @@ -1,6 +1,3 @@ -%Author : Christophe Poulain -%Licence : Released under the LaTeX Project Public License v1.3c -% or later, see http://www.latex-project.org/lppl.txtf %Constantes u:=1cm; v:=(sqrt3)/2; diff --git a/Master/texmf-dist/metapost/profcollege/PfC-LaTeX.mp b/Master/texmf-dist/metapost/profcollege/PfC-LaTeX.mp index daa206a603d..33d9848b634 100644 --- a/Master/texmf-dist/metapost/profcollege/PfC-LaTeX.mp +++ b/Master/texmf-dist/metapost/profcollege/PfC-LaTeX.mp @@ -1,16 +1,11 @@ -%Author : Christophe Poulain -%Licence : Released under the LaTeX Project Public License v1.3c -% or later, see http://www.latex-project.org/lppl.txtf vardef LATEX primary s = write "verbatimtex" to "mptextmp.mp"; write "%&latex" to "mptextmp.mp"; write "\documentclass[]{article}" to "mptextmp.mp"; + write "\usepackage{ProfCollege}" to "mptextmp.mp"; write "\usepackage[utf8]{inputenc}" to "mptextmp.mp"; write "\usepackage[T1]{fontenc}" to "mptextmp.mp"; write "\usepackage{fourier}" to "mptextmp.mp"; - write "\usepackage{mathtools,amssymb}" to "mptextmp.mp"; - write "\usepackage{siunitx}" to "mptextmp.mp"; - write "\sisetup{locale=FR,detect-all,output-decimal-marker={,},group-four-digits}" to "mptextmp.mp"; write "\usepackage[french]{babel}" to "mptextmp.mp"; write "\begin{document}" to "mptextmp.mp"; write "etex" to "mptextmp.mp"; diff --git a/Master/texmf-dist/metapost/profcollege/PfC-Svgnames.mp b/Master/texmf-dist/metapost/profcollege/PfC-Svgnames.mp index 3af1336dc33..3aa2cf23860 100644 --- a/Master/texmf-dist/metapost/profcollege/PfC-Svgnames.mp +++ b/Master/texmf-dist/metapost/profcollege/PfC-Svgnames.mp @@ -1,6 +1,3 @@ -%Author : Christophe Poulain -%Licence : Released under the LaTeX Project Public License v1.3c -% or later, see http://www.latex-project.org/lppl.txtf %D'après /usr/local/texlive/2020/texmf-dist/tex/latex/xcolor/svgnam.def color AliceBlue; AliceBlue = (.94,.972,1); color AntiqueWhite; AntiqueWhite = (.98,.92,.844); diff --git a/Master/texmf-dist/tex/latex/profcollege/PfC-EquationComposition1.tex b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationComposition1.tex deleted file mode 100644 index b513a6b1163..00000000000 --- a/Master/texmf-dist/tex/latex/profcollege/PfC-EquationComposition1.tex +++ /dev/null @@ -1,277 +0,0 @@ -% Licence : Released under the LaTeX Project Public License v1.3c -% or later, see http://www.latex-project.org/lppl.txtf -\newcommand{\EquaDeuxComposition}[5][]{%type ax+b=d ou b=cx+d$ - \useKVdefault[ClesEquation]% - \setKV[ClesEquation]{#1}% - \ifx\bla#2\bla%On échange en faisant attention à ne pas boucler : c doit être non vide - \EquaDeuxComposition[#1]{#4}{#5}{#2}{#3} - \else%cas ax+b=d - \xintifboolexpr{#2=0}{% - \xintifboolexpr{#3=#5}{%b=d - L'équation $\num{#3}=\num{#5}$ a une infinité de solution.}% - {%b<>d - L'équation $\num{#3}=\num{#5}$ n'a aucune solution.% - }% - }{%ELSE - \xintifboolexpr{#3=0}{%ax+b=d - \EquaBase[#1]{#2}{}{}{#5}% - }{%ax+b=d$ Ici - \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{} - \begin{align*} - \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{#5}}\tikzmark{E-\theNbequa}\\ - \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#5-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\\ - \tikzmark{C-\theNbequa}\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\ - \xintifboolexpr{\Coeffa=1}{}{\\} - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{A-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - \rightcomment{E-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - }{} - \xintifboolexpr{\Coeffa=1}{% - }{%\ifnum\cmtd>1 - \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{%ICI ? - \ifboolKV[ClesEquation]{FlecheDiv}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{} - } - } - \ifboolKV[ClesEquation]{Entier}{% - \SSimpliTest{\Coeffb}{\Coeffa}% - \ifboolKV[ClesEquation]{Simplification}{% - \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ - }{} - }{} - \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} - \end{align*} - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\num{#5}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$. - }{} - } - } - \fi -} - -\newcommand{\EquaTroisComposition}[5][]{%ax+b=cx ou ax=cx+d - \useKVdefault[ClesEquation]% - \setKV[ClesEquation]{#1}% - \ifx\bla#3\bla%on inverse en faisant attention à la boucle #3<->#5 - \ifx\bla#5\bla% - %% paramètre oublié - \else - \EquaTroisComposition[#1]{#4}{#5}{#2}{}% - \fi - \else - \xintifboolexpr{#2=0}{%b=cx - \EquaBase[#1]{#4}{}{}{#3} - }{% - \xintifboolexpr{#4=0}{%ax+b=0 - \EquaDeuxComposition[#1]{#2}{#3}{}{0} - }{%ax+b=cx - \xintifboolexpr{#2=#4}{% - \xintifboolexpr{#3=0}{%ax=ax - L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une infinité de solution.}% - {%ax+b=ax - L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ n'a aucune solution.% - }% - }{%% Cas délicat - \xintifboolexpr{#2>#4}{%ax+b=cx avec a>c - \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{} - \begin{align*} - \tikzmark{A-\theNbequa}\mathcolor{Ccompo}{\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\tikzmark{E-\theNbequa}\\ - \mathcolor{Ccompo}{\num{\fpeval{#2-#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{+\num{#4}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\\ - \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{0}\tikzmark{F-\theNbequa}\\ - \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{0-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\tikzmark{F-\theNbequa}\\ - \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\ - \xintifboolexpr{\Coeffa=1}{}{\\} - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} - \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} - \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - }{} - \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 - \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{ - \ifboolKV[ClesEquation]{FlecheDiv}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{} - } - \ifboolKV[ClesEquation]{Entier}{% - \SSimpliTest{\Coeffb}{\Coeffa}% - \ifboolKV[ClesEquation]{Simplification}{% - \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ - }{} - }{} - } - \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} - \end{align*} - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{} - }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\tikzmark{E-\theNbequa}\\ - \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#4-#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#2>0}{+\num{#2}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\ - \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa} - \xintifboolexpr{\Coeffa=1}{}{\\} - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} - \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} - }{} - \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 - \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\ - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{ - \ifboolKV[ClesEquation]{FlecheDiv}{% - \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{} - } - \ifboolKV[ClesEquation]{Entier}{% - \SSimpliTest{\Coeffb}{\Coeffa}% - \ifboolKV[ClesEquation]{Simplification}{% - \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\ - }{} - }{} - } - \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} - \end{align*} - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}% - }% - }% - }% - }% - \fi - }% - - -\newcommand{\ResolEquationComposition}[5][]{% - \useKVdefault[ClesEquation]% - \setKV[ClesEquation]{#1}% - \xintifboolexpr{#2=0}{% - \xintifboolexpr{#4=0}{% - \xintifboolexpr{#3=#5}{%b=d - L'équation $\num{#3}=\num{#5}$ a une infinité de solution.}% - {%b<>d - L'équation $\num{#3}=\num{#5}$ n'a aucune solution.% - }% - }% - {%0x+b=cx+d$ - \EquaDeuxComposition[#1]{#4}{#5}{#2}{#3}% - }% - }{% - \xintifboolexpr{#4=0}{%ax+b=0x+d - \EquaDeuxComposition[#1]{#2}{#3}{}{#5}% - } - {%ax+b=cx+d$ - \xintifboolexpr{#3=0}{% - \xintifboolexpr{#5=0}{%ax=cx - \EquaTroisComposition[#1]{#2}{0}{#4}{}% - }% - {%ax=cx+d - \EquaTroisComposition[#1]{#4}{#5}{#2}{}% - }% - }% - {\xintifboolexpr{#5=0}{%ax+b=cx - \EquaTroisComposition[#1]{#2}{#3}{#4}{}% - }% - {%ax+b=cx+d -- ici - \xintifboolexpr{#2=#4}{% - \xintifboolexpr{#3=#5}{%b=d - L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une infinité de solution.}% - {%b<>d - L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ n'a aucune solution.% - }% - }{ - %% Cas délicat - \xintifboolexpr{#2>#4}{%ax+b=cx+d avec a>c - \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{} - \begin{align*} - \tikzmark{A-\theNbequa}\mathcolor{Ccompo}{\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{E-\theNbequa}\\ - \mathcolor{Ccompo}{\num{\fpeval{#2-#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{+\num{#4}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ - \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{#5}}\tikzmark{F-\theNbequa}\\ - \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#5-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\\ - \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\ - \xintifboolexpr{\Coeffa=1}{}{\\} - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} - \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} - \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - }{} - \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 - \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{ - \ifboolKV[ClesEquation]{FlecheDiv}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{} - } - \ifboolKV[ClesEquation]{Entier}{% - \SSimpliTest{\Coeffb}{\Coeffa}% - \ifboolKV[ClesEquation]{Simplification}{% - \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ - }{} - }{} - } - \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} - \end{align*} - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.% - }{} - }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{E-\theNbequa}\\ - \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#4-#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#2>0}{+\num{#2}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ - \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{F-\theNbequa}\\ - \mathcolor{Ccompo}{\num{\fpeval{#3-#5}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ - \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{G-\theNbequa}%\\ - \xintifboolexpr{\Coeffa=1}{}{\\} - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} - \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} - \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}% - \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}% - }{} - \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 - \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\ - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{ - \ifboolKV[ClesEquation]{FlecheDiv}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{} - } - \ifboolKV[ClesEquation]{Entier}{% - \SSimpliTest{\Coeffb}{\Coeffa}% - \ifboolKV[ClesEquation]{Simplification}{% - \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\ - }{} - }{} - } - \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} - \end{align*} - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.% - }{}% - }% - }% - }% - }% - }% - }% -}% - - diff --git a/Master/texmf-dist/tex/latex/profcollege/PfC-EquationComposition2.tex b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationComposition2.tex new file mode 100644 index 00000000000..38493f89966 --- /dev/null +++ b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationComposition2.tex @@ -0,0 +1,275 @@ +% Licence : Released under the LaTeX Project Public License v1.3c +% or later, see http://www.latex-project.org/lppl.txtf +\newcommand{\EquaDeuxComposition}[5][]{%type ax+b=d ou b=cx+d$ + \useKVdefault[ClesEquation]% + \setKV[ClesEquation]{#1}% + \ifx\bla#2\bla%On échange en faisant attention à ne pas boucler : c doit être non vide + \EquaDeuxComposition[#1]{#4}{#5}{#2}{#3} + \else%cas ax+b=d + \xintifboolexpr{#2=0}{% + \xintifboolexpr{#3=#5}{%b=d + L'équation $\num{#3}=\num{#5}$ a une infinité de solutions.}% + {%b<>d + L'équation $\num{#3}=\num{#5}$ n'a aucune solution.% + }% + }{%ELSE + \xintifboolexpr{#3=0}{%ax+b=d + \EquaBase[#1]{#2}{}{}{#5}% + }{%ax+b=d$ Ici + \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{} + \begin{align*} + \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{#5}}\tikzmark{E-\theNbequa}\\ + \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#5-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\\ + \tikzmark{C-\theNbequa}\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\ + \xintifboolexpr{\Coeffa=1}{}{\\} + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{A-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + \rightcomment{E-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + }{} + \xintifboolexpr{\Coeffa=1}{% + }{%\ifnum\cmtd>1 + \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{%ICI ? + \ifboolKV[ClesEquation]{FlecheDiv}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{} + } + } + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{\Coeffb}{\Coeffa}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ + }{} + }{} + \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} + \end{align*} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\num{#5}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$. + }{} + } + } + \fi +} + +\newcommand{\EquaTroisComposition}[5][]{%ax+b=cx ou ax=cx+d + \useKVdefault[ClesEquation]% + \setKV[ClesEquation]{#1}% + \ifx\bla#3\bla%on inverse en faisant attention à la boucle #3<->#5 + \ifx\bla#5\bla% + %% paramètre oublié + \else + \EquaTroisComposition[#1]{#4}{#5}{#2}{}% + \fi + \else + \xintifboolexpr{#2=0}{%b=cx + \EquaBase[#1]{#4}{}{}{#3} + }{% + \xintifboolexpr{#4=0}{%ax+b=0 + \EquaDeuxComposition[#1]{#2}{#3}{}{0} + }{%ax+b=cx + \xintifboolexpr{#2=#4}{% + \xintifboolexpr{#3=0}{%ax=ax + L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une infinité de solutions.}% + {%ax+b=ax + L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ n'a aucune solution.% + }% + }{%% Cas délicat + \xintifboolexpr{#2>#4}{%ax+b=cx avec a>c + \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{} + \begin{align*} + \tikzmark{A-\theNbequa}\mathcolor{Ccompo}{\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\tikzmark{E-\theNbequa}\\ + \mathcolor{Ccompo}{\num{\fpeval{#2-#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{+\num{#4}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\\ + \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{0}\tikzmark{F-\theNbequa}\\ + \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{0-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\tikzmark{F-\theNbequa}\\ + \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\ + \xintifboolexpr{\Coeffa=1}{}{\\} + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} + \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} + \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + }{} + \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 + \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{ + \ifboolKV[ClesEquation]{FlecheDiv}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{} + } + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{\Coeffb}{\Coeffa}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ + }{} + }{} + } + \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} + \end{align*} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{} + }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\tikzmark{E-\theNbequa}\\ + \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#4-#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#2>0}{+\num{#2}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\ + \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa} + \xintifboolexpr{\Coeffa=1}{}{\\} + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} + \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} + }{} + \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 + \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\ + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{ + \ifboolKV[ClesEquation]{FlecheDiv}{% + \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{} + } + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{\Coeffb}{\Coeffa}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\ + }{} + }{} + } + \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} + \end{align*} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}% + }% + }% + }% + }% + \fi +}% + + +\newcommand{\ResolEquationComposition}[5][]{% + \useKVdefault[ClesEquation]% + \setKV[ClesEquation]{#1}% + \xintifboolexpr{#2=0}{% + \xintifboolexpr{#4=0}{% + \xintifboolexpr{#3=#5}{%b=d + L'équation $\num{#3}=\num{#5}$ a une infinité de solutions.}% + {%b<>d + L'équation $\num{#3}=\num{#5}$ n'a aucune solution.% + }% + }% + {%0x+b=cx+d$ + \EquaDeuxComposition[#1]{#4}{#5}{#2}{#3}% + }% + }{% + \xintifboolexpr{#4=0}{%ax+b=0x+d + \EquaDeuxComposition[#1]{#2}{#3}{}{#5}% + } + {%ax+b=cx+d$ + \xintifboolexpr{#3=0}{% + \xintifboolexpr{#5=0}{%ax=cx + \EquaTroisComposition[#1]{#2}{0}{#4}{}% + }% + {%ax=cx+d + \EquaTroisComposition[#1]{#4}{#5}{#2}{}% + }% + }% + {\xintifboolexpr{#5=0}{%ax+b=cx + \EquaTroisComposition[#1]{#2}{#3}{#4}{}% + }% + {%ax+b=cx+d -- ici + \xintifboolexpr{#2=#4}{% + \xintifboolexpr{#3=#5}{%b=d + L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une infinité de solutions.}% + {%b<>d + L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ n'a aucune solution.% + }% + }{ + %% Cas délicat + \xintifboolexpr{#2>#4}{%ax+b=cx+d avec a>c + \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{} + \begin{align*} + \tikzmark{A-\theNbequa}\mathcolor{Ccompo}{\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{E-\theNbequa}\\ + \mathcolor{Ccompo}{\num{\fpeval{#2-#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{+\num{#4}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ + \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{#5}}\tikzmark{F-\theNbequa}\\ + \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#5-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\\ + \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\ + \xintifboolexpr{\Coeffa=1}{}{\\} + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} + \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} + \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + }{} + \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 + \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{ + \ifboolKV[ClesEquation]{FlecheDiv}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{} + } + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{\Coeffb}{\Coeffa}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ + }{} + }{} + } + \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} + \end{align*} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.% + }{} + }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{E-\theNbequa}\\ + \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#4-#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#2>0}{+\num{#2}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ + \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{F-\theNbequa}\\ + \mathcolor{Ccompo}{\num{\fpeval{#3-#5}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ + \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{G-\theNbequa}%\\ + \xintifboolexpr{\Coeffa=1}{}{\\} + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} + \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} + \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}% + \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}% + }{} + \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 + \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\ + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{ + \ifboolKV[ClesEquation]{FlecheDiv}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{} + } + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{\Coeffb}{\Coeffa}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\ + }{} + }{} + } + \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} + \end{align*} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.% + }{}% + }% + }% + }% + }% + }% + }% +}% \ No newline at end of file diff --git a/Master/texmf-dist/tex/latex/profcollege/PfC-EquationSoustraction1.tex b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationSoustraction1.tex deleted file mode 100644 index 034aa7e2ed4..00000000000 --- a/Master/texmf-dist/tex/latex/profcollege/PfC-EquationSoustraction1.tex +++ /dev/null @@ -1,332 +0,0 @@ -% Licence : Released under the LaTeX Project Public License v1.3c -% or later, see http://www.latex-project.org/lppl.txtf -\newcommand{\EquaBase}[5][]{%type ax=d ou b=cx - \useKVdefault[ClesEquation]% - \setKV[ClesEquation]{#1}% - \ifx\bla#2\bla%on teste si le paramètre #2 est vide: - % si oui, on est dans le cas b=cx. Eh bien on échange :) - % Mais attention si les deux paramètres a et c sont vides... - \EquaBase[#1]{#4}{}{}{#3} - \else - % si non, on est dans le cas ax=d - \xintifboolexpr{#2=0}{% - \xintifboolexpr{#5=0}{% - L'équation $0\useKV[ClesEquation]{ELettre}=0$ a une infinité de solution.}{L'équation $0\useKV[ClesEquation]{Lettre}=\num{#5}$ n'a aucune solution.}% - }{%\else - \xintifboolexpr{#5=0}{L'équation $\num{#2}\useKV[ClesEquation]{Lettre}=0$ a une unique solution : $\useKV[ClesEquation]{Lettre}=0$.}{%\else - \begin{align*}% - \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}}{\num{#2}\useKV[ClesEquation]{Lettre}}&=\num{#5}\tikzmark{C-\theNbequa}\\ - \tikzmark{B-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{#5}}{\num{#2}}\tikzmark{D-\theNbequa}%\\ - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}% - \rightcomment{C-\theNbequa}{D-\theNbequa}{D-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}% - }{% - \ifboolKV[ClesEquation]{FlecheDiv}{% - \Leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}% - \Rightcomment{C-\theNbequa}{D-\theNbequa}{D-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}% - }{}% - }%% - \ifboolKV[ClesEquation]{Entier}{% - \SSimpliTest{#5}{#2}% - \ifboolKV[ClesEquation]{Simplification}{% - \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{#5}{#2}}{}%\\ - }{} - }{} - \ifboolKV[ClesEquation]{Fleches}{% - \stepcounter{Nbequa}}% - {\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{} - } - \end{align*} - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}=\num{#5}}{\num{#2}\useKV[ClesEquation]{Lettre}=\num{#5}}$ a une unique solution : $\displaystyle\useKV[ClesEquation]{Lettre}=\opdiv*{#5}{#2}{numequa}{resteequa}\opcmp{resteequa}{0}\ifopeq\opexport{numequa}{\numequa}\num{\numequa}\else\ifboolKV[ClesEquation]{Simplification}{\SSimplifie{#5}{#2}}{\frac{\num{#5}}{\num{#2}}}\fi$.% - }{} - } - } - \fi -} - -\newcommand{\EquaDeuxSoustraction}[5][]{%type ax+b=d ou b=cx+d$ - \useKVdefault[ClesEquation]% - \setKV[ClesEquation]{#1}% - \ifx\bla#2\bla%On échange en faisant attention à ne pas boucler : c doit être non vide - \EquaDeuxSoustraction[#1]{#4}{#5}{#2}{#3} - \else%cas ax+b=d - \xintifboolexpr{#2=0}{% - \xintifboolexpr{#3=#5}{%b=d - L'équation $\num{#3}=\num{#5}$ a une infinité de solution.}% - {%b<>d - L'équation $\num{#3}=\num{#5}$ n'a aucune solution.% - }% - }{%ELSE - \xintifboolexpr{#3=0}{%ax+b=d - \EquaBase[#1]{#2}{}{}{#5}% - }{%ax+b=d$ Ici - \begin{align*} - \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{E-\theNbequa}\\ - \ifboolKV[ClesEquation]{Decomposition}{% - \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=\num{#5}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\ - }{}% - \tikzmark{C-\theNbequa}\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\ - \xintifboolexpr{\Coeffa=1}{}{\\} - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{A-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - \rightcomment{E-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - }{} - \xintifboolexpr{\Coeffa=1}{% - }{%\ifnum\cmtd>1 - \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{%ICI ? - \ifboolKV[ClesEquation]{FlecheDiv}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{} - } - } - \ifboolKV[ClesEquation]{Entier}{% - \SSimpliTest{\Coeffb}{\Coeffa}% - \ifboolKV[ClesEquation]{Simplification}{% - \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ - }{} - }{} - \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} - \end{align*} - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\num{#5}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$. - }{} - } - } - \fi -} - -\newcommand{\EquaTroisSoustraction}[5][]{%ax+b=cx ou ax=cx+d - \useKVdefault[ClesEquation]% - \setKV[ClesEquation]{#1}% - \ifx\bla#3\bla%on inverse en faisant attention à la boucle #3<->#5 - \ifx\bla#5\bla% - %% paramètre oublié - \else - \EquaTroisSoustraction[#1]{#4}{#5}{#2}{}% - \fi - \else - \xintifboolexpr{#2=0}{%b=cx - \EquaBase[#1]{#4}{}{}{#3} - }{% - \xintifboolexpr{#4=0}{%ax+b=0 - \EquaDeuxSoustraction[#1]{#2}{#3}{}{0} - }{%ax+b=cx - \xintifboolexpr{#2=#4}{% - \xintifboolexpr{#3=0}{%ax=ax - L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une infinité de solution.}% - {%ax+b=ax - L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ n'a aucune solution.% - }% - }{%% Cas délicat - \xintifboolexpr{#2>#4}{%ax+b=cx avec a>c - \begin{align*} - \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\tikzmark{E-\theNbequa}\\ - \ifboolKV[ClesEquation]{Decomposition}{% - \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\ - }{} - \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\tikzmark{F-\theNbequa}\\ - \ifboolKV[ClesEquation]{Decomposition}{% - \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=0\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\tikzmark{F-\theNbequa}\\ - }{}% - \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\ - \xintifboolexpr{\Coeffa=1}{}{\\} - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} - \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} - \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - }{} - \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 - \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{ - \ifboolKV[ClesEquation]{FlecheDiv}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{} - } - \ifboolKV[ClesEquation]{Entier}{% - \SSimpliTest{\Coeffb}{\Coeffa}% - \ifboolKV[ClesEquation]{Simplification}{% - \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ - }{} - }{} - } - \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} - \end{align*} - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{} - }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\tikzmark{E-\theNbequa}\\ - \ifboolKV[ClesEquation]{Decomposition}{% - \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\ - }{} - \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa} - \xintifboolexpr{\Coeffa=1}{}{\\} - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} - \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} - }{} - \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 - \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\ - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{ - \ifboolKV[ClesEquation]{FlecheDiv}{% - \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{} - } - \ifboolKV[ClesEquation]{Entier}{% - \SSimpliTest{\Coeffb}{\Coeffa}% - \ifboolKV[ClesEquation]{Simplification}{% - \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\ - }{} - }{} - } - \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} - \end{align*} - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}% - }% - }% - }% - }% - \fi - }% - - -\newcommand{\ResolEquationSoustraction}[5][]{% - \useKVdefault[ClesEquation]% - \setKV[ClesEquation]{#1}% - \xintifboolexpr{#2=0}{% - \xintifboolexpr{#4=0}{% - \xintifboolexpr{#3=#5}{%b=d - L'équation $\num{#3}=\num{#5}$ a une infinité de solution.}% - {%b<>d - L'équation $\num{#3}=\num{#5}$ n'a aucune solution.% - }% - }% - {%0x+b=cx+d$ - \EquaDeuxSoustraction[#1]{#4}{#5}{}{#3}% - }% - }{% - \xintifboolexpr{#4=0}{%ax+b=0x+d - \EquaDeuxSoustraction[#1]{#2}{#3}{}{#5}% - } - {%ax+b=cx+d$ - \xintifboolexpr{#3=0}{% - \xintifboolexpr{#5=0}{%ax=cx - \EquaTroisSoustraction[#1]{#2}{0}{#4}{}% - }% - {%ax=cx+d - \EquaTroisSoustraction[#1]{#4}{#5}{#2}{}% - }% - }% - {\xintifboolexpr{#5=0}{%ax+b=cx - \EquaTroisSoustraction[#1]{#2}{#3}{#4}{}% - }% - {%ax+b=cx+d -- ici - \xintifboolexpr{#2=#4}{% - \xintifboolexpr{#3=#5}{%b=d - L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une infinité de solution.}% - {%b<>d - L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ n'a aucune solution.% - }% - }{ - %% Cas délicat - \xintifboolexpr{#2>#4}{%ax+b=cx+d avec a>c - \begin{align*} - \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{E-\theNbequa}\\ - \ifboolKV[ClesEquation]{Decomposition}{% - \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ - }{} - \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{F-\theNbequa}\\ - \ifboolKV[ClesEquation]{Decomposition}{% - \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=\num{#5}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\ - }{}% - \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\ - \xintifboolexpr{\Coeffa=1}{}{\\} - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} - \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} - \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% - }{} - \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 - \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{ - \ifboolKV[ClesEquation]{FlecheDiv}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{} - } - \ifboolKV[ClesEquation]{Entier}{% - \SSimpliTest{\Coeffb}{\Coeffa}% - \ifboolKV[ClesEquation]{Simplification}{% - \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ - }{} - }{} - } - \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} - \end{align*} - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.% - }{} - }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{E-\theNbequa}\\ - \ifboolKV[ClesEquation]{Decomposition}{% - \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ - }{} - \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{F-\theNbequa}\\ - \ifboolKV[ClesEquation]{Decomposition}{% - \num{#3}\mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}\\ - }{}% - \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{G-\theNbequa}%\\ - \xintifboolexpr{\Coeffa=1}{}{\\} - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} - \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} - \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}% - \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}% - }{} - \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 - \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\ - \ifboolKV[ClesEquation]{Fleches}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{ - \ifboolKV[ClesEquation]{FlecheDiv}{% - \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{} - } - \ifboolKV[ClesEquation]{Entier}{% - \SSimpliTest{\Coeffb}{\Coeffa}% - \ifboolKV[ClesEquation]{Simplification}{% - \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\ - }{} - }{} - } - \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} - \end{align*} - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.% - }{}% - }% - }% - }% - }% - }% - }% -}% - - diff --git a/Master/texmf-dist/tex/latex/profcollege/PfC-EquationSoustraction2.tex b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationSoustraction2.tex new file mode 100644 index 00000000000..f3ffd9453dc --- /dev/null +++ b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationSoustraction2.tex @@ -0,0 +1,345 @@ +% Licence : Released under the LaTeX Project Public License v1.3c +% or later, see http://www.latex-project.org/lppl.txtf +\newcommand{\EquaBase}[5][]{%type ax=d ou b=cx + \useKVdefault[ClesEquation]% + \setKV[ClesEquation]{#1}% + \ifx\bla#2\bla%on teste si le paramètre #2 est vide: + % si oui, on est dans le cas b=cx. Eh bien on échange :) + % Mais attention si les deux paramètres a et c sont vides... + \EquaBase[#1]{#4}{}{}{#3} + \else + % si non, on est dans le cas ax=d + \xintifboolexpr{#2=0}{% + \xintifboolexpr{#5=0}{% + L'équation $0\useKV[ClesEquation]{ELettre}=0$ a une infinité de solutions.}{L'équation $0\useKV[ClesEquation]{Lettre}=\num{#5}$ n'a aucune solution.}% + }{%\else + \xintifboolexpr{#5=0}{L'équation $\num{#2}\useKV[ClesEquation]{Lettre}=0$ a une unique solution : $\useKV[ClesEquation]{Lettre}=0$.}{%\else + \begin{align*}% + \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}}{\num{#2}\useKV[ClesEquation]{Lettre}}&=\num{#5}\tikzmark{C-\theNbequa}\\ + \tikzmark{B-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{#5}}{\num{#2}}\tikzmark{D-\theNbequa}%\\ + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}% + \rightcomment{C-\theNbequa}{D-\theNbequa}{D-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}% + }{% + \ifboolKV[ClesEquation]{FlecheDiv}{% + \Leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}% + \Rightcomment{C-\theNbequa}{D-\theNbequa}{D-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}% + }{}% + }%% + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{#5}{#2}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{#5}{#2}}{}%\\ + }{} + }{} + \ifboolKV[ClesEquation]{Fleches}{% + \stepcounter{Nbequa}}% + {\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{} + } + \end{align*} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}=\num{#5}}{\num{#2}\useKV[ClesEquation]{Lettre}=\num{#5}}$ a une unique solution : $\displaystyle\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\opdiv*{#5}{#2}{numequa}{resteequa}\opcmp{resteequa}{0}\ifopeq\opexport{numequa}{\numequa}\num{\numequa}\else\ifboolKV[ClesEquation]{Simplification}{\SSimplifie{#5}{#2}}{\frac{\num{#5}}{\num{#2}}}\fi$.% + }{} + } + } + \fi +} + +\newcommand{\EquaDeuxSoustraction}[5][]{%type ax+b=d ou b=cx+d$ + \useKVdefault[ClesEquation]% + \setKV[ClesEquation]{#1}% + \ifx\bla#2\bla%On échange en faisant attention à ne pas boucler : c doit être non vide + \EquaDeuxSoustraction[#1]{#4}{#5}{#2}{#3} + \else%cas ax+b=d + \xintifboolexpr{#2=0}{% + \xintifboolexpr{#3=#5}{%b=d + L'équation $\num{#3}=\num{#5}$ a une infinité de solutions.}% + {%b<>d + L'équation $\num{#3}=\num{#5}$ n'a aucune solution.% + }% + }{%ELSE + \xintifboolexpr{#3=0}{%ax+b=d + \EquaBase[#1]{#2}{}{}{#5}% + }{%ax+b=d$ Ici + \begin{align*} + \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{E-\theNbequa}\\ + \ifboolKV[ClesEquation]{Decomposition}{% + \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=\num{#5}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\ + }{}% + \tikzmark{C-\theNbequa}\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa} + \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{} + \xintifboolexpr{\Coeffa=1}{}{\\} + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{A-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + \rightcomment{E-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + }{} + \xintifboolexpr{\Coeffa=1}{% + }{%\ifnum\cmtd>1 + \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{%ICI ? + \ifboolKV[ClesEquation]{FlecheDiv}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{} + } + } + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{\Coeffb}{\Coeffa}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ + }{} + }{} + \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} + \end{align*} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\num{#5}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$. + }{} + } + } + \fi +} + +\newcommand{\EquaTroisSoustraction}[5][]{%ax+b=cx ou ax=cx+d + \useKVdefault[ClesEquation]% + \setKV[ClesEquation]{#1}% + \ifx\bla#3\bla%on inverse en faisant attention à la boucle #3<->#5 + \ifx\bla#5\bla% + %% paramètre oublié + \else + \EquaTroisSoustraction[#1]{#4}{#5}{#2}{}% + \fi + \else + \xintifboolexpr{#2=0}{%b=cx + \EquaBase[#1]{#4}{}{}{#3} + }{% + \xintifboolexpr{#4=0}{%ax+b=0 + \EquaDeuxSoustraction[#1]{#2}{#3}{}{0} + }{%ax+b=cx + \xintifboolexpr{#2=#4}{% + \xintifboolexpr{#3=0}{%ax=ax + L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une infinité de solutions.}% + {%ax+b=ax + L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ n'a aucune solution.% + }% + }{%% Cas délicat + \xintifboolexpr{#2>#4}{%ax+b=cx avec a>c + \begin{align*} + \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\tikzmark{E-\theNbequa}\\ + \ifboolKV[ClesEquation]{Decomposition}{% + \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\ + }{} + \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\tikzmark{F-\theNbequa}\\ + \ifboolKV[ClesEquation]{Decomposition}{% + \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=0\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\tikzmark{F-\theNbequa}\\ + }{}% + \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\ + %eric + \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{} + % eric + \xintifboolexpr{\Coeffa=1}{}{\\} + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} + \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} + \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + }{} + \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 + \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{ + \ifboolKV[ClesEquation]{FlecheDiv}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{} + } + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{\Coeffb}{\Coeffa}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ + }{} + }{} + } + \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} + \end{align*} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{} + }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\tikzmark{E-\theNbequa}\\ + \ifboolKV[ClesEquation]{Decomposition}{% + \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\ + }{} + \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa} + \xintifboolexpr{\Coeffa=1}{}{\\} + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} + \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} + }{} + % eric + \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}&=\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}}}{} + % eric + \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 + \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\ + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{ + \ifboolKV[ClesEquation]{FlecheDiv}{% + \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{} + } + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{\Coeffb}{\Coeffa}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\ + }{} + }{} + } + \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} + \end{align*} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}% + }% + }% + }% + }% + \fi + }% + + +\newcommand{\ResolEquationSoustraction}[5][]{% + \useKVdefault[ClesEquation]% + \setKV[ClesEquation]{#1}% + \xintifboolexpr{#2=0}{% + \xintifboolexpr{#4=0}{% + \xintifboolexpr{#3=#5}{%b=d + L'équation $\num{#3}=\num{#5}$ a une infinité de solutions.}% + {%b<>d + L'équation $\num{#3}=\num{#5}$ n'a aucune solution.% + }% + }% + {%0x+b=cx+d$ + \EquaDeuxSoustraction[#1]{#4}{#5}{}{#3}% + }% + }{% + \xintifboolexpr{#4=0}{%ax+b=0x+d + \EquaDeuxSoustraction[#1]{#2}{#3}{}{#5}% + } + {%ax+b=cx+d$ + \xintifboolexpr{#3=0}{% + \xintifboolexpr{#5=0}{%ax=cx + \EquaTroisSoustraction[#1]{#2}{0}{#4}{}% + }% + {%ax=cx+d + \EquaTroisSoustraction[#1]{#4}{#5}{#2}{}% + }% + }% + {\xintifboolexpr{#5=0}{%ax+b=cx + \EquaTroisSoustraction[#1]{#2}{#3}{#4}{}% + }% + {%ax+b=cx+d -- ici + \xintifboolexpr{#2=#4}{% + \xintifboolexpr{#3=#5}{%b=d + L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une infinité de solutions.}% + {%b<>d + L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ n'a aucune solution.% + }% + }{ + %% Cas délicat + \xintifboolexpr{#2>#4}{%ax+b=cx+d avec a>c + \begin{align*} + \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{E-\theNbequa}\\ + \ifboolKV[ClesEquation]{Decomposition}{% + \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ + }{} + \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{F-\theNbequa}\\ + \ifboolKV[ClesEquation]{Decomposition}{% + \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=\num{#5}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\ + }{}% + \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\ + % eric + \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{} + % eric + \xintifboolexpr{\Coeffa=1}{}{\\} + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} + \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$} + \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% + }{} + \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 + \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{ + \ifboolKV[ClesEquation]{FlecheDiv}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{} + } + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{\Coeffb}{\Coeffa}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ + }{} + }{} + } + \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} + \end{align*} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.% + }{} + }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{E-\theNbequa}\\ + \ifboolKV[ClesEquation]{Decomposition}{% + \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ + }{} + \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{F-\theNbequa}\\ + \ifboolKV[ClesEquation]{Decomposition}{% + \num{#3}\mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}\\ + }{}% + \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{G-\theNbequa}%\\ + % eric + \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}&=\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}}}{} + % eric + \xintifboolexpr{\Coeffa=1}{}{\\} + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} + \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$} + \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}% + \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}% + }{} + \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1 + \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\ + \ifboolKV[ClesEquation]{Fleches}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{ + \ifboolKV[ClesEquation]{FlecheDiv}{% + \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{} + } + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{\Coeffb}{\Coeffa}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\ + }{} + }{} + } + \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} + \end{align*} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.% + }{}% + }% + }% + }% + }% + }% + }% +}% + + diff --git a/Master/texmf-dist/tex/latex/profcollege/ProfCollege.sty b/Master/texmf-dist/tex/latex/profcollege/ProfCollege.sty index 121428955bd..215caf55034 100644 --- a/Master/texmf-dist/tex/latex/profcollege/ProfCollege.sty +++ b/Master/texmf-dist/tex/latex/profcollege/ProfCollege.sty @@ -1,65 +1,11 @@ % Author : Christophe Poulain % Licence : Released under the LaTeX Project Public License v1.3c % or later, see http://www.latex-project.org/lppl.txtf -%%%%%%% -% 90 : Reprise d'une partie de la doc. Quelques ajouts. -% 87-88 : amélioration \Thales. \Labyrinthe. -% 85 : passage à lua. -% 75 : plein de choses que j'ai oubliées :( -% 71 : Possibilité de choisir les fontes pour les figures MP -% 70 : Ajout de la commande \calculatrice. Coupure des calculs longs -% pour la moyenne et médiane. Egalités remarquables pour le -% développement. Tableau vide pour les stats. -% 67 : préparation au dépôt sur ctan.org -% 66 : Ajout de la commande \Ratio. -% 62 : Refonte des commandes !\Result! - Ajout d'une commande \Result -% dans SommeAngles. Rectification espace dans \Distri avec Reduction active. -% 61 : Simplication d'une fraction en version longue :) - Ajout -% d'options à la commande \lstinline!\Stat!. Ajout d'options à la -% commande \lstinline!\Thales!. -% 60 : Nouvelle présentation de la résolution d'une équation. Reprise -% et ajout d'une clé à la commande \SommeAngles. -% 59 : amélioration de la macro \Pythagore pour pouvoir enchaîner les -% calculs. Amélioration de la macro \Reperage pour améliorer -% la gestion de l'affichage sur les droites graduées. -% 58 : ajout d'un affichage des angles dans les diagrammes circulaires. -% 57 : ajout de la commande \Fraction. Ajout d'un VF dans la macro \QCM -% 56 : ajout de commandes "utiles" :) / Modification de \SommeAngles -% pour éviter les conflits. -% 55 : ajout d'une clé \Cle{Longue} dans la commande \Décomposition -% 54 : adaptations mineures :) à gmp -% 53 : ajout de la commande \QFlash -% 52 : ajout de la macro \QCM -% 51 : ajout de la macro \Relie -% 50 : Changement des clés. -% 37 : Reprise de la macro \Distri pour qu'elle accepte des valeurs -%décimales. -% 36 : Ajout d'un développement numérique. Reprise de la décomposition -% des nombres premiers (pour éviter conflit entre \newcount\c et la -% commande \c... Suppression de "spurious blank" -% 35 : Ajout d'une quatrième version de présentation de la résolution -% d'une équation - Nouvelle macro : Puissances. Ajout d'une option -% \EFacteurs pour les équations produit nul. Amélioration (rédaction) -% de \FonctionAffine - Ajout de la couleur de fond paramétrable dans -% les fleches PH et BH de \Propor -% 34 : Ajout de la commande \ResultatTrigo, \ResultatThalesx... Suppression de spurious blank. Corrections typographiques. Reprise de l'affichage de la moyenne dans la commande \Stat -% 33 : MAJ Distri : Problème d'espace en utilisant les nombres négatifs (1ere étape). -% 32 : MAJ Pythagore : Ajout de la clé PUnite - Possibilité de récupérer la valeur numérique obtenue par la macro Pythagore - Justification des textes dans les bulles. Ajout d'un FlecheCoefDebut dans \Propor. -% 31 : MAJ Pourcentage. Correction quelques bugs. Correction de \og spurious blank\fg. Oubli du RequirePackage{multido} :( -% 29 : MAJ Trigo (figure reprise pour utiliser \num de siunitx) -% 28 : Mise à jour de \Propor : flèches inversées \FlechesPH et \FlechesPB, homogénéité des flèches. Pourcentage. -% 27 : ajout du repérage -% 26 : ajout des schémas de proba + MAJ avec geometriesyr16 + MAJ Nombre premier. -% 25 : ajout des formules -% 24 : ajout d'une option pour les équations $X^2=a$ -% 23 : ajout d'une option pour les équations produit. -% 22 : ajout d'une option TColonnes dans la macro Tableaux -% 21 : Ajout d'une vérification dans la macro \ResolEquation - Correction de quelques bugs dans la résolution d'équation. -% 20: ajout d'une macro simpliste (car pas beaucoup d'utilité) sur les fonctions. -% 19 : Modification AAntécédent dans Affine + Amélioration Pythagore (Cas des triangles rectangles isocèles, dans le calcul de la longueur d'un côté) \NeedsTeXFormat{LaTeX2e} -\ProvidesPackage{ProfCollege}[2021/01/30 v0.90 Aide pour l'utilisation de LaTeX au collège] +\ProvidesPackage{ProfCollege}[2021/03/10 v0.95 Aide pour l'utilisation de LaTeX au collège] + +\RequirePackage{verbatim} \RequirePackage{mathtools}%Amélioration des rendus \RequirePackage{amssymb} @@ -77,6 +23,14 @@ \newcommand\speed[1]{\SI{#1}{\kmh}} \newcommand\Speed[1]{\SI[per-mode=symbol]{#1}{\kmh}} +\DeclareSIUnit{\are}{a} +\DeclareSIUnit{\annee}{an} +\DeclareSIUnit{\mois}{mois} +\DeclareSIUnit{\jour}{j} +\DeclareSIUnit{\quintal}{q} +\DeclareSIUnit{\octet}{o} +\DeclareSIUnit{\fahrenheit}{\degree F} + \RequirePackage[table,svgnames]{xcolor}%Gestion des couleurs \RequirePackage{xstring}%Gestion de chaines de caractères \RequirePackage{simplekv}%Gestion de paramètres sous forme de clés @@ -90,24 +44,24 @@ \if@shellescape \RequirePackage[shellescape,latex]{gmp}%inclusion de figures metapost "à la volée"% -\gmpoptions{everymp={prologues:=3; input PfC-LaTeX; input PfC-Svgnames; input PfC-Constantes; input PfC-Geometrie;}} +\gmpoptions{everymp={prologues:=3; input PfC-LaTeX; input PfC-Svgnames; input PfC-Constantes; input PfC-Geometrie; input PfC-Afficheur;}} \usempxclass{article} +\usempxpackage{ProfCollege} \usempxpackage[utf8]{inputenc} \usempxpackage[T1]{fontenc} \usempxpackage{fourier} \usempxpackage[french]{babel} \usempxpackage{pifont} -\usempxpackage[locale=FR]{siunitx} \else \RequirePackage[latex]{gmp}%inclusion de figures metapost "à la volée"% -\gmpoptions{everymp={prologues:=3; input PfC-LaTeX; input PfC-Svgnames; input PfC-Constantes; input PfC-Geometrie;}} +\gmpoptions{everymp={prologues:=3; input PfC-LaTeX; input PfC-Svgnames; input PfC-Constantes; input PfC-Geometrie; input PfC-Afficheur;}} \usempxclass{article} +\usempxpackage{ProfCollege} \usempxpackage[utf8]{inputenc} \usempxpackage[T1]{fontenc} \usempxpackage{fourier} \usempxpackage[french]{babel} \usempxpackage{pifont} -\usempxpackage[locale=FR]{siunitx} \fi \RequirePackage{xintexpr} @@ -138,17 +92,15 @@ \RequirePackage{stackengine} \RequirePackage[thicklines]{cancel} -%\ifpdftex -%\RequirePackage[babel=true,kerning=true]{microtype}%Pour gérer le souci du ; dans tikz avec pdftex... -%\fi +\RequirePackage{nicematrix}%pour le tableur % https://stackoverflow.com/questions/3391103/how-to-make-the-grayed-round-box-using-tiks \RequirePackage{environ} +% -%%% 80 \ifluatex \RequirePackage{luamplib} -\everymplib{input PfC-Svgnames; input PfC-Constantes; input PfC-Geometrie; beginfig(1);} +\everymplib{input PfC-Svgnames; input PfC-Constantes; input PfC-Geometrie; input PfC-Afficheur; beginfig(1);} \everyendmplib{endfig;} \fi @@ -180,9 +132,9 @@ \hfil\crcr #1\crcr}}\,} \catcode`\@=12 -%%%%%%%%%%%%%%%%%%%%% +%%% %% Commandes "utiles" -%%%%%%%%%%%%%%%%%%%%% +%%% %encadrer avec des "sommets arrondis" \newsavebox{\logobox} @@ -217,9 +169,28 @@ } } -%%%%%%%%%%%%%%%%% +\newcommand\MultiCol[2]{% + \setsepchar[*]{/}% + \readlist*\ListeNombreCol{#1}% + \setsepchar[*]{§}% + \readlist*\ListeContenuCol{#2}% + \xintFor* ##1 in {\xintSeq {1}{\ListeNombreCollen}}\do{% + \begin{minipage}{\ListeNombreCol[##1]\linewidth} + \ListeContenuCol[##1] + \end{minipage}% + \xintifboolexpr{##1<\ListeNombreCollen}{\hfill}{}% + }% +}% + +\newcommand\Demain{% + \advance\day by 1% + \today% + \advance\day by -1% +} + +%%% % Tables Addition-Multiplication -%%%%%%%%%%%%%%%%% +%%% \setKVdefault[Tables]{Addition=false,Multiplication=true,Seul=false,Debut=0,Fin=10,Couleur=white} % pour mémoire @@ -303,7 +274,6 @@ }% }% - \newcommand\Tables[2][]{% \useKVdefault[Tables]% \setKV[Tables]{#1}% @@ -322,15 +292,82 @@ }% }% -%%%%%%%%%%%%%% +%%% +% Rangement des nombres +%%% +\setKVdefault[ClesRgt]{Croissant,Decroissant=false,Strict,Fraction=false,Details=false} + +\DTLgnewdb{mtnumedb}% +\DTLgnewdb{mtnumeretourdb}% + +\newcommand\Rangement[2][]{% + \useKVdefault[ClesRgt]% + \setKV[ClesRgt]{#1}% + \ifboolKV[ClesRgt]{Fraction}{% + \setsepchar[*]{,*/}%\ignoreemptyitems% + \readlist*\ListeRgt{#2}% + % on cherche le dénominateur commun + \ppcm=1\relax + \foreachitem\x\in\ListeRgt{% + \PPCM{\fpeval{\ListeRgt[\xcnt,2]}}{\fpeval{\the\ppcm}}% + }% + % On crée la liste des rangements. + \DTLcleardb{mtnumedb}% + % on les trie pour les ranger par ordre croissant + \foreachitem\x\in\ListeRgt{% + \DTLnewrow{mtnumedb}% + \itemtomacro\ListeRgt[\xcnt,1]\y% + \DTLnewdbentry{mtnumedb}{Numeric}{\fpeval{\y*\the\ppcm/\ListeRgt[\xcnt,2]}}% + }% + % On trie + \ifboolKV[ClesRgt]{Decroissant}{% + % On trie la liste + \dtlsort{Numeric=descending}{mtnumedb}{\dtlicompare}% + \ifboolKV[ClesRgt]{Details}{\ensuremath{\DTLforeach{mtnumedb}{\numeroDonnee=Numeric}{\frac{\num{\numeroDonnee}}{\num{\the\ppcm}}\DTLiflastrow{}{\ifboolKV[ClesRgt]{Strict}{>}{\geqslant}}}}}{% + \ensuremath{\DTLforeach{mtnumedb}{\numeroDonnee=Numeric}{\Simplification{\numeroDonnee}{\ppcm}\DTLiflastrow{}{\ifboolKV[ClesRgt]{Strict}{>}{\geqslant}}}}% + } + }{% + % On trie la liste + \dtlsort{Numeric}{mtnumedb}{\dtlicompare}% + \ifboolKV[ClesRgt]{Details}{% + \ensuremath{\DTLforeach{mtnumedb}{\numeroDonnee=Numeric}{\frac{\num{\numeroDonnee}}{\num{\the\ppcm}}\DTLiflastrow{}{\ifboolKV[ClesRgt]{Strict}{<}{\leqslant}}}}% + }{% + \ensuremath{\DTLforeach{mtnumedb}{\numeroDonnee=Numeric}{\Simplification{\numeroDonnee}{\ppcm}\DTLiflastrow{}{\ifboolKV[ClesRgt]{Strict}{<}{\leqslant}}}}% + } + }% + }{% + \setsepchar{,}\ignoreemptyitems% + \readlist*\ListeRgt{#2}% + % on crée la base de données des valeurs + \DTLcleardb{mtdb}% + % on les trie pour les ranger par ordre croissant + \foreachitem\x\in\ListeRgt{% + \DTLnewrow{mtdb}% + \itemtomacro\ListeRgt[\xcnt]\y% + \DTLnewdbentry{mtdb}{Numeric}{\y}% + }% + % + \ifboolKV[ClesRgt]{Decroissant}{% + % On trie la liste + \dtlsort{Numeric=descending}{mtdb}{\dtlicompare}% + \ensuremath{\DTLforeach{mtdb}{\numeroDonnee=Numeric}{\num{\numeroDonnee}\DTLiflastrow{}{\ifboolKV[ClesRgt]{Strict}{>}{\geqslant}}}}% + }{% + % On trie la liste + \dtlsort{Numeric}{mtdb}{\dtlicompare}% + \ensuremath{\DTLforeach{mtdb}{\numeroDonnee=Numeric}{\num{\numeroDonnee}\DTLiflastrow{}{\ifboolKV[ClesRgt]{Strict}{<}{\leqslant}}}}% + }% + } +}% + +%%% % Labyrinthe -%%%%%%%%%%%%%% +%%% \setKVdefault[Labyrinthe]{Lignes=6,Colonnes=3,Longueur=4,Hauteur=2,Passages=false,EcartH=1,EcartV=1,CouleurF=gray!50,Texte=\color{black}} \newcommand\Labyrinthe[3][]{% \useKVdefault[Labyrinthe]% \setKV[Labyrinthe]{#1}% - \setsepchar[*]{,*/}%\ignoreemptyitems% + \setsepchar[*]{,*/}% \readlist*\ListeLaby{#2}% \ifboolKV[Labyrinthe]{Passages}{% \readlist*\ListeLabySol{#3}% @@ -393,21 +430,21 @@ définitions de {\ttfamily Colonnes} et {\ttfamily Lignes} !}}% } -%%%%%%%%%%%%%%% +%%% % Calculatrice -%%%%%%%%%%%%%%% +%%% %https://tex.stackexchange.com/questions/290321/mimicking-a-calculator-inputs-and-screen -\definecolor{lightorange}{rgb}{0.9,0.4,0} -\definecolor{lightestorange}{rgb}{1,0.8,0.5} -\definecolor{darkorange}{rgb}{0.2,0.1,0} - -\colorlet{blackened}{black!90!white} -\colorlet{blackish}{black!70!white} -\colorlet{greyish}{black!60!white} -\colorlet{whiteish}{white} -\colorlet{orangeish}{yellow!90!red} -\colorlet{greenish}{green!16!gray} -\colorlet{redish}{red!80!black} +\definecolor{lightorange}{rgb}{0.9,0.4,0}% +\definecolor{lightestorange}{rgb}{1,0.8,0.5}% +\definecolor{darkorange}{rgb}{0.2,0.1,0}% + +\colorlet{blackened}{black!90!white}% +\colorlet{blackish}{black!70!white}% +\colorlet{greyish}{black!60!white}% +\colorlet{whiteish}{white}% +\colorlet{orangeish}{yellow!90!red}% +\colorlet{greenish}{green!16!gray}% +\colorlet{redish}{red!80!black}% \tcbset{calbackground/.style={ enhanced, @@ -427,7 +464,7 @@ colbacklower=greenish, colframe=white, autoparskip, - }} + }}% \newtcbox{\KY}[1][]{ enhanced, @@ -444,7 +481,7 @@ fontupper=\footnotesize\sffamily, coltext=orangeish, before upper=\vrule width 0pt height 2ex depth 1ex\relax, -} +}% \newtcbox{\KYm}[1][]{ enhanced, @@ -462,7 +499,7 @@ coltext=orangeish, before upper=\vrule width 0pt height 2ex depth 1ex\relax$, after upper=$, -} +}% \newtcbox{\KN}{ enhanced, @@ -479,9 +516,7 @@ fontupper=\footnotesize\sffamily, coltext=whiteish, before upper=\vrule width 0pt height 2ex depth 1ex\relax, -} - -\parindent0pt +}% \newtcolorbox{calc}[1][]{% enhanced,bicolor, @@ -504,13 +539,13 @@ at (frame.north east) {#1};} } -\def\MPCalculatrice#1#2{ +\def\MPCalculatrice#1#2#3{ % #1 Calcul %2 réponse \ifluatex \mplibforcehmode \begin{mplibcode} input PfC-Calculatrice; - LCD(#1)(#2); + LCD(#1)(#2)(#3); \end{mplibcode} \else \begin{mpost}[mpsettings={input PfC-Calculatrice;}] @@ -519,7 +554,7 @@ \fi } -\setKVdefault[ClesCalculatrice]{Ecran=false} +\setKVdefault[ClesCalculatrice]{Ecran=false,NbLignes=0} \newcommand\Calculatrice[2][]{% \setstackgap{L}{0.775\baselineskip}% @@ -528,7 +563,7 @@ \ifboolKV[ClesCalculatrice]{Ecran}{% \setsepchar[*]{,*/}% \readlist\ListeCalc{#2}% - \MPCalculatrice{\ListeCalc[1,1]}{\ListeCalc[1,2]}% + \MPCalculatrice{\ListeCalc[1,1]}{\ListeCalc[1,2]}{\useKV[ClesCalculatrice]{NbLignes}}% }{% \setsepchar[*]{,*/}% \readlist\ListeCalc{#2}% @@ -538,34 +573,49 @@ \setstackgap{L}{\baselineskip}% }% - -%%%%%%%%%%%%%%%% -%%% Questions Flash -%%%%%%%%%%%%%%%% +%%% +% Questions Flash +%%% \tcbset{Expression/.style={colback=white,valign=center,left=0mm,right=0mm,top=1mm,bottom=1mm,colframe=white}}% \tcbset{ExpressionSerie1/.style={colback=\useKV[ClesFlash]{Couleur1},left=0mm,right=0mm,top=1mm,bottom=1mm}}% \tcbset{ExpressionSerie2/.style={colback=\useKV[ClesFlash]{Couleur2},left=0mm,right=0mm,top=1mm,bottom=1mm}}% \tcbset{ExpressionSerie3/.style={colback=\useKV[ClesFlash]{Couleur3},left=0mm,right=0mm,top=1mm,bottom=1mm}} \tcbset{ExpressionSerie4/.style={colback=\useKV[ClesFlash]{Couleur4},left=0mm,right=0mm,top=1mm,bottom=1mm}} -\tcbset{BoiteExpression/.style={enhanced,nobeforeafter,tcbox raise - base,colback=white,right=3.5mm,left=3.5mm,halign=center,colframe=black}} +\tcbset{BoiteExpression/.style={enhanced,nobeforeafter,tcbox raise base,colback=white,right=3.5mm,left=3.5mm,halign=center,colframe=black}} \newtcolorbox{CadreNombre}[1][]{% Expression,#1} -\setKVdefault[ClesFlash]{Hauteur=0.2\textheight,Simple=false,Intrus=false,Kahout=false,Daily=false,Expression=false,Mental=false,Mesure=false,Heure=false,Decimal=false,Operation=Multiplie,Numeration=false,Evaluation=false,Pause=false,Couleur1=blue!10,Couleur2=orange!10,Couleur3=green!10,Couleur4=yellow!10} +\setKVdefault[ClesFlash]{Hauteur=0.2\textheight,Simple=false,Intrus=false,Kahout=false,Daily=false,Expression=false,Mental=false,Mesure=false,Heure=false,Decimal=false,Operation=Multiplie,Numeration=false,Evaluation=false,Pause=false,Couleur1=blue!10,Couleur2=orange!10,Couleur3=green!10,Couleur4=yellow!10,Numerique=false,Seul=false} \newlength{\HauteurFlash} -\tikzset{ - arrow/.style={ - draw, - minimum height=1.25cm, - inner sep=0.25em, - shape=signal, - signal from=west, - signal to=east, - signal pointer angle=150, - } +\def\MPAfficheur#1#2#3{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + u:=0.5u; + draw Afficheur(#1 div10,0); + draw Afficheur(#1 mod10,0) shifted(u*(1,0)); + draw Afficheur(10,0) shifted(u*(2,0)); + draw Afficheur(#2 div10,0) shifted(u*(3,0)); + draw Afficheur(#2 mod10,0) shifted(u*(4,0)); + draw Afficheur(10,0) shifted(u*(5,0)); + draw Afficheur(#3 div10,0) shifted(u*(6,0)); + draw Afficheur(#3 mod10,0) shifted(u*(7,0)); + \end{mplibcode} + \else + \begin{mpost} + u:=0.5u; + draw Afficheur(#1 div10,0); + draw Afficheur(#1 mod10,0) shifted(u*(1,0)); + draw Afficheur(10,0) shifted(u*(2,0)); + draw Afficheur(#2 div10,0) shifted(u*(3,0)); + draw Afficheur(#2 mod10,0) shifted(u*(4,0)); + draw Afficheur(10,0) shifted(u*(5,0)); + draw Afficheur(#3 div10,0) shifted(u*(6,0)); + draw Afficheur(#3 mod10,0) shifted(u*(7,0)); + \end{mpost} + \fi } \def\MPHorloge#1#2#3{ @@ -683,7 +733,7 @@ \newcommand\QFHeure{% \begin{CadreNombre} - {\Large L'HEURE DU JOUR est : }\raisebox{-0.9cm}{\MPHorloge{\NbHeures}{\NbMinutes}{\NbSecondes}} + {\Large L'HEURE DU JOUR est : }\ifboolKV[ClesFlash]{Numerique}{\raisebox{-0.3cm}{\MPAfficheur{\NbHeures}{\NbMinutes}{\NbSecondes}}}{\raisebox{-0.9cm}{{\MPHorloge{\NbHeures}{\NbMinutes}{\NbSecondes}}}} \ifboolKV[ClesFlash]{Pause}{\pause}{} \begin{tcolorbox}[ExpressionSerie1] $\square$ \textbf{\ListeFlash[1,2] :} @@ -734,26 +784,37 @@ \end{CadreNombre} } +\tikzset{ + arrow/.style={ + draw, + minimum height=1.25cm, + inner sep=0.25em, + shape=signal, + signal from=west, + signal to=east, + signal pointer angle=150, + } +} + \newcommand\QFDaily{% - \begin{tikzpicture} - \begin{scope}[start chain=transition going right,node - distance=-\pgflinewidth] - \foreach \s in {1,...,\ListeFlashlen}{% - \xintifboolexpr{\s = 1}{% - \node[arrow,on chain] {\Huge\bfseries\ListeFlash[\s]}; - \ifboolKV[ClesFlash]{Pause}{\pause}{} + \begin{tikzpicture}% + \begin{scope}[start chain=transition going right,node distance=-\pgflinewidth]% + \foreach \s in {1,...,\ListeFlashlen}{% + \xintifboolexpr{\s = 1}{% + \node[arrow,on chain] {\Huge\bfseries\ListeFlash[\s]};% + \ifboolKV[ClesFlash]{Pause}{\pause}{}% + }{% + \xintifboolexpr{\s = \ListeFlashlen}{% + \node[arrow,on chain] {\Huge\bfseries?};% }{% - \xintifboolexpr{\s = \ListeFlashlen}{% - \node[arrow,on chain] {\Huge\bfseries?}; - }{% - \node[arrow,on chain] {\ListeFlash[\s]}; - \ifboolKV[ClesFlash]{Pause}{\pause}{} - } - } - } - \end{scope} - \end{tikzpicture} -} + \node[arrow,on chain] {\ListeFlash[\s]};% + \ifboolKV[ClesFlash]{Pause}{\pause}{}% + }% + }% + }% + \end{scope}% + \end{tikzpicture}% +}% \newcommand\QFDecimal{% \begin{CadreNombre} @@ -761,7 +822,7 @@ \tcbox[BoiteExpression]{\num{\ListeFlash[1,1]}} \ifboolKV[ClesFlash]{Pause}{\pause}{} \begin{tcolorbox}[ExpressionSerie1] - $\square$ \textbf{\'Ecriture en fraction décimale :} + $\square$ \textbf{\'Ecris-le en fraction décimale :} \tcbox[BoiteExpression]{$\dfrac{\phantom{1000000}}{\phantom{1000000}}$} \end{tcolorbox} \ifboolKV[ClesFlash]{Pause}{\pause}{} @@ -845,264 +906,296 @@ \end{CadreNombre} } +\newcommand\BoiteFlash[1]{% + \ifx\bla#1\bla% + \tcbox[BoiteExpression]{\phantom{10000000}}% + \else + \tcbox[BoiteExpression]{#1}% + \fi +} + +\newcommand\QFVide{% + \begin{CadreNombre} + {\ListeFlash[1]} + \xintFor* ##1 in {\xintSeq {1}{\ListeFlashlen-1}}\do{% + \ifboolKV[ClesFlash]{Pause}{\pause}{} + \begin{tcolorbox}[ExpressionSerie##1] + \ListeFlash[1+##1] + \end{tcolorbox} + } + \end{CadreNombre} +} + \newcommand\QFlash[2][]{% - \useKVdefault[ClesFlash] - \setKV[ClesFlash]{#1} - \setlength{\HauteurFlash}{\useKV[ClesFlash]{Hauteur}} - \colorlet{CouleurUn}{\useKV[ClesFlash]{Couleur1}} - \colorlet{CouleurDeux}{\useKV[ClesFlash]{Couleur2}} - \colorlet{CouleurTrois}{\useKV[ClesFlash]{Couleur3}} - \colorlet{CouleurQuatre}{\useKV[ClesFlash]{Couleur4}} + \useKVdefault[ClesFlash]% + \setKV[ClesFlash]{#1}% + \setlength{\HauteurFlash}{\useKV[ClesFlash]{Hauteur}}% + \colorlet{CouleurUn}{\useKV[ClesFlash]{Couleur1}}% + \colorlet{CouleurDeux}{\useKV[ClesFlash]{Couleur2}}% + \colorlet{CouleurTrois}{\useKV[ClesFlash]{Couleur3}}% + \colorlet{CouleurQuatre}{\useKV[ClesFlash]{Couleur4}}% \ifboolKV[ClesFlash]{Evaluation}{% - \ifboolKV[ClesFlash]{Numeration}{% - \setsepchar[*]{,*/}% + \ifboolKV[ClesFlash]{Seul}{% + \setsepchar[*]{/}% \readlist*\ListeFlash{#2}% - \QFNumeration% + \QFVide% }{% - \ifboolKV[ClesFlash]{Heure}{% + \ifboolKV[ClesFlash]{Numeration}{% \setsepchar[*]{,*/}% \readlist*\ListeFlash{#2}% - \StrMid{\ListeFlash[1,1]}{1}{2}[\NbHeures]% - \StrMid{\ListeFlash[1,1]}{3}{4}[\NbMinutes]% - \StrMid{\ListeFlash[1,1]}{5}{6}[\NbSecondes]% - \QFHeure% + \QFNumeration% }{% - \ifboolKV[ClesFlash]{Mesure}{% + \ifboolKV[ClesFlash]{Heure}{% \setsepchar[*]{,*/}% \readlist*\ListeFlash{#2}% - \QFMesure% + \StrMid{\ListeFlash[1,1]}{1}{2}[\NbHeures]% + \StrMid{\ListeFlash[1,1]}{3}{4}[\NbMinutes]% + \StrMid{\ListeFlash[1,1]}{5}{6}[\NbSecondes]% + \QFHeure% }{% - \ifboolKV[ClesFlash]{Daily}{% - \setsepchar[*]{/}% + \ifboolKV[ClesFlash]{Mesure}{% + \setsepchar[*]{,*/}% \readlist*\ListeFlash{#2}% - \QFDaily% + \QFMesure% }{% - \ifboolKV[ClesFlash]{Decimal}{% - \setsepchar[*]{,*/}% + \ifboolKV[ClesFlash]{Daily}{% + \setsepchar[*]{/}% \readlist*\ListeFlash{#2}% - \begin{frame} - \QFDecimal% - \end{frame} + \QFDaily% }{% - \ifboolKV[ClesFlash]{Mental}{% + \ifboolKV[ClesFlash]{Decimal}{% \setsepchar[*]{,*/}% \readlist*\ListeFlash{#2}% - \QFMental% + \QFDecimal% }{% - \ifboolKV[ClesFlash]{Expression}{% + \ifboolKV[ClesFlash]{Mental}{% \setsepchar[*]{,*/}% \readlist*\ListeFlash{#2}% - \QFExpression% + \QFMental% }{% - \setsepchar[*]{/}% - \readlist*\ListeFlash{#2}% - \ifboolKV[ClesFlash]{Simple}{% - \ListeFlash[1] - \begin{tcolorbox}[valign=center] - \ListeFlash[2] - \end{tcolorbox} + \ifboolKV[ClesFlash]{Expression}{% + \setsepchar[*]{,*/}% + \readlist*\ListeFlash{#2}% + \QFExpression% }{% - \setsepchar[*]{*/}% + \setsepchar[*]{/}% \readlist*\ListeFlash{#2}% - \ifboolKV[ClesFlash]{Kahout}{% - \setsepchar[*]{*/}% - \readlist*\ListeFlash{#2}% - \begin{tcolorbox}[halign=center,valign=center] - \ListeFlash[1,1] + \ifboolKV[ClesFlash]{Simple}{% + \ListeFlash[1] + \begin{tcolorbox}[valign=center] + \ListeFlash[2] \end{tcolorbox} - % \par - \begin{multicols}{4} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurUn!150,colback=CouleurUn,halign=center,valign=center] - \ListeFlash[1,2] - \end{tcolorbox} - % \hfill% - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurDeux!150,colback=CouleurDeux,halign=center,valign=center] - \ListeFlash[1,3] - \end{tcolorbox} - % \hfill% - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurTrois!150,colback=CouleurTrois,halign=center,valign=center] - \ListeFlash[1,4] - \end{tcolorbox} - % \hfill% - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurQuatre!150,colback=CouleurQuatre,halign=center,valign=center] - \ListeFlash[1,5] - \end{tcolorbox} - \end{multicols} }{% \setsepchar[*]{*/}% \readlist*\ListeFlash{#2}% - \begin{tcolorbox}[halign=center,valign=center] - \ListeFlash[1,1] - \end{tcolorbox} - \begin{multicols}{4} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurUn!150,colback=white,boxrule=1mm,halign=center,valign=center] - \ListeFlash[1,2] - \end{tcolorbox} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurDeux!150,colback=white,boxrule=1mm,halign=center,valign=center] - \ListeFlash[1,3] - \end{tcolorbox} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurTrois!150,boxrule=1mm,colback=white,halign=center,valign=center] - \ListeFlash[1,4] + \ifboolKV[ClesFlash]{Kahout}{% + \setsepchar[*]{*/}% + \readlist*\ListeFlash{#2}% + \begin{tcolorbox}[halign=center,valign=center] + \ListeFlash[1,1] \end{tcolorbox} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurQuatre!150,colback=white,boxrule=1mm,halign=center,valign=center] - \ListeFlash[1,5] + % \par + \begin{multicols}{4} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurUn!150,colback=CouleurUn,halign=center,valign=center] + \ListeFlash[1,2] + \end{tcolorbox} + % \hfill% + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurDeux!150,colback=CouleurDeux,halign=center,valign=center] + \ListeFlash[1,3] + \end{tcolorbox} + % \hfill% + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurTrois!150,colback=CouleurTrois,halign=center,valign=center] + \ListeFlash[1,4] + \end{tcolorbox} + % \hfill% + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurQuatre!150,colback=CouleurQuatre,halign=center,valign=center] + \ListeFlash[1,5] + \end{tcolorbox} + \end{multicols} + }{% + \setsepchar[*]{*/}% + \readlist*\ListeFlash{#2}% + \begin{tcolorbox}[halign=center,valign=center] + \ListeFlash[1,1] \end{tcolorbox} - \end{multicols} + \begin{multicols}{4} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurUn!150,colback=white,boxrule=1mm,halign=center,valign=center] + \ListeFlash[1,2] + \end{tcolorbox} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurDeux!150,colback=white,boxrule=1mm,halign=center,valign=center] + \ListeFlash[1,3] + \end{tcolorbox} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurTrois!150,boxrule=1mm,colback=white,halign=center,valign=center] + \ListeFlash[1,4] + \end{tcolorbox} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurQuatre!150,colback=white,boxrule=1mm,halign=center,valign=center] + \ListeFlash[1,5] + \end{tcolorbox} + \end{multicols} + }% }% }% }% }% - } + }% }% }% }% }% }{% - \ifboolKV[ClesFlash]{Numeration}{% - \setsepchar[*]{,*/}% + \ifboolKV[ClesFlash]{Seul}{% + \setsepchar[*]{/}% \readlist*\ListeFlash{#2}% \begin{frame} - \QFNumeration% + \QFVide% \end{frame} }{% - \ifboolKV[ClesFlash]{Heure}{% + \ifboolKV[ClesFlash]{Numeration}{% \setsepchar[*]{,*/}% \readlist*\ListeFlash{#2}% - \StrMid{\ListeFlash[1,1]}{1}{2}[\NbHeures]% - \StrMid{\ListeFlash[1,1]}{3}{4}[\NbMinutes]% - \StrMid{\ListeFlash[1,1]}{5}{6}[\NbSecondes]% \begin{frame} - \QFHeure% + \QFNumeration% \end{frame} }{% - \ifboolKV[ClesFlash]{Mesure}{% + \ifboolKV[ClesFlash]{Heure}{% \setsepchar[*]{,*/}% \readlist*\ListeFlash{#2}% + \StrMid{\ListeFlash[1,1]}{1}{2}[\NbHeures]% + \StrMid{\ListeFlash[1,1]}{3}{4}[\NbMinutes]% + \StrMid{\ListeFlash[1,1]}{5}{6}[\NbSecondes]% \begin{frame} - \QFMesure% + \QFHeure% \end{frame} }{% - \ifboolKV[ClesFlash]{Daily}{% - \setsepchar[*]{/}% + \ifboolKV[ClesFlash]{Mesure}{% + \setsepchar[*]{,*/}% \readlist*\ListeFlash{#2}% \begin{frame} - \QFDaily + \QFMesure% \end{frame} }{% - \ifboolKV[ClesFlash]{Decimal}{% - \setsepchar[*]{,*/}% + \ifboolKV[ClesFlash]{Daily}{% + \setsepchar[*]{/}% \readlist*\ListeFlash{#2}% \begin{frame} - \QFDecimal% + \QFDaily% \end{frame} }{% - \ifboolKV[ClesFlash]{Mental}{% + \ifboolKV[ClesFlash]{Decimal}{% \setsepchar[*]{,*/}% \readlist*\ListeFlash{#2}% \begin{frame} - \QFMental% + \QFDecimal% \end{frame} - }{ - \ifboolKV[ClesFlash]{Expression}{% + }{% + \ifboolKV[ClesFlash]{Mental}{% \setsepchar[*]{,*/}% \readlist*\ListeFlash{#2}% \begin{frame} - \QFExpression% + \QFMental% \end{frame} }{% - \setsepchar[*]{/}% - \readlist*\ListeFlash{#2}% - \ifboolKV[ClesFlash]{Simple}{% + \ifboolKV[ClesFlash]{Expression}{% + \setsepchar[*]{,*/}% + \readlist*\ListeFlash{#2}% \begin{frame} - \ListeFlash[1] - \begin{tcolorbox}[valign=center] - \ListeFlash[2] - \end{tcolorbox} + \QFExpression% \end{frame} }{% - \setsepchar[*]{,*/}% + \setsepchar[*]{/}% \readlist*\ListeFlash{#2}% - \ifboolKV[ClesFlash]{Kahout}{% - \setsepchar[*]{*/}% - \readlist*\ListeFlash{#2}% + \ifboolKV[ClesFlash]{Simple}{% \begin{frame} + \ListeFlash[1] \begin{tcolorbox}[valign=center] - \ListeFlash[1,1] + \ListeFlash[2] \end{tcolorbox} - \vfill - \ifboolKV[ClesFlash]{Pause}{\pause}{} - \begin{columns}[T] - \begin{column}{0.45\linewidth} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurUn!150,colback=CouleurUn,halign=center,valign=center] - \ListeFlash[1,2] - \end{tcolorbox} - \end{column} - \ifboolKV[ClesFlash]{Pause}{\pause}{} - \begin{column}{0.45\linewidth} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurDeux!150,colback=CouleurDeux,halign=center,valign=center] - \ListeFlash[1,3] - \end{tcolorbox} - \end{column} - \end{columns} - \bigskip - \ifboolKV[ClesFlash]{Pause}{\pause}{} - \begin{columns}[T] - \begin{column}{0.45\linewidth} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurTrois!150,colback=CouleurTrois,halign=center,valign=center] - \ListeFlash[1,4] - \end{tcolorbox} - \end{column} - \ifboolKV[ClesFlash]{Pause}{\pause}{} - \begin{column}{0.45\linewidth} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurQuatre!150,colback=CouleurQuatre,halign=center,valign=center] - \ListeFlash[1,5] - \end{tcolorbox} - \end{column} - \end{columns} \end{frame} }{% - \setsepchar[*]{*/}% + \setsepchar[*]{,*/}% \readlist*\ListeFlash{#2}% - \begin{frame} - \begin{tcolorbox}[valign=center] - \ListeFlash[1,1] - \end{tcolorbox} - \vfill - \ifboolKV[ClesFlash]{Pause}{\pause}{} - \begin{columns}[T] - \begin{column}{0.45\linewidth} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurUn!150,colback=white,boxrule=1mm,halign=center,valign=center] - \ListeFlash[1,2] - \end{tcolorbox} - \end{column} + \ifboolKV[ClesFlash]{Kahout}{% + \setsepchar[*]{*/}% + \readlist*\ListeFlash{#2}% + \begin{frame} + \begin{tcolorbox}[valign=center] + \ListeFlash[1,1] + \end{tcolorbox} + \vfill \ifboolKV[ClesFlash]{Pause}{\pause}{} - \begin{column}{0.45\linewidth} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurDeux!150,colback=white,boxrule=1mm,halign=center,valign=center] - \ListeFlash[1,3] - \end{tcolorbox} - \end{column} - \end{columns} - \bigskip - \ifboolKV[ClesFlash]{Pause}{\pause}{} - \begin{columns}[T] - \begin{column}{0.45\linewidth} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurTrois!150,boxrule=1mm,colback=white,halign=center,valign=center] - \ListeFlash[1,4] - \end{tcolorbox} - \end{column} + \begin{columns}[T] + \begin{column}{0.45\linewidth} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurUn!150,colback=CouleurUn,halign=center,valign=center] + \ListeFlash[1,2] + \end{tcolorbox} + \end{column} + \ifboolKV[ClesFlash]{Pause}{\pause}{} + \begin{column}{0.45\linewidth} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurDeux!150,colback=CouleurDeux,halign=center,valign=center] + \ListeFlash[1,3] + \end{tcolorbox} + \end{column} + \end{columns} + \bigskip \ifboolKV[ClesFlash]{Pause}{\pause}{} - \begin{column}{0.45\linewidth} - \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurQuatre!150,colback=white,boxrule=1mm,halign=center,valign=center] - \ListeFlash[1,5] - \end{tcolorbox} - \end{column} - \end{columns} - \end{frame} + \begin{columns}[T] + \begin{column}{0.45\linewidth} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurTrois!150,colback=CouleurTrois,halign=center,valign=center] + \ListeFlash[1,4] + \end{tcolorbox} + \end{column} + \ifboolKV[ClesFlash]{Pause}{\pause}{} + \begin{column}{0.45\linewidth} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurQuatre!150,colback=CouleurQuatre,halign=center,valign=center] + \ListeFlash[1,5] + \end{tcolorbox} + \end{column} + \end{columns} + \end{frame} + }{% + \setsepchar[*]{*/}% + \readlist*\ListeFlash{#2}% + \begin{frame} + \begin{tcolorbox}[valign=center] + \ListeFlash[1,1] + \end{tcolorbox} + \vfill + \ifboolKV[ClesFlash]{Pause}{\pause}{} + \begin{columns}[T] + \begin{column}{0.45\linewidth} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurUn!150,colback=white,boxrule=1mm,halign=center,valign=center] + \ListeFlash[1,2] + \end{tcolorbox} + \end{column} + \ifboolKV[ClesFlash]{Pause}{\pause}{} + \begin{column}{0.45\linewidth} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurDeux!150,colback=white,boxrule=1mm,halign=center,valign=center] + \ListeFlash[1,3] + \end{tcolorbox} + \end{column} + \end{columns} + \bigskip + \ifboolKV[ClesFlash]{Pause}{\pause}{} + \begin{columns}[T] + \begin{column}{0.45\linewidth} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurTrois!150,boxrule=1mm,colback=white,halign=center,valign=center] + \ListeFlash[1,4] + \end{tcolorbox} + \end{column} + \ifboolKV[ClesFlash]{Pause}{\pause}{} + \begin{column}{0.45\linewidth} + \begin{tcolorbox}[height=\HauteurFlash,colframe=CouleurQuatre!150,colback=white,boxrule=1mm,halign=center,valign=center] + \ListeFlash[1,5] + \end{tcolorbox} + \end{column} + \end{columns} + \end{frame} + }% }% }% }% }% - } + }% }% }% }% @@ -1110,12 +1203,209 @@ }% }% -%%%%%%%%%%%%% -%%% Fractions -%%%%%%%%%%%%% -\setKVdefault[ClesFraction]{Rayon=2cm,Disque,Regulier=false,Segment=false,Rectangle=false,Longueur=5cm,Largeur=2cm,Cotes=5,Couleur=green,Reponse=false,Multiple=1,Hachures=false,Epaisseur=1} +%%% +% Fractions +%%% +\setKVdefault[ClesFraction]{Rayon=2cm,Disque,Regulier=false,Segment=false,Rectangle=false,Longueur=5cm,Largeur=2cm,Cotes=5,Triangle=false,Parts=3,Couleur=green,Reponse=false,Multiple=1,Hachures=false,Epaisseur=1} + +\def\MPFractionTriangle#1#2#3#4#5{ + % #1 longueur du côté + % #2 partage sur le côté + % #3 num + % #4 déno (attention : = #2^2) + % #5 couleur + \ifluatex + \mplibforcehmode + \begin{mplibcode} + nbtriangle=0; + + vardef Ligne(expr longueur)= + for k=0 upto 2*(longueur-1): + nbtriangle:=nbtriangle+1; + if (k mod 2)=0: + M[nbtriangle]=(Tria shifted(0.5*k*(1/nbparts)*(B-A))) shifted((nbparts-longueur)*(1/nbparts)*(C-A)); + else: + M[nbtriangle]=(Trir shifted(0.5*(k-1)*(1/nbparts)*(B-A))) shifted((nbparts-longueur)*(1/nbparts)*(C-A)); + fi; + endfor; + enddef; + + pair A,B,C; + A=u*(0.5,0.5); + B-A=(#1,0); + C=rotation(B,A,60); + + nbparts:=#2; + + path M[]; + + path Tria,Trir; + Tria=polygone(A,(1/nbparts)[A,B],(1/nbparts)[A,C]); + Trir=symetrie(Tria,(1/nbparts)[A,B],(1/nbparts)[A,C]); + + for k=nbparts downto 1: + Ligne(k); + endfor; + + for k=1 upto #3: + fill M[k] withcolor #5; + endfor; + + for k=1 upto nbparts: + trace segment((k/nbparts)[A,B],(k/nbparts)[A,C]); + trace segment((k/nbparts)[B,A],(k/nbparts)[B,C]); + trace segment((k/nbparts)[C,A],(k/nbparts)[C,B]); + endfor; + \end{mplibcode} + \else + \begin{mpost} + nbtriangle=0; + + vardef Ligne(expr longueur)= + for k=0 upto 2*(longueur-1): + nbtriangle:=nbtriangle+1; + if (k mod 2)=0: + M[nbtriangle]=(Tria shifted(0.5*k*(1/nbparts)*(B-A))) shifted((nbparts-longueur)*(1/nbparts)*(C-A)); + else: + M[nbtriangle]=(Trir shifted(0.5*(k-1)*(1/nbparts)*(B-A))) shifted((nbparts-longueur)*(1/nbparts)*(C-A)); + fi; + endfor; + enddef; + + pair A,B,C; + A=u*(0.5,0.5); + B-A=(#1,0); + C=rotation(B,A,60); + + nbparts:=#2; + + path M[]; + + path Tria,Trir; + Tria=polygone(A,(1/nbparts)[A,B],(1/nbparts)[A,C]); + Trir=symetrie(Tria,(1/nbparts)[A,B],(1/nbparts)[A,C]); + + for k=nbparts downto 1: + Ligne(k); + endfor; + + for k=1 upto #3: + fill M[k] withcolor #5; + endfor; + + for k=1 upto nbparts: + trace segment((k/nbparts)[A,B],(k/nbparts)[A,C]); + trace segment((k/nbparts)[B,A],(k/nbparts)[B,C]); + trace segment((k/nbparts)[C,A],(k/nbparts)[C,B]); + endfor; + \end{mpost} + \fi + } + + \def\MPFractionTriangleH#1#2#3#4#5#6{ + % #1 longueur du côté + % #2 partage sur le côté + % #3 num + % #4 déno (attention : = #2^2) + % #5 couleur + % #6 épaisseur + \ifluatex + \mplibforcehmode + \begin{mplibcode} + nbtriangle=0; + + vardef Ligne(expr longueur)= + for k=0 upto 2*(longueur-1): + nbtriangle:=nbtriangle+1; + if (k mod 2)=0: + M[nbtriangle]=(Tria shifted(0.5*k*(1/nbparts)*(B-A))) shifted((nbparts-longueur)*(1/nbparts)*(C-A)); + else: + M[nbtriangle]=(Trir shifted(0.5*(k-1)*(1/nbparts)*(B-A))) shifted((nbparts-longueur)*(1/nbparts)*(C-A)); + fi; + endfor; + enddef; + + pair A,B,C; + A=u*(0.5,0.5); + B-A=(#1,0); + C=rotation(B,A,60); + + nbparts:=#2; + + path M[]; + + path Tria,Trir; + Tria=polygone(A,(1/nbparts)[A,B],(1/nbparts)[A,C]); + Trir=symetrie(Tria,(1/nbparts)[A,B],(1/nbparts)[A,C]); -\def\MPFractionRegulier#1#2#3#4#5{ + for k=nbparts downto 1: + Ligne(k); + endfor; + + diversite=floor(uniformdeviate(#2**2-#3-1)); + + for k=(1+diversite) upto (#3+diversite): + drawoptions(withpen pencircle scaled #6); + trace hachurage(M[k],90,0.2,0) withcolor #5; + endfor; + drawoptions(withpen pencircle scaled #6); + for k=1 upto nbparts: + trace segment((k/nbparts)[A,B],(k/nbparts)[A,C]); + trace segment((k/nbparts)[B,A],(k/nbparts)[B,C]); + trace segment((k/nbparts)[C,A],(k/nbparts)[C,B]); + endfor; + \end{mplibcode} + \else + \begin{mpost} + nbtriangle=0; + + vardef Ligne(expr longueur)= + for k=0 upto 2*(longueur-1): + nbtriangle:=nbtriangle+1; + if (k mod 2)=0: + M[nbtriangle]=(Tria shifted(0.5*k*(1/nbparts)*(B-A))) shifted((nbparts-longueur)*(1/nbparts)*(C-A)); + else: + M[nbtriangle]=(Trir shifted(0.5*(k-1)*(1/nbparts)*(B-A))) shifted((nbparts-longueur)*(1/nbparts)*(C-A)); + fi; + endfor; + enddef; + + pair A,B,C; + A=u*(0.5,0.5); + B-A=(#1,0); + C=rotation(B,A,60); + + nbparts:=#2; + + path M[]; + + path Tria,Trir; + Tria=polygone(A,(1/nbparts)[A,B],(1/nbparts)[A,C]); + Trir=symetrie(Tria,(1/nbparts)[A,B],(1/nbparts)[A,C]); + + for k=nbparts downto 1: + Ligne(k); + endfor; + + diversite=floor(uniformdeviate(#2**2-#3-1)); + + for k=(1+diversite) upto (#3+diversite): + drawoptions(withpen pencircle scaled #6); + trace hachurage(M[k],90,0.2,0) withcolor #5; + endfor; + drawoptions(withpen pencircle scaled #6); + + for k=1 upto nbparts: + trace segment((k/nbparts)[A,B],(k/nbparts)[A,C]); + trace segment((k/nbparts)[B,A],(k/nbparts)[B,C]); + trace segment((k/nbparts)[C,A],(k/nbparts)[C,B]); + endfor; + \end{mpost} + \fi + } + + +\def\MPFractionRegulier#1#2#3#4#5{% % #1 rayon, #2 nb côtés, #3 num, #4 deno, #5 couleur \ifluatex \mplibforcehmode @@ -1506,47 +1796,99 @@ \fi } +\def\MPFractionSegmentH#1#2#3#4#5{ + \ifluatex + \mplibforcehmode + \begin{mplibcode} + pair A,C,B[]; + A=(0,0); + C-A=(#1,0); + for k=0 upto #3: + B[k]=(k/#3)[A,C]; + endfor; + drawoptions(withpen pencircle scaled#5); + draw hachurage(polygone(B[0]+u*(0,-0.15),B[#2]+u*(0,-0.15),B[#2]+u*(0,0.15),B[0]+u*(0,0.15)),120,0.2,0) + withcolor #4; + drawoptions(withpen pencircle scaled#5); + draw segment(A,C); + marque_p:="tiretv"; + for k=0 upto #3: + pointe(B[k]); + endfor; + \end{mplibcode} + \else + \begin{mpost} + pair A,C,B[]; + A=(0,0); + C-A=(#1,0); + for k=0 upto #3: + B[k]=(k/#3)[A,C]; + endfor; + drawoptions(withpen pencircle scaled#5); + draw hachurage(polygone(B[0]+u*(0,-0.15),B[#2]+u*(0,-0.15),B[#2]+u*(0,0.15),B[0]+u*(0,0.15)),120,0.2,0) + withcolor #4; + drawoptions(withpen pencircle scaled#5); + draw segment(A,C); + marque_p:="tiretv"; + for k=0 upto #3: + pointe(B[k]); + endfor; + \end{mpost} + \fi +} + \newcommand\Fraction[2][]{% \useKVdefault[ClesFraction]% \setKV[ClesFraction]{#1}% \setsepchar[*]{/}% \readlist*\ListeFraction{#2}% - %\ListeFractionlen -- Le numérateur est \ListeFraction[1] et le - %dénominateur est \ListeFraction[2]. - \ifboolKV[ClesFraction]{Regulier}{% + \ifboolKV[ClesFraction]{Triangle}{% \ifboolKV[ClesFraction]{Reponse}{}{\setKV[ClesFraction]{Couleur=white}}% - \ifboolKV[ClesFraction]{Hachures}{% - \MPFractionRegulierH{\useKV[ClesFraction]{Rayon}}{\useKV[ClesFraction]{Cotes}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}{\useKV[ClesFraction]{Epaisseur}}% + \ifboolKV[ClesFraction]{Hachures}{% + \MPFractionTriangleH{\useKV[ClesFraction]{Longueur}}{\useKV[ClesFraction]{Parts}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}{\useKV[ClesFraction]{Epaisseur}}% }{% - \MPFractionRegulier{\useKV[ClesFraction]{Rayon}}{\useKV[ClesFraction]{Cotes}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}% + \MPFractionTriangle{\useKV[ClesFraction]{Longueur}}{\useKV[ClesFraction]{Parts}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}% } }{% - \ifboolKV[ClesFraction]{Segment}{% + \ifboolKV[ClesFraction]{Regulier}{% \ifboolKV[ClesFraction]{Reponse}{}{\setKV[ClesFraction]{Couleur=white}}% - \MPFractionSegment{\useKV[ClesFraction]{Longueur}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}% - }{ - \ifboolKV[ClesFraction]{Rectangle}{%rectangle + \ifboolKV[ClesFraction]{Hachures}{% + \MPFractionRegulierH{\useKV[ClesFraction]{Rayon}}{\useKV[ClesFraction]{Cotes}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}{\useKV[ClesFraction]{Epaisseur}}% + }{% + \MPFractionRegulier{\useKV[ClesFraction]{Rayon}}{\useKV[ClesFraction]{Cotes}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}% + } + }{% + \ifboolKV[ClesFraction]{Segment}{% \ifboolKV[ClesFraction]{Reponse}{}{\setKV[ClesFraction]{Couleur=white}}% \ifboolKV[ClesFraction]{Hachures}{% - \MPFractionRectangleH{\useKV[ClesFraction]{Longueur}}{\useKV[ClesFraction]{Largeur}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}{\useKV[ClesFraction]{Multiple}}{\useKV[ClesFraction]{Epaisseur}}% + \MPFractionSegmentH{\useKV[ClesFraction]{Longueur}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}{\useKV[ClesFraction]{Epaisseur}}% }{% - \MPFractionRectangle{\useKV[ClesFraction]{Longueur}}{\useKV[ClesFraction]{Largeur}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}{\useKV[ClesFraction]{Multiple}}% + \MPFractionSegment{\useKV[ClesFraction]{Longueur}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}% } - }{%disque - \ifboolKV[ClesFraction]{Reponse}{}{\setKV[ClesFraction]{Couleur=white}}% - \ifboolKV[ClesFraction]{Hachures}{% - \MPFractionDisqueH{\useKV[ClesFraction]{Rayon}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}{\useKV[ClesFraction]{Epaisseur}}% - }{% - \MPFractionDisque{\useKV[ClesFraction]{Rayon}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}% - }% - }% + }{ + \ifboolKV[ClesFraction]{Rectangle}{%rectangle + \ifboolKV[ClesFraction]{Reponse}{}{\setKV[ClesFraction]{Couleur=white}}% + \ifboolKV[ClesFraction]{Hachures}{% + \MPFractionRectangleH{\useKV[ClesFraction]{Longueur}}{\useKV[ClesFraction]{Largeur}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}{\useKV[ClesFraction]{Multiple}}{\useKV[ClesFraction]{Epaisseur}}% + }{% + \MPFractionRectangle{\useKV[ClesFraction]{Longueur}}{\useKV[ClesFraction]{Largeur}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}{\useKV[ClesFraction]{Multiple}}% + } + }{%disque + \ifboolKV[ClesFraction]{Reponse}{}{\setKV[ClesFraction]{Couleur=white}}% + \ifboolKV[ClesFraction]{Hachures}{% + \MPFractionDisqueH{\useKV[ClesFraction]{Rayon}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}{\useKV[ClesFraction]{Epaisseur}}% + }{% + \MPFractionDisque{\useKV[ClesFraction]{Rayon}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}% + }% + }% + }% }% }% }% -%%%%%%%%%%%%%%%% -%%% Réponses à relier -%%%%%%%%%%%%%%%% +%%% +% Réponses à relier +%%% \setKVdefault[ClesRelie]{Solution=false,LargeurG=5cm,LargeurD=2cm,Stretch=1.5,Ecart=2cm} \newcommand\Relie[2][]{% @@ -1603,63 +1945,86 @@ \setcounter{NbRelie}{0}% }% -%%%%%%%%%%%%%%%%%% -%% QCM -%%%%%%%%%%%%%%%%%% -\setKVdefault[ClesQCM]{Reponses=3,Solution=false,Stretch=1,Largeur=2cm,Couleur=gray!15,Titre=false,Nom=Réponse,Alph=false,VF=false,Depart=1,Alterne=false} +%%% +% QCM +%%% +\setKVdefault[ClesQCM]{Reponses=3,Solution=false,Stretch=1,Largeur=2cm,Couleur=gray!15,Titre=false,Nom=Réponse,NomV=Vrai,NomF=Faux,Alph=false,AlphT=false,VF=false,Depart=1,Alterne=false,Noms={A/B/C},Multiple=false} \newlength{\LargeurQCM} \newcounter{QuestionQCM} +\newcounter{TitreQCM} \newcommand\QCM[2][]{% \useKVdefault[ClesQCM]% \setKV[ClesQCM]{#1}% \setcounter{QuestionQCM}{\fpeval{\useKV[ClesQCM]{Depart}-1}}% + \setcounter{TitreQCM}{0} \setsepchar[*]{,*&}\ignoreemptyitems% \readlist*\ListeQCM{#2}% - \ifboolKV[ClesQCM]{VF}{% - \setKV[ClesQCM]{Reponses=2} + \ifboolKV[ClesQCM]{Multiple}{% \renewcommand{\arraystretch}{\useKV[ClesQCM]{Stretch}}% \setlength{\LargeurQCM}{\fpeval{(\linewidth-\useKV[ClesQCM]{Reponses}*(3*\tabcolsep+\useKV[ClesQCM]{Largeur}))}pt}% \xdef\NBcases{\fpeval{\useKV[ClesQCM]{Reponses}+1}}% + \xdef\ListeNom{\useKV[ClesQCM]{Noms}}% + \setsepchar[*]{/}% + \readlist*\ListeNomsMul{\ListeNom}% \begin{tabular}{|p{\LargeurQCM}|*{\useKV[ClesQCM]{Reponses}}{>{\centering\arraybackslash}p{\useKV[ClesQCM]{Largeur}}|}}% \cline{2-\NBcases}% - \multicolumn{1}{c|}{}&Vrai&Faux\\ - \hline% - \xintFor* ##1 in {\xintSeq {1}{\ListeQCMlen}}\do{% - \stepcounter{QuestionQCM}\ifboolKV[ClesQCM]{Alph}{\textbf{\Alph{QuestionQCM}}/}{\ifboolKV[ClesQCM]{Alterne}{\modulo{\theQuestionQCM}{2}\ifnum\remainder=0\cellcolor{gray!15}\fi}{}\textbf{\theQuestionQCM/}}~\ListeQCM[##1,1]\xintFor* ##2 in {\xintSeq {1}{\useKV[ClesQCM]{Reponses}}}\do{% - &\ifboolKV[ClesQCM]{Alterne}{\modulo{\theQuestionQCM}{2}\ifnum\remainder=0\cellcolor{gray!15}\fi}{}\ifboolKV[ClesQCM]{Solution}{\xintifboolexpr{##2=\ListeQCM[##1,2]}{$\boxtimes$}{$\square$}}{$\square$}% - }\\ - }% - \hline% - \end{tabular} - }{% - \renewcommand{\arraystretch}{\useKV[ClesQCM]{Stretch}}% - \setlength{\LargeurQCM}{\fpeval{(\linewidth-\useKV[ClesQCM]{Reponses}*(3*\tabcolsep+\useKV[ClesQCM]{Largeur}))}pt}% - \xdef\NBcases{\fpeval{\useKV[ClesQCM]{Reponses}+1}}% - \begin{tabular}{|p{\LargeurQCM}|*{\useKV[ClesQCM]{Reponses}}{>{\centering\arraybackslash}p{\useKV[ClesQCM]{Largeur}}|}}% - \ifboolKV[ClesQCM]{Titre}{\cline{2-\NBcases}% \multicolumn{1}{c|}{}\xintFor* ##2 in {\xintSeq {1}{\useKV[ClesQCM]{Reponses}}}\do{% - &\useKV[ClesQCM]{Nom} ##2}% + &\ListeNomsMul[##2]}% \\ - }{} \hline% \xintFor* ##1 in {\xintSeq {1}{\ListeQCMlen}}\do{% - \stepcounter{QuestionQCM}\ifboolKV[ClesQCM]{Alph}{\textbf{\Alph{QuestionQCM}}/}{\textbf{\theQuestionQCM/}}~\ListeQCM[##1,1]\xintFor* ##2 in {\xintSeq {1}{\useKV[ClesQCM]{Reponses}}}\do{% - &\ifboolKV[ClesQCM]{Solution}{\xdef\NumeroReponse{\fpeval{\useKV[ClesQCM]{Reponses}+2}}\xintifboolexpr{##2=\ListeQCM[##1,\NumeroReponse]}{\cellcolor{\useKV[ClesQCM]{Couleur}}}{}}{}\ListeQCM[##1,##2+1]% + \stepcounter{QuestionQCM}\ifboolKV[ClesQCM]{Alterne}{\modulo{\theQuestionQCM}{2}\ifnum\remainder=0\cellcolor{gray!15}\fi}{}\ifboolKV[ClesQCM]{Alph}{\textbf{\Alph{QuestionQCM}}/}{\textbf{\theQuestionQCM/}}~\ListeQCM[##1,1]\xintFor* ##2 in {\xintSeq {1}{\useKV[ClesQCM]{Reponses}}}\do{% + &\ifboolKV[ClesQCM]{Alterne}{\modulo{\theQuestionQCM}{2}\ifnum\remainder=0\cellcolor{gray!15}\fi}{}\ifboolKV[ClesQCM]{Solution}{\xintifboolexpr{\ListeQCM[##1,\fpeval{##2+1}]=1}{$\boxtimes$}{$\square$}}{$\square$}% }\\ }% \hline% \end{tabular}% + }{% + \ifboolKV[ClesQCM]{VF}{% + \setKV[ClesQCM]{Reponses=2} + \renewcommand{\arraystretch}{\useKV[ClesQCM]{Stretch}}% + \setlength{\LargeurQCM}{\fpeval{(\linewidth-\useKV[ClesQCM]{Reponses}*(3*\tabcolsep+\useKV[ClesQCM]{Largeur}))}pt}% + \xdef\NBcases{\fpeval{\useKV[ClesQCM]{Reponses}+1}}% + \begin{tabular}{|p{\LargeurQCM}|*{\useKV[ClesQCM]{Reponses}}{>{\centering\arraybackslash}p{\useKV[ClesQCM]{Largeur}}|}}% + \cline{2-\NBcases}% + \multicolumn{1}{c|}{}&\useKV[ClesQCM]{NomV}&\useKV[ClesQCM]{NomF}\\ + \hline% + \xintFor* ##1 in {\xintSeq {1}{\ListeQCMlen}}\do{% + \stepcounter{QuestionQCM}\ifboolKV[ClesQCM]{Alterne}{\modulo{\theQuestionQCM}{2}\ifnum\remainder=0\cellcolor{gray!15}\fi}{}\ifboolKV[ClesQCM]{Alph}{\textbf{\Alph{QuestionQCM}}/}{\textbf{\theQuestionQCM/}}~\ListeQCM[##1,1]\xintFor* ##2 in {\xintSeq {1}{\useKV[ClesQCM]{Reponses}}}\do{% + &\ifboolKV[ClesQCM]{Alterne}{\modulo{\theQuestionQCM}{2}\ifnum\remainder=0\cellcolor{gray!15}\fi}{}\ifboolKV[ClesQCM]{Solution}{\xintifboolexpr{##2=\ListeQCM[##1,2]}{$\boxtimes$}{$\square$}}{$\square$}% + }\\ + }% + \hline% + \end{tabular} + }{% + \renewcommand{\arraystretch}{\useKV[ClesQCM]{Stretch}}% + \setlength{\LargeurQCM}{\fpeval{(\linewidth-\useKV[ClesQCM]{Reponses}*(3*\tabcolsep+\useKV[ClesQCM]{Largeur}))}pt}% + \xdef\NBcases{\fpeval{\useKV[ClesQCM]{Reponses}+1}}% + \begin{tabular}{|p{\LargeurQCM}|*{\useKV[ClesQCM]{Reponses}}{>{\centering\arraybackslash}p{\useKV[ClesQCM]{Largeur}}|}}% + \ifboolKV[ClesQCM]{Titre}{\cline{2-\NBcases}% + \multicolumn{1}{c|}{}\xintFor* ##2 in {\xintSeq {1}{\useKV[ClesQCM]{Reponses}}}\do{% + &\stepcounter{TitreQCM}\useKV[ClesQCM]{Nom} \ifboolKV[ClesQCM]{AlphT}{\Alph{TitreQCM}}{##2}}% + \\ + }{} + \hline% + \xintFor* ##1 in {\xintSeq {1}{\ListeQCMlen}}\do{% + \stepcounter{QuestionQCM}\ifboolKV[ClesQCM]{Alterne}{\modulo{\theQuestionQCM}{2}\ifnum\remainder=0\cellcolor{gray!15}\fi}{}\ifboolKV[ClesQCM]{Alph}{\textbf{\Alph{QuestionQCM}}/}{\textbf{\theQuestionQCM/}}~\ListeQCM[##1,1]\xintFor* ##2 in {\xintSeq {1}{\useKV[ClesQCM]{Reponses}}}\do{% + &\ifboolKV[ClesQCM]{Alterne}{\modulo{\theQuestionQCM}{2}\ifnum\remainder=0\cellcolor{gray!15}\fi}{}\ifboolKV[ClesQCM]{Solution}{\xdef\NumeroReponse{\fpeval{\useKV[ClesQCM]{Reponses}+2}}\xintifboolexpr{##2=\ListeQCM[##1,\NumeroReponse]}{\cellcolor{\useKV[ClesQCM]{Couleur}}}{}}{}\ListeQCM[##1,##2+1]% + }\\ + }% + \hline% + \end{tabular}% + }% }% } -%%%%%%%%%%%%%%%%%%%%% -%%%% Somme des angles -%%%%%%%%%%%%%%%%%%%%% +%%% +% Somme des angles +%%% -\setKVdefault[ClesSommeAngle]{Detail=true,Figure=false,Isocele=false}% +\setKVdefault[ClesSommeAngle]{Detail=true,Isocele=false,Figure=false,FigureSeule=false,Angle=0}% -% On définit la figure à utiliser -\def\MPFigureSommeAngle#1#2#3#4#5#6{ +\def\MPFigureSommeAngle#1#2#3#4#5#6#7{ % #1 Premier sommet % #2 Deuxième sommet % #3 Troisième sommet @@ -1679,11 +2044,9 @@ O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour éventuellement moins de lassitude :) - numeric Angle; - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); + A:=A rotatedabout(O,#7); + B:=B rotatedabout(O,#7); + C:=C rotatedabout(O,#7); % On définit le centre du cercle inscrit (I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C]; (I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C]; @@ -1715,16 +2078,13 @@ draw Codelongueur(A,B,A,C,2); marque_s:=marque_s*2; label(btex $\ang{#4}$ etex,B+0.95u*unitvector(I-B)); - % label(btex $\ang{#5}$ etex,C+0.95u*unitvector(I-C)); label(btex ? etex,A+0.95u*unitvector(I-A)); else: -% if (#4=180-#5-#4) or (#5=180-#5-#4): marque_s:=marque_s/2; draw Codelongueur(A,B,A,C,2); marque_s:=marque_s*2; label(btex $\ang{#4}$ etex,A+0.95u*unitvector(I-A)); label(btex ? etex,B+0.95u*unitvector(I-B)); - % label(btex $\ang{#5}$ etex,C+0.95u*unitvector(I-C)); fi; else: label(btex $\ang{#4}$ etex,B+0.95u*unitvector(I-B)); @@ -1747,11 +2107,9 @@ O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour éventuellement moins de lassitude :) - numeric Angle; - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); + A:=A rotatedabout(O,#7); + B:=B rotatedabout(O,#7); + C:=C rotatedabout(O,#7); % On définit le centre du cercle inscrit (I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C]; (I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C]; @@ -1783,16 +2141,13 @@ draw Codelongueur(A,B,A,C,2); marque_s:=marque_s*2; label(btex $\ang{#4}$ etex,B+0.95u*unitvector(I-B)); - % label(btex $\ang{#5}$ etex,C+0.95u*unitvector(I-C)); label(btex ? etex,A+0.95u*unitvector(I-A)); else: - %if (#4=180-#5-#4) or (#5=180-#5-#4): marque_s:=marque_s/2; draw Codelongueur(A,B,A,C,2); marque_s:=marque_s*2; label(btex $\ang{#4}$ etex,A+0.95u*unitvector(I-A)); label(btex ? etex,B+0.95u*unitvector(I-B)); - % label(btex $\ang{#5}$ etex,C+0.95u*unitvector(I-C)); fi; else: label(btex $\ang{#4}$ etex,B+0.95u*unitvector(I-B)); @@ -1863,33 +2218,45 @@ \StrMid{#2}{2}{2}[\NomB]% \StrMid{#2}{3}{3}[\NomC]% % Figure ou pas ? - \ifboolKV[ClesSommeAngle]{Figure}{% - \begin{multicols}{2}% - {\em La figure est donnée à titre indicatif.}% - \ifx#3\bla\bla% - \xdef\Intermed{\fpeval{0.5*(180-#4)}}% - \[\MPFigureSommeAngle{\NomA}{\NomB}{\NomC}{#4}{\Intermed}{0}\]% - \else% - \ifx#4\bla\bla% - \[\MPFigureSommeAngle{\NomA}{\NomB}{\NomC}{#3}{#3}{0}\]% - \else% - \[\MPFigureSommeAngle{\NomA}{\NomB}{\NomC}{#3}{#4}{1}\]% - \fi% - \fi% - \par\columnbreak\par% - % on rédige + \ifboolKV[ClesSommeAngle]{FigureSeule}{% + \ifx#3\bla\bla% + \xdef\Intermed{\fpeval{0.5*(180-#4)}}% + \MPFigureSommeAngle{\NomA}{\NomB}{\NomC}{#4}{\Intermed}{0}{\useKV[ClesSommeAngle]{Angle}}% + \else% + \ifx#4\bla\bla% + \MPFigureSommeAngle{\NomA}{\NomB}{\NomC}{#3}{#3}{0}{\useKV[ClesSommeAngle]{Angle}}% + \else% + \MPFigureSommeAngle{\NomA}{\NomB}{\NomC}{#3}{#4}{1}{\useKV[ClesSommeAngle]{Angle}}% + \fi% + \fi% + }{% + \ifboolKV[ClesSommeAngle]{Figure}{% + \begin{multicols}{2}% + {\em La figure est donnée à titre indicatif.}% + \ifx#3\bla\bla% + \xdef\Intermed{\fpeval{0.5*(180-#4)}}% + \[\MPFigureSommeAngle{\NomA}{\NomB}{\NomC}{#4}{\Intermed}{0}{\useKV[ClesSommeAngle]{Angle}}\]% + \else% + \ifx#4\bla\bla% + \[\MPFigureSommeAngle{\NomA}{\NomB}{\NomC}{#3}{#3}{0}{\useKV[ClesSommeAngle]{Angle}}\]% + \else% + \[\MPFigureSommeAngle{\NomA}{\NomB}{\NomC}{#3}{#4}{1}{\useKV[ClesSommeAngle]{Angle}}\]% + \fi% + \fi% + \par\columnbreak\par% + % on rédige + \RedactionSomme[#1]{#2}{#3}{#4}% + \end{multicols}% + }{% on rédige \RedactionSomme[#1]{#2}{#3}{#4}% - \end{multicols}% - }{% on rédige - \RedactionSomme[#1]{#2}{#3}{#4}% + }% }% }% -%%%%%%%%%%%%%%%% -%% Le théorème de Pythagore -%%%%%%%%%%%%%%%% -% On définit le trousseau de clés optionnelles -\setKVdefault[ClesPythagore]{Exact=false,AvantRacine=false,Racine=false,Entier=false,Egalite=false,Precision=2,Soustraction=false,Figure=false,Angle=0,Reciproque=false,ReciColonnes=false,Faible=false,Unite=cm,EnchaineA=false,EnchaineB=false,EnchaineC=false,ValeurA=0,ValeurB=0,ValeurC=0} +%%% +% Le théorème de Pythagore +%%% +\setKVdefault[ClesPythagore]{Exact=false,AvantRacine=false,Racine=false,Entier=false,Egalite=false,Precision=2,Soustraction=false,Figure=false,FigureSeule=false,Angle=0,Reciproque=false,ReciColonnes=false,Faible=false,Unite=cm,EnchaineA=false,EnchaineB=false,EnchaineC=false,ValeurA=0,ValeurB=0,ValeurC=0} % On définit les figures à utiliser \def\MPFigurePytha#1#2#3#4#5#6{% @@ -1926,19 +2293,20 @@ decalage=3mm; if #4<#5 : if ypart(B)>ypart(O) : - label(btex \num{#4} etex rotated angle(C-B),1/2[C,B]-decalage*(unitvector(A-B))); - label(btex \num{#5} etex rotated(angle(B-A)),1/2[A,B]-decalage*(unitvector(C-B))); - else: - label(btex \num{#4} etex rotated angle(B-C),1/2[C,B]-decalage*(unitvector(A-B))); - label(btex \num{#5} etex rotated(angle(A-B)),1/2[A,B]-decalage*(unitvector(C-B))); - fi + label(btex \num{#4} etex,1/2[C,B]-decalage*(unitvector(A-B))); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); + else: + label(btex \num{#4} etex,1/2[C,B]-decalage*(unitvector(A-B))); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); + fi else: if ypart(B)>ypart(O) : - label(btex \num{#4} etex rotated angle(C-A),1/2[C,A]-decalage*(unitvector(C-A) rotated 90)); - label(btex \num{#5} etex rotated(angle(C-B)),1/2[C,B]-decalage*(unitvector(C-B))); - else: - label(btex \num{#4} etex rotated angle(A-C),1/2[A,C]+decalage*(unitvector(A-C) rotated 90)); - label(btex \num{#5} etex rotated(angle(A-B)),1/2[A,B]-decalage*(unitvector(C-B))); + label(btex \num{#4} etex,1/2[C,A]-decalage*(unitvector(C-A) rotated 90)); + label(btex \num{#5} etex,1/2[C,B]+decalage*(unitvector(B-A))); + else: + label(btex \num{#4} etex,1/2[A,C]+decalage*(unitvector(A-C) + rotated 90)); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); fi; fi; label(btex #3 etex,1.2[O,A]); @@ -1971,20 +2339,20 @@ decalage=3mm; if #4<#5 : if ypart(B)>ypart(O) : - label(LATEX("\num{"&decimal(#4)&"}") rotated - angle(C-B),1/2[C,B]-decalage*(unitvector(A-B))); - label(LATEX("\num{"&decimal(#5)&"}") rotated(angle(B-A)),1/2[A,B]-decalage*(unitvector(C-B))); - else: - label(LATEX("\num{"&decimal(#4)&"}") rotated angle(B-C),1/2[C,B]-decalage*(unitvector(A-B))); - label(LATEX("\num{"&decimal(#5)&"}") rotated(angle(A-B)),1/2[A,B]-decalage*(unitvector(C-B))); - fi + label(btex \num{#4} etex,1/2[C,B]-decalage*(unitvector(A-B))); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); + else: + label(btex \num{#4} etex,1/2[C,B]-decalage*(unitvector(A-B))); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); + fi else: if ypart(B)>ypart(O) : - label(LATEX("\num{"&decimal(#4)&"}") rotated angle(C-A),1/2[C,A]-decalage*(unitvector(C-A) rotated 90)); - label(LATEX("\num{"&decimal(#5)&"}") rotated(angle(C-B)),1/2[C,B]-decalage*(unitvector(C-B))); - else: - label(LATEX("\num{"&decimal(#4)&"}") rotated angle(A-C),1/2[A,C]+decalage*(unitvector(A-C) rotated 90)); - label(LATEX("\num{"&decimal(#5)&"}") rotated(angle(A-B)),1/2[A,B]-decalage*(unitvector(C-B))); + label(btex \num{#4} etex,1/2[C,A]-decalage*(unitvector(C-A) rotated 90)); + label(btex \num{#5} etex,1/2[C,B]+decalage*(unitvector(B-A))); + else: + label(btex \num{#4} etex,1/2[A,C]+decalage*(unitvector(A-C) + rotated 90)); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); fi; fi; label(btex #3 etex,1.2[O,A]); @@ -2018,23 +2386,18 @@ A:=A rotatedabout(O,#7); B:=B rotatedabout(O,#7); C:=C rotatedabout(O,#7); - % On définit l'angle droit - % D-B=7*unitvector(C-B); - % F-B=7*unitvector(A-B); - % E-D=F-B; draw A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; draw B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; draw C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; - % draw D--E--F; decalage=3mm; if ypart(B)>ypart(O) : - label(btex \num{#4} etex rotated angle(C-A),1/2[C,A]-decalage*(unitvector(C-A) rotated 90)); - label(btex \num{#5} etex rotated(angle(C-B)),1/2[C,B]-decalage*(unitvector(C-B))); - label(btex \num{#6} etex rotated(angle(B-A)),1/2[A,B]-decalage*(unitvector(C-B))); + label(btex \num{#4} etex,1/2[C,A]-decalage*(unitvector(C-A) rotated 90)); + label(btex \num{#5} etex,1/2[C,B]-decalage*(unitvector(C-B))); + label(btex \num{#6} etex,1/2[A,B]-decalage*(unitvector(C-B))); else: - label(btex \num{#4} etex rotated angle(A-C),1/2[A,C]+decalage*(unitvector(A-C) rotated 90)); - label(btex \num{#5} etex rotated(angle(A-B)),1/2[A,B]-decalage*(unitvector(C-B))); - label(btex \num{#6} etex rotated angle(C-B),1/2[C,B]-decalage*(unitvector(A-B))); + label(btex \num{#4} etex,1/2[A,C]+decalage*(unitvector(A-C) rotated 90)); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); + label(btex \num{#6} etex,1/2[C,B]-decalage*(unitvector(A-B))); fi; label(btex #1 etex,1.2[O,A]); label(btex #2 etex,1.2[O,B]); @@ -2055,14 +2418,9 @@ A:=A rotatedabout(O,#7); B:=B rotatedabout(O,#7); C:=C rotatedabout(O,#7); - % On définit l'angle droit - % D-B=7*unitvector(C-B); - % F-B=7*unitvector(A-B); - % E-D=F-B; draw A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; draw B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; draw C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; - % draw D--E--F; decalage=3mm; if ypart(B)>ypart(O) : label(LATEX("\num{"&decimal(#4)&"}") rotated angle(C-A),1/2[C,A]-decalage*(unitvector(C-A) rotated 90)); @@ -2098,20 +2456,54 @@ \opcopy{#4}{A2}% \opcopy{#5}{A3}% % On trace une figure ou pas ? - \ifboolKV[ClesPythagore]{Figure}{%Utilisation obligatoire de l'option --shell-escape de la compilation - \begin{multicols}{2} - {\em La figure est donnée à titre indicatif.}% - \[\MPFigureReciPytha{\NomA}{\NomB}{\NomC}{#3}{#4}{#5}{\useKV[ClesPythagore]{Angle}}\]% - \par\columnbreak\par% - % on rédige + \ifboolKV[ClesPythagore]{FigureSeule}{% + \MPFigureReciPytha{\NomA}{\NomB}{\NomC}{#3}{#4}{#5}{\useKV[ClesPythagore]{Angle}}% + }{% + \ifboolKV[ClesPythagore]{Figure}{%Utilisation obligatoire de l'option --shell-escape de la compilation + \begin{multicols}{2} + {\em La figure est donnée à titre indicatif.}% + \[\MPFigureReciPytha{\NomA}{\NomB}{\NomC}{#3}{#4}{#5}{\useKV[ClesPythagore]{Angle}}\]% + \par\columnbreak\par% + % on rédige + Dans le triangle $#2$, $[\NomA\NomC]$ est le plus grand côté.% + \ifboolKV[ClesPythagore]{ReciColonnes}{% + \[ + \begin{array}{cccc|cccc} + &&\NomA\NomC^2&&&\NomA\NomB^2&+&\NomB\NomC^2\\ + &&\opexport{A1}{\Aun}\num{\Aun}^2&&&\opexport{A2}{\Adeux}\num{\Adeux}^2&+&\opexport{A3}{\Atrois}\num{\Atrois}^2\\ + &&\opmul*{A1}{A1}{a1}&&&\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}&+&\opmul*{A3}{A3}{a3}\opexport{a3}{\Atrois}\num{\Atrois}\\ + &&\opexport{a1}{\Aun}\num{\Aun}&&&\multicolumn{3}{c}{\opadd*{a2}{a3}{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}}\\ + \end{array} + \] + }{% + \[\left. + \begin{array}{l} + \NomA\NomC^2=\opexport{A1}{\Aun}\num{\Aun}^2=\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}\\ + \\ + \NomA\NomB^2+\NomB\NomC^2=\opexport{A2}{\Adeux}\num{\Adeux}^2+\opexport{A3}{\Atrois}\num{\Atrois}^2=\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}+\opmul*{A3}{A3}{a3}\opexport{a3}{\Atrois}\num{\Atrois}=\opadd*{a2}{a3}{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}\\ + \end{array} + \right\}\opcmp{a1}{a4}\ifopeq\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2\fi\opcmp{a1}{a4}\ifopneq\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2\fi + \] + } + \ifboolKV[ClesPythagore]{Egalite}{% + \opcmp{a1}{a4}\ifopeq Comme $\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2$, alors l'égalité de Pythagore est vérifiée. Donc le triangle $#2$ est rectangle en $\NomB$.\fi% + \opcmp{a1}{a4}\ifopneq Comme $\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2$, alors l'égalité de Pythagore n'est pas vérifiée. Donc le triangle $#2$ n'est pas rectangle.\fi% + }{% + \opcmp{a1}{a4}\ifopeq Comme $\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2$, alors le triangle $#2$ est rectangle + en $\NomB$ d'après la réciproque du théorème de Pythagore.\fi% + \opcmp{a1}{a4}\ifopneq Comme $\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2$, alors le + triangle $#2$ n'est pas rectangle\ifboolKV[ClesPythagore]{Faible}{.}{ d'après la contraposée du théorème de Pythagore.}\fi% + } + \end{multicols} + }{% Dans le triangle $#2$, $[\NomA\NomC]$ est le plus grand côté.% \ifboolKV[ClesPythagore]{ReciColonnes}{% \[ \begin{array}{cccc|cccc} - \NomA\NomC^2&&&&&\NomA\NomB^2&+&\NomB\NomC^2\\ - \opexport{A1}{\Aun}\num{\Aun}^2&&&&&\opexport{A2}{\Adeux}\num{\Adeux}^2&+&\opexport{A3}{\Atrois}\num{\Atrois}^2\\ - \opmul*{A1}{A1}{a1}&&&&&\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}&+&\opmul*{A3}{A3}{a3}\opexport{a3}{\Atrois}\num{\Atrois}\\ - \opexport{a1}{\Aun}\num{\Aun}&&&&&\multicolumn{3}{c}{\opadd*{a2}{a3}{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}}\\ + &&\NomA\NomC^2&&&\NomA\NomB^2&+&\NomB\NomC^2\\ + &&\opexport{A1}{\Aun}\num{\Aun}^2&&&\opexport{A2}{\Adeux}\num{\Adeux}^2&+&\opexport{A3}{\Atrois}\num{\Atrois}^2\\ + &&\opmul*{A1}{A1}{a1}&&&\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}&+&\opmul*{A3}{A3}{a3}\opexport{a3}{\Atrois}\num{\Atrois}\\ + &&\opexport{a1}{\Aun}\num{\Aun}&&&\multicolumn{3}{c}{\opadd*{a2}{a3}{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}}\\ \end{array} \] }{% @@ -2123,7 +2515,7 @@ \end{array} \right\}\opcmp{a1}{a4}\ifopeq\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2\fi\opcmp{a1}{a4}\ifopneq\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2\fi \] - } + }% \ifboolKV[ClesPythagore]{Egalite}{% \opcmp{a1}{a4}\ifopeq Comme $\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2$, alors l'égalité de Pythagore est vérifiée. Donc le triangle $#2$ est rectangle en $\NomB$.\fi% \opcmp{a1}{a4}\ifopneq Comme $\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2$, alors l'égalité de Pythagore n'est pas vérifiée. Donc le triangle $#2$ n'est pas rectangle.\fi% @@ -2132,39 +2524,9 @@ en $\NomB$ d'après la réciproque du théorème de Pythagore.\fi% \opcmp{a1}{a4}\ifopneq Comme $\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2$, alors le triangle $#2$ n'est pas rectangle\ifboolKV[ClesPythagore]{Faible}{.}{ d'après la contraposée du théorème de Pythagore.}\fi% - } - \end{multicols} - }{% - Dans le triangle $#2$, $[\NomA\NomC]$ est le plus grand côté.% - \ifboolKV[ClesPythagore]{ReciColonnes}{% - \[ - \begin{array}{cccc|cccc} - \NomA\NomC^2&&&&&\NomA\NomB^2&+&\NomB\NomC^2\\ - \opexport{A1}{\Aun}\num{\Aun}^2&&&&&\opexport{A2}{\Adeux}\num{\Adeux}^2&+&\opexport{A3}{\Atrois}\num{\Atrois}^2\\ - \opmul*{A1}{A1}{a1}&&&&&\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}&+&\opmul*{A3}{A3}{a3}\opexport{a3}{\Atrois}\num{\Atrois}\\ - \opexport{a1}{\Aun}\num{\Aun}&&&&&\multicolumn{3}{c}{\opadd*{a2}{a3}{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}}\\ - \end{array} - \] - }{% - \[\left. - \begin{array}{l} - \NomA\NomC^2=\opexport{A1}{\Aun}\num{\Aun}^2=\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}\\ - \\ - \NomA\NomB^2+\NomB\NomC^2=\opexport{A2}{\Adeux}\num{\Adeux}^2+\opexport{A3}{\Atrois}\num{\Atrois}^2=\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}+\opmul*{A3}{A3}{a3}\opexport{a3}{\Atrois}\num{\Atrois}=\opadd*{a2}{a3}{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}\\ - \end{array} - \right\}\opcmp{a1}{a4}\ifopeq\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2\fi\opcmp{a1}{a4}\ifopneq\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2\fi - \] - } - \ifboolKV[ClesPythagore]{Egalite}{% - \opcmp{a1}{a4}\ifopeq Comme $\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2$, alors l'égalité de Pythagore est vérifiée. Donc le triangle $#2$ est rectangle en $\NomB$.\fi% - \opcmp{a1}{a4}\ifopneq Comme $\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2$, alors l'égalité de Pythagore n'est pas vérifiée. Donc le triangle $#2$ n'est pas rectangle.\fi% - }{% - \opcmp{a1}{a4}\ifopeq Comme $\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2$, alors le triangle $#2$ est rectangle - en $\NomB$ d'après la réciproque du théorème de Pythagore.\fi% - \opcmp{a1}{a4}\ifopneq Comme $\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2$, alors le - triangle $#2$ n'est pas rectangle\ifboolKV[ClesPythagore]{Faible}{.}{ d'après la contraposée du théorème de Pythagore.}\fi% - } - } + }% + }% + }% }{% % [xlop] paramètres de calcul \opcopy{#3}{A1}% @@ -2175,74 +2537,73 @@ \StrMid{#2}{2}{2}[\NomB]% \StrMid{#2}{3}{3}[\NomC]% % On trace une figure ou pas ? - \ifboolKV[ClesPythagore]{Figure}{%Utilisation obligatoire de l'option --shell-escape de la compilation - \begin{multicols}{2}% - {\em La figure est donnée à titre indicatif.}% - \[\MPFigurePytha{\NomA}{\NomB}{\NomC}{#3}{#4}{\useKV[ClesPythagore]{Angle}}\] - \par\columnbreak\par% + \ifboolKV[ClesPythagore]{FigureSeule}{% + \MPFigurePytha{\NomA}{\NomB}{\NomC}{#3}{#4}{\useKV[ClesPythagore]{Angle}} + }{% + \ifboolKV[ClesPythagore]{Figure}{%Utilisation obligatoire de l'option --shell-escape de la compilation + \begin{multicols}{2}% + {\em La figure est donnée à titre indicatif.}% + \[\MPFigurePytha{\NomA}{\NomB}{\NomC}{#3}{#4}{\useKV[ClesPythagore]{Angle}}\] + \par\columnbreak\par% + % On démarre la résolution + \ifboolKV[ClesPythagore]{Egalite}{Comme le triangle $#2$ est rectangle en $\NomB$, alors l'égalité de Pythagore est vérifiée :}{Dans le triangle $#2$ rectangle en $\NomB$, le th\'eor\`eme de Pythagore permet d'\'ecrire :% + }% + \xintifboolexpr{#3<#4 || #3=#4}{%\ifnum#3<#4% + \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2+#4^2),\useKV[ClesPythagore]{Precision})}}% + \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2+#4^2),\useKV[ClesPythagore]{Precision})}}% + \begin{align*} + \NomA\NomC^2&=\NomA\NomB^2+\NomB\NomC^2\\ + \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opcopy{\useKV[ClesPythagore]{ValeurA}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\ + \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\ + \NomA\NomC^2&=\opadd*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\ + \ifboolKV[ClesPythagore]{AvantRacine}{}{% + \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomC&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}} + \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomC&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}{\NomA\NomC&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}}%\\ + }% + \end{align*} + }{%\else% + \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2-#4^2),\useKV[ClesPythagore]{Precision})}}% + \begin{align*} + \NomA\NomC^2&=\NomA\NomB^2+\NomB\NomC^2\\ + \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}&=\NomA\NomB^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\ + \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}&=\NomA\NomB^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\ + \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}-\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\ + \NomA\NomB^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\ + \ifboolKV[ClesPythagore]{AvantRacine}{}{% + \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomB&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}} + \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomB&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}{\NomA\NomB&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}}%\\ + }% + \end{align*} + }%\fi% + \end{multicols} + }{% % On démarre la résolution \ifboolKV[ClesPythagore]{Egalite}{Comme le triangle $#2$ est rectangle en $\NomB$, alors l'égalité de Pythagore est vérifiée :}{Dans le triangle $#2$ rectangle en $\NomB$, le th\'eor\`eme de Pythagore permet d'\'ecrire :% }% \xintifboolexpr{#3<#4 || #3=#4}{%\ifnum#3<#4% - \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2+#4^2),\useKV[ClesPythagore]{Precision})}}% \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2+#4^2),\useKV[ClesPythagore]{Precision})}}% \begin{align*} \NomA\NomC^2&=\NomA\NomB^2+\NomB\NomC^2\\ \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opcopy{\useKV[ClesPythagore]{ValeurA}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\ \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\ \NomA\NomC^2&=\opadd*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\ - \ifboolKV[ClesPythagore]{AvantRacine}{}{% - \\ - \ifboolKV[ClesPythagore]{Entier}{}{\NomA\NomC&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}\\} - \ifboolKV[ClesPythagore]{Racine}{}{\ifboolKV[ClesPythagore]{Exact}{\NomA\NomC&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}{\NomA\NomC&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}}%\\ + \ifboolKV[ClesPythagore]{AvantRacine}{}{% + \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomC&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}} + \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomC&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}{\NomA\NomC&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}}%\\ } \end{align*} - }{%\else% + }{%\else \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2-#4^2),\useKV[ClesPythagore]{Precision})}}% - \begin{align*} - \NomA\NomC^2&=\NomA\NomB^2+\NomB\NomC^2\\ - \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}&=\NomA\NomB^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\ - \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}&=\NomA\NomB^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\ - \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}-\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\ - \NomA\NomB^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\ - \ifboolKV[ClesPythagore]{AvantRacine}{}{% - \\ - \ifboolKV[ClesPythagore]{Entier}{}{\NomA\NomB&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}\\} - \ifboolKV[ClesPythagore]{Racine}{}{\ifboolKV[ClesPythagore]{Exact}{\NomA\NomB&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}{\NomA\NomB&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}}%\\ - } - \end{align*} - }%\fi% - \end{multicols} - }{% - % On démarre la résolution - \ifboolKV[ClesPythagore]{Egalite}{Comme le triangle $#2$ est rectangle en $\NomB$, alors l'égalité de Pythagore est vérifiée :}{Dans le triangle $#2$ rectangle en $\NomB$, le th\'eor\`eme de Pythagore permet d'\'ecrire :% - }% - \xintifboolexpr{#3<#4 || #3=#4}{%\ifnum#3<#4% - \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2+#4^2),\useKV[ClesPythagore]{Precision})}}% - \begin{align*} - \NomA\NomC^2&=\NomA\NomB^2+\NomB\NomC^2\\ - \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opcopy{\useKV[ClesPythagore]{ValeurA}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\ - \NomA\NomC^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\ - \NomA\NomC^2&=\opadd*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\ - \ifboolKV[ClesPythagore]{AvantRacine}{}{% - \\ - \ifboolKV[ClesPythagore]{Entier}{}{\NomA\NomC&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}\\} - \ifboolKV[ClesPythagore]{Racine}{}{\ifboolKV[ClesPythagore]{Exact}{\NomA\NomC&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}{\NomA\NomC&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}}%\\ - } - \end{align*} - }{%\else - \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2-#4^2),\useKV[ClesPythagore]{Precision})}}% - \ifboolKV[ClesPythagore]{Soustraction}{% - \begin{align*} + \ifboolKV[ClesPythagore]{Soustraction}{% + \begin{align*} \NomA\NomB^2&=\NomA\NomC^2-\NomB\NomC^2\\ \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opexport{A1}{\Aun}\num{\Aun}^2}-\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}{\opexport{A2}{\Adeux}\num{\Adeux}^2}\\ \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}-\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\ - \NomA\NomB^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\ - \ifboolKV[ClesPythagore]{AvantRacine}{}{% - \\ - \ifboolKV[ClesPythagore]{Entier}{}{\NomA\NomB&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}\\} - \ifboolKV[ClesPythagore]{Racine}{}{\ifboolKV[ClesPythagore]{Exact}{\NomA\NomB&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}{\NomA\NomB&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}}%\\ - } + \NomA\NomB^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\ + \ifboolKV[ClesPythagore]{AvantRacine}{}{% + \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomB&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}} + \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomB&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}{\NomA\NomB&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}}%\\ + } \end{align*} }{% \begin{align*} @@ -2252,20 +2613,20 @@ \NomA\NomB^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}}-\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\num{\Adeux}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}}\\ \NomA\NomB^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\ \ifboolKV[ClesPythagore]{AvantRacine}{}{% - \\ - \ifboolKV[ClesPythagore]{Entier}{}{\NomA\NomB&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}\\} - \ifboolKV[ClesPythagore]{Racine}{}{\ifboolKV[ClesPythagore]{Exact}{\NomA\NomB&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}{\NomA\NomB&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}}%\\ + \ifboolKV[ClesPythagore]{Entier}{}{\\\NomA\NomB&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}}% + \ifboolKV[ClesPythagore]{Racine}{}{\\\ifboolKV[ClesPythagore]{Exact}{\NomA\NomB&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}{\NomA\NomB&\approx\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}~\text{\useKV[ClesPythagore]{Unite}}}}%\\ } \end{align*} }% - }%\fi% + }%\fi% + }% }% }% }% -%%%%%%%%%%%%%%%%% -%% Distributivité -%%%%%%%%%%%%%%%%% +%%% +% Distributivité +%%% % https://tex.stackexchange.com/questions/168972/draw-arrows-to-show-multiplication-pattern-distributive-property/169278?noredirect=1 \newcommand{\Tikzmark}[1]{% \tikz[remember picture,baseline,inner sep=0pt]{% @@ -2303,8 +2664,7 @@ % y a dans un "seul calcul". \setcounter{NbCalculDistri}{0} -\setKVdefault[ClesDistributivite]{Etape=1,Lettre=x,Fleches=false,AideMul=false,Reduction=false,AideAdda=false,AideAddb=false,CouleurAide=red,CouleurReduction=black,CouleurFH=blue,CouleurFB=red,Somme=false,Difference=false,RAZ=false,Oppose=false,All=false,NomExpression=A,Fin=4,Numerique=false,Remarquable=false,Echange=0}%,AideAdd=false - %inutile ? +\setKVdefault[ClesDistributivite]{Etape=1,Lettre=x,Fleches=false,AideMul=false,Reduction=false,AideAdda=false,AideAddb=false,CouleurAide=red,CouleurReduction=black,CouleurFH=blue,CouleurFB=red,Somme=false,Difference=false,RAZ=false,Oppose=false,All=false,NomExpression=A,Fin=4,Numerique=false,Remarquable=false,Echange=0}%,AideAdd=false:inutile ? \newcommand\Affichage[4][]{% \setKV[ClesDistributivite]{#1}%On lit les arguments optionnels @@ -2332,9 +2692,7 @@ \useKVdefault[ClesDistributivite]%obligatoire car la macro n'est pas dans un groupe. \setKV[ClesDistributivite]{#1}%On lit les arguments optionnels \ifboolKV[ClesDistributivite]{RAZ}{\xdef\SommeA{0}\xdef\SommeB{0}\xdef\SommeC{0}% - % 80 \setcounter{NbCalculDistri}{0}% - % fin 80 }{}% \colorlet{DCAide}{\useKV[ClesDistributivite]{CouleurAide}}% \colorlet{DCReduction}{\useKV[ClesDistributivite]{CouleurReduction}}% @@ -2343,193 +2701,183 @@ \xintifboolexpr{\useKV[ClesDistributivite]{Echange}>0}{% \DistriEchange[#1]{#2}{#3}{#4}{#5}% }{% - \ifboolKV[ClesDistributivite]{Remarquable}{% - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=1}{% - \ifx\bla#4\bla(\Affichage{0}{#2}{#3})^2\else(\Affichage{0}{#2}{#3})(\Affichage{0}{#4}{#5})\fi% - }{} - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=2}{\ifx\bla#4\bla\xintifboolexpr{#3>0}{\xintifboolexpr{#2=1}{}{(\num{#2}}\useKV[ClesDistributivite]{Lettre}\xintifboolexpr{#2=1}{}{)}^2+2\times\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesDistributivite]{Lettre}\times\num{#3}+\num{#3}^2}{\xintifboolexpr{#2=1}{}{(\num{#2}}\useKV[ClesDistributivite]{Lettre}\xintifboolexpr{#2=1}{}{)}^2-2\times\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesDistributivite]{Lettre}\times\num{\fpeval{0-#3}}+\num{\fpeval{0-#3}}^2}\else\xintifboolexpr{#2=1}{}{(\num{#2}}\useKV[ClesDistributivite]{Lettre}\xintifboolexpr{#2=1}{}{)}^2-\num{#3}^2\fi}{} - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=3}{% - %80 - \xintifboolexpr{\theNbCalculDistri>1}{\setcounter{NbCalculDistri}{0}}{}% - \stepcounter{NbCalculDistri}% - % fin 80 - \ifx\bla#4\bla% - \xdef\Multi{\fpeval{#2*#2}}% - \xdef\Multij{\fpeval{#2*#3}}% - \xdef\Multik{\fpeval{#3*#2}}% - \xdef\Multil{\fpeval{#3*#3}}% - %% ils sont redéfinis pour pouvoir envisager la somme de deux - %% expressions à développer - \xdef\Multim{\fpeval{#2*#3+#3*#2}}% - \ifboolKV[ClesDistributivite]{Oppose}{% - \xdef\Multi{\fpeval{-\Multi}}% - \xdef\Multim{\fpeval{-\Multim}}% - \xdef\Multil{\fpeval{-\Multil}}% - \xintifboolexpr{\Multi=0}{}{\xintifboolexpr{\Multi<0}{(}{}\Affichage{\Multi}{0}{0}\xintifboolexpr{\Multi<0}{)}{}}% - \xintifboolexpr{\Multim=0}{}{\xintifboolexpr{\Multim>0}{+}{+(}\Affichage{0}{\Multim}{0}\xintifboolexpr{\Multim<0}{)}{}}% - \xintifboolexpr{\Multil=0}{}{\xintifboolexpr{\Multil>0}{+}{+(}\Affichage{0}{0}{\Multil}\xintifboolexpr{\Multil<0}{)}{}}% - }{% - \Affichage{\Multi}{\Multim}{\Multil}% - } - \ifboolKV[ClesDistributivite]{Somme}{\xdef\SommeA{\fpeval{\SommeA+#2*#2}}\xdef\SommeB{\fpeval{\SommeB+#2*#3+#3*#2}}\xdef\SommeC{\fpeval{\SommeC+#3*#3}}}{}% - \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-#2*#2}}\xdef\SommeB{\fpeval{\SommeB-#2*#3-#3*#2}}\xdef\SommeC{\fpeval{\SommeC-#3*#3}}}{}% - \else% - \xdef\Multi{\fpeval{#2*#4}}% - \xdef\Multij{\fpeval{#2*#5}}% - \xdef\Multik{\fpeval{#3*#4}}% - \xdef\Multil{\fpeval{#3*#5}}% - %% ils sont redéfinis pour pouvoir envisager la somme de deux - %% expressions à développer - \xdef\Multim{\fpeval{#2*#5+#3*#4}}% - \ifboolKV[ClesDistributivite]{Oppose}{% - \xdef\Multi{\fpeval{-\Multi}}% - \xdef\Multim{\fpeval{-\Multim}}% - \xdef\Multil{\fpeval{-\Multil}}% - \xintifboolexpr{\Multi=0}{}{\xintifboolexpr{\Multi<0}{(}{}\Affichage{\Multi}{0}{0}\xintifboolexpr{\Multi<0}{)}{}}% - \xintifboolexpr{\Multim=0}{}{\xintifboolexpr{\Multim>0}{+}{+(}\Affichage{0}{\Multim}{0}\xintifboolexpr{\Multim<0}{)}{}}% - \xintifboolexpr{\Multil=0}{}{\xintifboolexpr{\Multil>0}{+}{+(}\Affichage{0}{0}{\Multil}\xintifboolexpr{\Multil<0}{)}{}}% - }{% - \Affichage{\Multi}{\Multim}{\Multil}% - } - \ifboolKV[ClesDistributivite]{Somme}{\xdef\SommeA{\fpeval{\SommeA+#2*#4}}\xdef\SommeB{\fpeval{\SommeB+#2*#5+#3*#4}}\xdef\SommeC{\fpeval{\SommeC+#3*#5}}}{}% - \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-#2*#4}}\xdef\SommeB{\fpeval{\SommeB-#2*#5-#3*#4}}\xdef\SommeC{\fpeval{\SommeC-#3*#5}}}{}% - \fi% - }{}% - }{% - \ifboolKV[ClesDistributivite]{Numerique}{% - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=0}{% - \num{\fpeval{#2+#3}}\times\num{\fpeval{#4+#5}}\multido{\i=2+1}{4}{=\Distri[Numerique,Etape=\i]{#2}{#3}{#4}{#5}}% - }{% - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=-1}{% - \Distri[Numerique,Etape=3]{#2}{#3}{#4}{#5}\multido{\i=2+-1}{2}{=\Distri[Numerique,Etape=\i]{#2}{#3}{#4}{#5}}=\num{\fpeval{(#2+#3)*(#4+#5)}}% + \ifboolKV[ClesDistributivite]{Remarquable}{% + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=1}{% + \ifx\bla#4\bla(\Affichage{0}{#2}{#3})^2\else(\Affichage{0}{#2}{#3})(\Affichage{0}{#4}{#5})\fi% + }{} + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=2}{\ifx\bla#4\bla\xintifboolexpr{#3>0}{\xintifboolexpr{#2=1}{}{(\num{#2}}\useKV[ClesDistributivite]{Lettre}\xintifboolexpr{#2=1}{}{)}^2+2\times\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesDistributivite]{Lettre}\times\num{#3}+\num{#3}^2}{\xintifboolexpr{#2=1}{}{(\num{#2}}\useKV[ClesDistributivite]{Lettre}\xintifboolexpr{#2=1}{}{)}^2-2\times\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesDistributivite]{Lettre}\times\num{\fpeval{0-#3}}+\num{\fpeval{0-#3}}^2}\else\xintifboolexpr{#2=1}{}{(\num{#2}}\useKV[ClesDistributivite]{Lettre}\xintifboolexpr{#2=1}{}{)}^2-\num{#3}^2\fi}{} + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=3}{% + \xintifboolexpr{\theNbCalculDistri>1}{\setcounter{NbCalculDistri}{0}}{}% + \stepcounter{NbCalculDistri}% + \ifx\bla#4\bla% + \xdef\Multi{\fpeval{#2*#2}}% + \xdef\Multij{\fpeval{#2*#3}}% + \xdef\Multik{\fpeval{#3*#2}}% + \xdef\Multil{\fpeval{#3*#3}}% + %% ils sont redéfinis pour pouvoir envisager la somme de deux + %% expressions à développer + \xdef\Multim{\fpeval{#2*#3+#3*#2}}% + \ifboolKV[ClesDistributivite]{Oppose}{% + \xdef\Multi{\fpeval{-\Multi}}% + \xdef\Multim{\fpeval{-\Multim}}% + \xdef\Multil{\fpeval{-\Multil}}% + \xintifboolexpr{\Multi=0}{}{\xintifboolexpr{\Multi<0}{(}{}\Affichage{\Multi}{0}{0}\xintifboolexpr{\Multi<0}{)}{}}% + \xintifboolexpr{\Multim=0}{}{\xintifboolexpr{\Multim>0}{+}{+(}\Affichage{0}{\Multim}{0}\xintifboolexpr{\Multim<0}{)}{}}% + \xintifboolexpr{\Multil=0}{}{\xintifboolexpr{\Multil>0}{+}{+(}\Affichage{0}{0}{\Multil}\xintifboolexpr{\Multil<0}{)}{}}% }{% - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=1}{\num{\fpeval{#2+#3}}\times\num{\fpeval{#4+#5}}}{}% - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=2}{\num{\fpeval{#2+#3}}\times(\num{#4}\xintifboolexpr{#5>0}{+}{-}\num{\fpeval{abs(#5)}})}{}% - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=3}{\num{#3}\times\num{#4}\xintifboolexpr{#5>0}{+}{-}\num{#3}\times\num{\fpeval{abs(#5)}}}{}% - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=4}{\num{\fpeval{#3*#4}}\xintifboolexpr{#5>0}{+}{-}\num{\fpeval{abs(#3*#5)}}}{}% - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=5}{\num{\fpeval{#3*#4+#3*#5}}}{}% - }% - }% + \Affichage{\Multi}{\Multim}{\Multil}% + } + \ifboolKV[ClesDistributivite]{Somme}{\xdef\SommeA{\fpeval{\SommeA+#2*#2}}\xdef\SommeB{\fpeval{\SommeB+#2*#3+#3*#2}}\xdef\SommeC{\fpeval{\SommeC+#3*#3}}}{}% + \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-#2*#2}}\xdef\SommeB{\fpeval{\SommeB-#2*#3-#3*#2}}\xdef\SommeC{\fpeval{\SommeC-#3*#3}}}{}% + \else% + \xdef\Multi{\fpeval{#2*#4}}% + \xdef\Multij{\fpeval{#2*#5}}% + \xdef\Multik{\fpeval{#3*#4}}% + \xdef\Multil{\fpeval{#3*#5}}% + %% ils sont redéfinis pour pouvoir envisager la somme de deux + %% expressions à développer + \xdef\Multim{\fpeval{#2*#5+#3*#4}}% + \ifboolKV[ClesDistributivite]{Oppose}{% + \xdef\Multi{\fpeval{-\Multi}}% + \xdef\Multim{\fpeval{-\Multim}}% + \xdef\Multil{\fpeval{-\Multil}}% + \xintifboolexpr{\Multi=0}{}{\xintifboolexpr{\Multi<0}{(}{}\Affichage{\Multi}{0}{0}\xintifboolexpr{\Multi<0}{)}{}}% + \xintifboolexpr{\Multim=0}{}{\xintifboolexpr{\Multim>0}{+}{+(}\Affichage{0}{\Multim}{0}\xintifboolexpr{\Multim<0}{)}{}}% + \xintifboolexpr{\Multil=0}{}{\xintifboolexpr{\Multil>0}{+}{+(}\Affichage{0}{0}{\Multil}\xintifboolexpr{\Multil<0}{)}{}}% + }{% + \Affichage{\Multi}{\Multim}{\Multil}% + } + \ifboolKV[ClesDistributivite]{Somme}{\xdef\SommeA{\fpeval{\SommeA+#2*#4}}\xdef\SommeB{\fpeval{\SommeB+#2*#5+#3*#4}}\xdef\SommeC{\fpeval{\SommeC+#3*#5}}}{}% + \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-#2*#4}}\xdef\SommeB{\fpeval{\SommeB-#2*#5-#3*#4}}\xdef\SommeC{\fpeval{\SommeC-#3*#5}}}{}% + \fi% + }{}% }{% - \ifboolKV[ClesDistributivite]{All}{% - \xdef\NomLettre{\useKV[ClesDistributivite]{NomExpression}}% - \xdef\NomFin{\useKV[ClesDistributivite]{Fin}}% - \xintFor* ##1 in {\xintSeq {1}{\useKV[ClesDistributivite]{Fin}-1}}\do - {\NomLettre&=\Distri[Etape=##1]{#2}{#3}{#4}{#5}\\}% - \NomLettre&=\Distri[Etape=\NomFin]{#2}{#3}{#4}{#5}% + \ifboolKV[ClesDistributivite]{Numerique}{% + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=0}{% + \num{\fpeval{#2+#3}}\times\num{\fpeval{#4+#5}}\multido{\i=2+1}{4}{=\Distri[Numerique,Etape=\i]{#2}{#3}{#4}{#5}}% + }{% + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=-1}{% + \Distri[Numerique,Etape=3]{#2}{#3}{#4}{#5}\multido{\i=2+-1}{2}{=\Distri[Numerique,Etape=\i]{#2}{#3}{#4}{#5}}=\num{\fpeval{(#2+#3)*(#4+#5)}}% + }{% + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=1}{\num{\fpeval{#2+#3}}\times\num{\fpeval{#4+#5}}}{}% + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=2}{\num{\fpeval{#2+#3}}\times(\num{#4}\xintifboolexpr{#5>0}{+}{-}\num{\fpeval{abs(#5)}})}{}% + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=3}{\num{#3}\times\num{#4}\xintifboolexpr{#5>0}{+}{-}\num{#3}\times\num{\fpeval{abs(#5)}}}{}% + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=4}{\num{\fpeval{#3*#4}}\xintifboolexpr{#5>0}{+}{-}\num{\fpeval{abs(#3*#5)}}}{}% + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=5}{\num{\fpeval{#3*#4+#3*#5}}}{}% + }% + }% }{% - % Etape 1 - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=1}{% - \xintifboolexpr{#2=0}{% - }{\xintifboolexpr{#3=0}{}{(}}\Tikzmark{\Affichage[#1]{0}{#2}{0}}% - \ifboolKV[ClesDistributivite]{AideAdda}{\mathcolor{DCAide}{+(}}{}% - \xintifboolexpr{#3>0}{\xintifboolexpr{#2=0}{}{+}}{\xintifboolexpr{#3<0}{-}{}}\Tikzmark{\Affichage[#1]{0}{0}{\fpeval{abs(#3)}}}% - \ifboolKV[ClesDistributivite]{AideAdda}{\mathcolor{DCAide}{)}}{}% - \xintifboolexpr{#2=0}{}{\xintifboolexpr{#3=0}{}{)}}% - % - \ifboolKV[ClesDistributivite]{AideMul}{\times}{}%on aide dans le cas double - \xdef\Multi{\fpeval{#4*#5}}%affichage auto si (a+b)xk - % - \xintifboolexpr{\Multi=0}{\times% - \xintifboolexpr{#4<0}{(}{\xintifboolexpr{#5<0}{(}{}}}{(}% - \Tikzmark{\Affichage[#1]{0}{#4}{0}}% - \ifboolKV[ClesDistributivite]{AideAddb}{\mathcolor{DCAide}{+(}}{}% - \xintifboolexpr{#5>0}{\xintifboolexpr{#4=0}{}{+}}{\xintifboolexpr{#5<0}{\xintifboolexpr{#4=0}{{-}}{-}}{}}\Tikzmark{\Affichage[#1]{0}{0}{\fpeval{abs(#5)}}}% - \ifboolKV[ClesDistributivite]{AideAddb}{\mathcolor{DCAide}{)}}{}% - \xintifboolexpr{\Multi=0}{% - \xintifboolexpr{#4<0}{)}{\xintifboolexpr{#5<0}{)}{}}}{)}% - \ifboolKV[ClesDistributivite]{Fleches}{% - \xdef\Multi{\fpeval{#2*#3*#4*#5}}% + \ifboolKV[ClesDistributivite]{All}{% + \xdef\NomLettre{\useKV[ClesDistributivite]{NomExpression}}% + \xdef\NomFin{\useKV[ClesDistributivite]{Fin}}% + \xintFor* ##1 in {\xintSeq {1}{\useKV[ClesDistributivite]{Fin}-1}}\do + {\NomLettre&=\Distri[Etape=##1]{#2}{#3}{#4}{#5}\\}% + \NomLettre&=\Distri[Etape=\NomFin]{#2}{#3}{#4}{#5}% + }{% + % Etape 1 + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=1}{% + \xintifboolexpr{#2=0}{% + }{\xintifboolexpr{#3=0}{}{(}}\Tikzmark{\Affichage[#1]{0}{#2}{0}}% + \ifboolKV[ClesDistributivite]{AideAdda}{\mathcolor{DCAide}{+(}}{}% + \xintifboolexpr{#3>0}{\xintifboolexpr{#2=0}{}{+}}{\xintifboolexpr{#3<0}{-}{}}\Tikzmark{\Affichage[#1]{0}{0}{\fpeval{abs(#3)}}}% + \ifboolKV[ClesDistributivite]{AideAdda}{\mathcolor{DCAide}{)}}{}% + \xintifboolexpr{#2=0}{}{\xintifboolexpr{#3=0}{}{)}}% + % + \ifboolKV[ClesDistributivite]{AideMul}{\times}{}%on aide dans le cas double + \xdef\Multi{\fpeval{#4*#5}}%affichage auto si (a+b)xk + % + \xintifboolexpr{\Multi=0}{\times% + \xintifboolexpr{#4<0}{(}{\xintifboolexpr{#5<0}{(}{}}}{(}% + \Tikzmark{\Affichage[#1]{0}{#4}{0}}% + \ifboolKV[ClesDistributivite]{AideAddb}{\mathcolor{DCAide}{+(}}{}% + \xintifboolexpr{#5>0}{\xintifboolexpr{#4=0}{}{+}}{\xintifboolexpr{#5<0}{\xintifboolexpr{#4=0}{{-}}{-}}{}}\Tikzmark{\Affichage[#1]{0}{0}{\fpeval{abs(#5)}}}% + \ifboolKV[ClesDistributivite]{AideAddb}{\mathcolor{DCAide}{)}}{}% \xintifboolexpr{\Multi=0}{% - \xdef\Multij{\fpeval{#2*#3}}%\relax - \xintifboolexpr{\Multij=0}{\xintifboolexpr{#2=0}{\DrawArrowSimple{1}}{\DrawArrowSimple{0}}}{\xintifboolexpr{#4=0}{\DrawArrowSimpleRenverse{3}}{\DrawArrowSimpleRenverse{2}}}% - }{% - \DrawArrow% + \xintifboolexpr{#4<0}{)}{\xintifboolexpr{#5<0}{)}{}}}{)}% + \ifboolKV[ClesDistributivite]{Fleches}{% + \xdef\Multi{\fpeval{#2*#3*#4*#5}}% + \xintifboolexpr{\Multi=0}{% + \xdef\Multij{\fpeval{#2*#3}}%\relax + \xintifboolexpr{\Multij=0}{\xintifboolexpr{#2=0}{\DrawArrowSimple{1}}{\DrawArrowSimple{0}}}{\xintifboolexpr{#4=0}{\DrawArrowSimpleRenverse{3}}{\DrawArrowSimpleRenverse{2}}}% + }{% + \DrawArrow% + }% + }{}\setcounter{NbDistri}{0}% + }{} + % Etape 2 + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=2}{% + \xdef\Multi{\fpeval{#2*#4}}% + \xintifboolexpr{\Multi=0}{}{% + \xintifboolexpr{#2<0}{(}{}\Affichage[#1]{0}{#2}{0}\xintifboolexpr{#2<0}{)}{}\times\xintifboolexpr{#4<0}{(}{}\Affichage[#1]{0}{#4}{0}\xintifboolexpr{#4<0}{)}{}% + } + \xdef\Multij{\fpeval{#2*#5}}% + \xintifboolexpr{\Multij=0}{}{% + \xintifboolexpr{\Multi=0}{}{+}% + \xintifboolexpr{#2<0}{(}{}\Affichage[#1]{0}{#2}{0}\xintifboolexpr{#2<0}{)}{}\times\xintifboolexpr{#5<0}{(}{}\Affichage[#1]{0}{0}{#5}\xintifboolexpr{#5<0}{)}{}% }% - }{}\setcounter{NbDistri}{0}% - }{} - % Etape 2 - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=2}{% - \xdef\Multi{\fpeval{#2*#4}}% - \xintifboolexpr{\Multi=0}{}{% - \xintifboolexpr{#2<0}{(}{}\Affichage[#1]{0}{#2}{0}\xintifboolexpr{#2<0}{)}{}\times\xintifboolexpr{#4<0}{(}{}\Affichage[#1]{0}{#4}{0}\xintifboolexpr{#4<0}{)}{}% - } - \xdef\Multij{\fpeval{#2*#5}}% - \xintifboolexpr{\Multij=0}{}{% - \xintifboolexpr{\Multi=0}{}{+}% - \xintifboolexpr{#2<0}{(}{}\Affichage[#1]{0}{#2}{0}\xintifboolexpr{#2<0}{)}{}\times\xintifboolexpr{#5<0}{(}{}\Affichage[#1]{0}{0}{#5}\xintifboolexpr{#5<0}{)}{}% - }% - \xdef\Multik{\fpeval{#3*#4}}% - \xintifboolexpr{\Multik=0}{}{% - \xintifboolexpr{\Multi=0}{}{+}% - \xintifboolexpr{#3<0}{(}{}\Affichage[#1]{0}{0}{#3}\xintifboolexpr{#3<0}{)}{}\times\xintifboolexpr{#4<0}{(}{}\Affichage[#1]{0}{#4}{0}\xintifboolexpr{#4<0}{)}{}% - }% - \xdef\Multil{\fpeval{#3*#5}}% - \xintifboolexpr{\Multil=0}{}{+% - \xintifboolexpr{#3<0}{(}{}\Affichage[#1]{0}{0}{#3}\xintifboolexpr{#3<0}{)}{}\times\xintifboolexpr{#5<0}{(}{}\Affichage[#1]{0}{0}{#5}\xintifboolexpr{#5<0}{)}{}% - }% - }{}% - % Etape 3 - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=3}{% - %80 - \stepcounter{NbCalculDistri}% - % fin 80 - \xdef\Multi{\fpeval{#2*#4}}% - \xdef\Multij{\fpeval{#2*#5}}% - \xdef\Multik{\fpeval{#3*#4}}% - \xdef\Multil{\fpeval{#3*#5}}% - %% ils sont redéfinis pour pouvoir envisager la somme de deux - %% expressions à développer - %80 - \xintifboolexpr{\theNbCalculDistri>1}{\xintifboolexpr{\Multi<0}{(\Affichage{\Multi}{0}{0})}{\Affichage{\Multi}{0}{0}}}{\Affichage{\Multi}{0}{0}}% - %fin 80 - \ifboolKV[ClesDistributivite]{Reduction}{\mathunderline{DCReduction}{% - \xintifboolexpr{\Multij=0}{}{\xintifboolexpr{\Multi=0}{}{{}+}\xintifboolexpr{\Multij<0}{(}{}\Affichage{0}{\Multij}{0}\xintifboolexpr{\Multij<0}{)}{}}% - \xintifboolexpr{\Multik=0}{}{\xintifboolexpr{\Multil=0}{\xintifboolexpr{#2=0}{}{+}}{+}\xintifboolexpr{\Multik<0}{(}{}\Affichage{0}{\Multik}{0}\xintifboolexpr{\Multik<0}{)}{}}% + \xdef\Multik{\fpeval{#3*#4}}% + \xintifboolexpr{\Multik=0}{}{% + \xintifboolexpr{\Multi=0}{}{+}% + \xintifboolexpr{#3<0}{(}{}\Affichage[#1]{0}{0}{#3}\xintifboolexpr{#3<0}{)}{}\times\xintifboolexpr{#4<0}{(}{}\Affichage[#1]{0}{#4}{0}\xintifboolexpr{#4<0}{)}{}% }% - }{% - \xintifboolexpr{\Multij=0}{}{\xintifboolexpr{\Multi=0}{}{+}\xintifboolexpr{\Multij<0}{(}{}\Affichage{0}{\Multij}{0}\xintifboolexpr{\Multij<0}{)}{}}% - \xintifboolexpr{\Multik=0}{}{\xintifboolexpr{\Multil=0}{\xintifboolexpr{#2=0}{}{+}}{+}\xintifboolexpr{\Multik<0}{(}{}\Affichage{0}{\Multik}{0}\xintifboolexpr{\Multik<0}{)}{}}% - }% - \xintifboolexpr{\Multil=0}{}{+}\xintifboolexpr{\Multil<0}{(}{}\Affichage{0}{0}{\Multil}\xintifboolexpr{\Multil<0}{)}{}% - }{}% - % Etape 4 - \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=4}{% - \xdef\Multi{\fpeval{#2*#4}}% - \xdef\Multij{\fpeval{#2*#5}}% - \xdef\Multik{\fpeval{#3*#4}}% - \xdef\Multil{\fpeval{#3*#5}}% - %% ils sont redéfinis pour pouvoir envisager la somme de deux - %% expressions à développer - \xdef\Multim{\fpeval{#2*#5+#3*#4}}% - %80 - \xintifboolexpr{\theNbCalculDistri>1}{\setcounter{NbCalculDistri}{0}}{}% - \stepcounter{NbCalculDistri}% - %fin 80 - \ifboolKV[ClesDistributivite]{Oppose}{% - \xdef\Multi{\fpeval{-\Multi}}% - \xdef\Multim{\fpeval{-\Multim}}% - \xdef\Multil{\fpeval{-\Multil}}% - \xintifboolexpr{\Multi=0}{}{\xintifboolexpr{\Multi<0}{(}{}\Affichage{\Multi}{0}{0}\xintifboolexpr{\Multi<0}{)}{}}% - \xintifboolexpr{\Multim=0}{}{\xintifboolexpr{\Multim>0}{+}{+(}\Affichage{0}{\Multim}{0}\xintifboolexpr{\Multim<0}{)}{}}% - \xintifboolexpr{\Multil=0}{}{\xintifboolexpr{\Multil>0}{+}{+(}\Affichage{0}{0}{\Multil}\xintifboolexpr{\Multil<0}{)}{}}% - }{% - %80 + \xdef\Multil{\fpeval{#3*#5}}% + \xintifboolexpr{\Multil=0}{}{+% + \xintifboolexpr{#3<0}{(}{}\Affichage[#1]{0}{0}{#3}\xintifboolexpr{#3<0}{)}{}\times\xintifboolexpr{#5<0}{(}{}\Affichage[#1]{0}{0}{#5}\xintifboolexpr{#5<0}{)}{}% + }% + }{}% + % Etape 3 + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=3}{% + \stepcounter{NbCalculDistri}% + \xdef\Multi{\fpeval{#2*#4}}% + \xdef\Multij{\fpeval{#2*#5}}% + \xdef\Multik{\fpeval{#3*#4}}% + \xdef\Multil{\fpeval{#3*#5}}% + %% ils sont redéfinis pour pouvoir envisager la somme de deux + %% expressions à développer \xintifboolexpr{\theNbCalculDistri>1}{\xintifboolexpr{\Multi<0}{(\Affichage{\Multi}{0}{0})}{\Affichage{\Multi}{0}{0}}}{\Affichage{\Multi}{0}{0}}% - \xintifboolexpr{\Multim=0}{}{% - \xintifboolexpr{\Multim>0}{+\Affichage{0}{\Multim}{0}}{-\Affichage{0}{\fpeval{-\Multim}}{0}}% + \ifboolKV[ClesDistributivite]{Reduction}{\mathunderline{DCReduction}{% + \xintifboolexpr{\Multij=0}{}{\xintifboolexpr{\Multi=0}{}{{}+}\xintifboolexpr{\Multij<0}{(}{}\Affichage{0}{\Multij}{0}\xintifboolexpr{\Multij<0}{)}{}}% + \xintifboolexpr{\Multik=0}{}{\xintifboolexpr{\Multil=0}{\xintifboolexpr{#2=0}{}{+}}{+}\xintifboolexpr{\Multik<0}{(}{}\Affichage{0}{\Multik}{0}\xintifboolexpr{\Multik<0}{)}{}}% + }% + }{% + \xintifboolexpr{\Multij=0}{}{\xintifboolexpr{\Multi=0}{}{+}\xintifboolexpr{\Multij<0}{(}{}\Affichage{0}{\Multij}{0}\xintifboolexpr{\Multij<0}{)}{}}% + \xintifboolexpr{\Multik=0}{}{\xintifboolexpr{\Multil=0}{\xintifboolexpr{#2=0}{}{+}}{\xintifboolexpr{#2=0}{}{+}}\xintifboolexpr{\Multik<0}{(}{}\Affichage{0}{\Multik}{0}\xintifboolexpr{\Multik<0}{)}{}}% }% - \xintifboolexpr{\Multil=0}{}{\xintifboolexpr{\Multil<0}{-\Affichage{0}{0}{\fpeval{-\Multil}}}{+\Affichage{0}{0}{\Multil}}}%\Affichage{\Multi}{\Multim}{\Multil}% - % fin 80 - } - \ifboolKV[ClesDistributivite]{Somme}{\xdef\SommeA{\fpeval{\SommeA+#2*#4}}\xdef\SommeB{\fpeval{\SommeB+#2*#5+#3*#4}}\xdef\SommeC{\fpeval{\SommeC+#3*#5}}}{}% - \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-#2*#4}}\xdef\SommeB{\fpeval{\SommeB-#2*#5-#3*#4}}\xdef\SommeC{\fpeval{\SommeC-#3*#5}}}{}% - }{}% + \xintifboolexpr{\Multil=0}{}{+}\xintifboolexpr{\Multil<0}{(}{}\Affichage{0}{0}{\Multil}\xintifboolexpr{\Multil<0}{)}{}% + }{}% + % Etape 4 + \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=4}{% + \xdef\Multi{\fpeval{#2*#4}}% + \xdef\Multij{\fpeval{#2*#5}}% + \xdef\Multik{\fpeval{#3*#4}}% + \xdef\Multil{\fpeval{#3*#5}}% + %% ils sont redéfinis pour pouvoir envisager la somme de deux + %% expressions à développer + \xdef\Multim{\fpeval{#2*#5+#3*#4}}% + \xintifboolexpr{\theNbCalculDistri>1}{\setcounter{NbCalculDistri}{0}}{}% + \stepcounter{NbCalculDistri}% + \ifboolKV[ClesDistributivite]{Oppose}{% + \xdef\Multi{\fpeval{-\Multi}}% + \xdef\Multim{\fpeval{-\Multim}}% + \xdef\Multil{\fpeval{-\Multil}}% + \xintifboolexpr{\Multi=0}{}{\xintifboolexpr{\Multi<0}{(}{}\Affichage{\Multi}{0}{0}\xintifboolexpr{\Multi<0}{)}{}}% + \xintifboolexpr{\Multim=0}{}{\xintifboolexpr{\Multim>0}{+}{+(}\Affichage{0}{\Multim}{0}\xintifboolexpr{\Multim<0}{)}{}}% + \xintifboolexpr{\Multil=0}{}{\xintifboolexpr{\Multil>0}{+}{+(}\Affichage{0}{0}{\Multil}\xintifboolexpr{\Multil<0}{)}{}}% + }{% + \xintifboolexpr{\theNbCalculDistri>1}{\xintifboolexpr{\Multi<0}{(\Affichage{\Multi}{0}{0})}{\Affichage{\Multi}{0}{0}}}{\Affichage{\Multi}{0}{0}}% + \xintifboolexpr{\Multim=0}{}{% + \xintifboolexpr{\Multim>0}{+\Affichage{0}{\Multim}{0}}{-\Affichage{0}{\fpeval{-\Multim}}{0}}% + }% + \xintifboolexpr{\Multil=0}{}{\xintifboolexpr{\Multil<0}{-\Affichage{0}{0}{\fpeval{-\Multil}}}{+\Affichage{0}{0}{\Multil}}}% + } + \ifboolKV[ClesDistributivite]{Somme}{\xdef\SommeA{\fpeval{\SommeA+#2*#4}}\xdef\SommeB{\fpeval{\SommeB+#2*#5+#3*#4}}\xdef\SommeC{\fpeval{\SommeC+#3*#5}}}{}% + \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-#2*#4}}\xdef\SommeB{\fpeval{\SommeB-#2*#5-#3*#4}}\xdef\SommeC{\fpeval{\SommeC-#3*#5}}}{}% + }{}% + }% }% }% }% }% - }% }% \newcommand{\Resultat}[1][]{% @@ -2560,9 +2908,7 @@ \useKVdefault[ClesDistributivite]%obligatoire car la macro n'est pas dans un groupe. \setKV[ClesDistributivite]{#1}%On lit les arguments optionnels \ifboolKV[ClesDistributivite]{RAZ}{\xdef\SommeA{0}\xdef\SommeB{0}\xdef\SommeC{0}% - % 80 \setcounter{NbCalculDistri}{0}% - % fin 80 }{}% \colorlet{DCAide}{\useKV[ClesDistributivite]{CouleurAide}}% \colorlet{DCReduction}{\useKV[ClesDistributivite]{CouleurReduction}}% @@ -2583,10 +2929,8 @@ \fi% }{} \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=3}{% - % 80 \xintifboolexpr{\theNbCalculDistri>1}{\setcounter{NbCalculDistri}{0}}{}% \stepcounter{NbCalculDistri}% - % fin 80 \ifx\bla#4\bla% \xdef\Multi{\fpeval{#2*#2}}% \xdef\Multij{\fpeval{#2*#3}}% @@ -2776,9 +3120,7 @@ }{} % Etape 3 \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=3}{% - % 80 \stepcounter{NbCalculDistri}% - % fin 80 \xdef\Multi{\fpeval{#2*#4}}% \xdef\Multij{\fpeval{#2*#5}}% \xdef\Multik{\fpeval{#3*#4}}% @@ -2786,9 +3128,7 @@ %% ils sont redéfinis pour pouvoir envisager la somme de deux %% expressions à développer \xintifboolexpr{\useKV[ClesDistributivite]{Echange}=1}{% - % 80 \xintifboolexpr{\theNbCalculDistri>1}{\xintifboolexpr{\Multi<0}{(\AffichageEchange{0}{\Multi}{0})}{\AffichageEchange{0}{\Multi}{0}}}{\AffichageEchange{0}{\Multi}{0}}% - %fin 80\AffichageEchange{0}{\Multi}{0}%pas de soulignement de réduction ici \xintifboolexpr{\Multij=0}{}{\xintifboolexpr{\Multi=0}{}{+}\xintifboolexpr{\Multij<0}{(}{}\AffichageEchange{\Multij}{0}{0}\xintifboolexpr{\Multij<0}{)}{}}% \xintifboolexpr{\Multik=0}{}{\xintifboolexpr{\Multil=0}{\xintifboolexpr{#2=0}{}{+}}{+}\xintifboolexpr{\Multik<0}{(}{}\AffichageEchange{0}{0}{\Multik}\xintifboolexpr{\Multik<0}{)}{}}% \xintifboolexpr{\Multil=0}{}{+}\xintifboolexpr{\Multil<0}{(}{}\AffichageEchange{0}{\Multil}{0}\xintifboolexpr{\Multil<0}{)}{}% @@ -2797,9 +3137,7 @@ \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-\Multik}}\xdef\SommeB{\fpeval{\SommeB-\Multim}}\xdef\SommeC{\fpeval{\SommeC-\Multij}}}{}% }{}% \xintifboolexpr{\useKV[ClesDistributivite]{Echange}=2}{% - % 80 \xintifboolexpr{\theNbCalculDistri>1}{\xintifboolexpr{\Multi<0}{(\AffichageEchange{0}{\Multi}{0})}{\AffichageEchange{0}{\Multi}{0}}}{\AffichageEchange{0}{\Multi}{0}}% - %fin 80\AffichageEchange{0}{\Multi}{0}%pas de soulignement de réduction ici \xintifboolexpr{\Multij=0}{}{\xintifboolexpr{\Multi=0}{}{+}\xintifboolexpr{\Multij<0}{(}{}\AffichageEchange{0}{0}{\Multij}\xintifboolexpr{\Multij<0}{)}{}}% \xintifboolexpr{\Multik=0}{}{\xintifboolexpr{\Multil=0}{\xintifboolexpr{#2=0}{}{+}}{+}\xintifboolexpr{\Multik<0}{(}{}\AffichageEchange{\Multik}{0}{0}\xintifboolexpr{\Multik<0}{)}{}}% \xintifboolexpr{\Multil=0}{}{+}\xintifboolexpr{\Multil<0}{(}{}\AffichageEchange{0}{\Multil}{0}\xintifboolexpr{\Multil<0}{)}{}% @@ -2808,9 +3146,7 @@ \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-\Multij}}\xdef\SommeB{\fpeval{\SommeB-\Multim}}\xdef\SommeC{\fpeval{\SommeC-\Multik}}}{}% }{}% \xintifboolexpr{\useKV[ClesDistributivite]{Echange}=3}{% - % 80 \xintifboolexpr{\theNbCalculDistri>1}{\xintifboolexpr{\Multi<0}{(\AffichageEchange{\Multi}{0}{0})}{\AffichageEchange{\Multi}{0}{0}}}{\AffichageEchange{\Multi}{0}{0}}% - %fin 80\AffichageEchange{\Multi}{0}{0}%pas de soulignement de réduction ici \xintifboolexpr{\Multij=0}{}{\xintifboolexpr{\Multi=0}{}{+}\xintifboolexpr{\Multij<0}{(}{}\AffichageEchange{0}{\Multij}{0}\xintifboolexpr{\Multij<0}{)}{}}% \xintifboolexpr{\Multik=0}{}{\xintifboolexpr{\Multil=0}{\xintifboolexpr{#2=0}{}{+}}{+}\xintifboolexpr{\Multik<0}{(}{}\AffichageEchange{0}{\Multik}{0}\xintifboolexpr{\Multik<0}{)}{}}% \xintifboolexpr{\Multil=0}{}{+}\xintifboolexpr{\Multil<0}{(}{}\AffichageEchange{0}{0}{\Multil}\xintifboolexpr{\Multil<0}{)}{}% @@ -2827,10 +3163,8 @@ \xdef\Multil{\fpeval{#3*#5}}% %% ils sont redéfinis pour pouvoir envisager la somme de deux %% expressions à développer - % 80 \xintifboolexpr{\theNbCalculDistri>1}{\setcounter{NbCalculDistri}{0}}{}% \stepcounter{NbCalculDistri}% - %fin 80 \xintifboolexpr{\useKV[ClesDistributivite]{Echange}=1}{% \xdef\Multim{\fpeval{#2*#4+#3*#5}}% \ifboolKV[ClesDistributivite]{Oppose}{% @@ -2841,13 +3175,11 @@ \xintifboolexpr{\Multimo=0}{}{\xintifboolexpr{\Multimo>0}{+}{+(}\Affichage{0}{\Multimo}{0}\xintifboolexpr{\Multimo<0}{)}{}}% \xintifboolexpr{\Multijo=0}{}{\xintifboolexpr{\Multijo>0}{+}{+(}\Affichage{0}{0}{\Multijo}\xintifboolexpr{\Multijo<0}{)}{}}% }{% - % 80 \xintifboolexpr{\theNbCalculDistri>1}{\xintifboolexpr{\Multik<0}{(\Affichage{\Multik}{0}{0})}{\Affichage{\Multik}{0}{0}}}{\Affichage{\Multik}{0}{0}}% \xintifboolexpr{\Multim=0}{}{% \xintifboolexpr{\Multim>0}{+\Affichage{0}{\Multim}{0}}{-\Affichage{0}{\fpeval{-\Multim}}{0}}% }% \xintifboolexpr{\Multij=0}{}{\xintifboolexpr{\Multij<0}{-\Affichage{0}{0}{\fpeval{-\Multij}}}{+\Affichage{0}{0}{\Multij}}}% - % fin 80 }% \ifboolKV[ClesDistributivite]{Somme}{\xdef\SommeA{\fpeval{\SommeA+\Multik}}\xdef\SommeB{\fpeval{\SommeB+\Multim}}\xdef\SommeC{\fpeval{\SommeC+\Multij}}}{}% \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-\Multik}}\xdef\SommeB{\fpeval{\SommeB-\Multim}}\xdef\SommeC{\fpeval{\SommeC-\Multij}}}{}% @@ -2862,13 +3194,11 @@ \xintifboolexpr{\Multimo=0}{}{\xintifboolexpr{\Multimo>0}{+}{+(}\Affichage{0}{\Multimo}{0}\xintifboolexpr{\Multimo<0}{)}{}}% \xintifboolexpr{\Multiko=0}{}{\xintifboolexpr{\Multiko>0}{+}{+(}\Affichage{0}{0}{\Multiko}\xintifboolexpr{\Multiko<0}{)}{}}% }{% - % 80 \xintifboolexpr{\theNbCalculDistri>1}{\xintifboolexpr{\Multij<0}{(\Affichage{\Multij}{0}{0})}{\Affichage{\Multij}{0}{0}}}{\Affichage{\Multij}{0}{0}}% \xintifboolexpr{\Multim=0}{}{% \xintifboolexpr{\Multim>0}{+\Affichage{0}{\Multim}{0}}{-\Affichage{0}{\fpeval{-\Multim}}{0}}% }% \xintifboolexpr{\Multik=0}{}{\xintifboolexpr{\Multik<0}{-\Affichage{0}{0}{\fpeval{-\Multik}}}{+\Affichage{0}{0}{\Multik}}}% - % fin 80\Affichage{\Multij}{\Multim}{\Multik}% }% \ifboolKV[ClesDistributivite]{Somme}{\xdef\SommeA{\fpeval{\SommeA+\Multij}}\xdef\SommeB{\fpeval{\SommeB+\Multim}}\xdef\SommeC{\fpeval{\SommeC+\Multik}}}{}% \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-\Multij}}\xdef\SommeB{\fpeval{\SommeB-\Multim}}\xdef\SommeC{\fpeval{\SommeC-\Multik}}}{}% @@ -2883,13 +3213,11 @@ \xintifboolexpr{\Multimo=0}{}{\xintifboolexpr{\Multimo>0}{+}{+(}\Affichage{0}{\Multimo}{0}\xintifboolexpr{\Multimo<0}{)}{}}% \xintifboolexpr{\Multio=0}{}{\xintifboolexpr{\Multio>0}{+}{+(}\Affichage{0}{0}{\Multio}\xintifboolexpr{\Multio<0}{)}{}}% }{% - % 80 \xintifboolexpr{\theNbCalculDistri>1}{\xintifboolexpr{\Multil<0}{(\Affichage{\Multil}{0}{0})}{\Affichage{\Multil}{0}{0}}}{\Affichage{\Multil}{0}{0}}% \xintifboolexpr{\Multim=0}{}{% \xintifboolexpr{\Multim>0}{+\Affichage{0}{\Multim}{0}}{-\Affichage{0}{\fpeval{-\Multim}}{0}}% }% \xintifboolexpr{\Multi=0}{}{\xintifboolexpr{\Multi<0}{-\Affichage{0}{0}{\fpeval{-\Multi}}}{+\Affichage{0}{0}{\Multi}}}% - % fin 80\Affichage{\Multil}{\Multim}{\Multi}% } \ifboolKV[ClesDistributivite]{Somme}{\xdef\SommeA{\fpeval{\SommeA+\Multil}}\xdef\SommeB{\fpeval{\SommeB+\Multim}}\xdef\SommeC{\fpeval{\SommeC+\Multi}}}{}% \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-\Multil}}\xdef\SommeB{\fpeval{\SommeB-\Multim}}\xdef\SommeC{\fpeval{\SommeC-\Multi}}}{}% @@ -2901,9 +3229,9 @@ }% }% -%%%%%%%%%%%%%%% -%Nombre Premier -%%%%%%%%%%%%%%% +%%% +% Nombre Premier +%%% \setKVdefault[ClesNombrePremier]{Tableau=false,TableauVertical=false,TableauVerticalVide=false,Exposant=false,Longue=false,All=false,Arbre=false,ArbreVide=false,ArbreComplet=false,Diviseurs=false,DiviseursT=false,Dot=\dotfill} \newcommand\Decomposition[2][]{% @@ -2930,7 +3258,7 @@ pair Ancre[]; numeric decalage; decalage=10mm; - + vardef PremierSimple(expr NB)= b:=2; depart:=NB; @@ -3393,7 +3721,6 @@ vardef Positions(expr Step)= \dnpvv=\numexpr\dnpvv+1\relax \cnpvv=\numexpr\anpvv/\bnpvv\relax \anpvv=\cnpvv\relax - %\num{\the\bnpvv}% \else% \bnpvv=\numexpr\bnpvv+1\relax% \fi% @@ -3419,7 +3746,6 @@ vardef Positions(expr Step)= \dnpmv=\numexpr\dnpmv+1\relax \cnpmv=\numexpr\anpmv/\bnpmv\relax \anpmv=\cnpmv\relax - %\num{\the\bnpmv} \else% \bnpmv=\numexpr\bnpmv+1\relax% \fi% @@ -3469,7 +3795,7 @@ vardef Positions(expr Step)= \anp=#1\relax% \bnp=2\relax% \premier=-1\relax% - % Pour déterminer le nombre d'étapes + % Pour déterminer le nombre d'étapes \whiledo{\anp > 1}{% \modulo{\the\anp}{\the\bnp} \ifnum\remainder=0\relax% @@ -3479,7 +3805,7 @@ vardef Positions(expr Step)= \else% \bnp=\numexpr\bnp+1\relax% \fi% - } + }% \ifnum\premier=0% Le nombre \num{#1} est un nombre premier.% \else% @@ -3536,22 +3862,21 @@ vardef Positions(expr Step)= \else% \ifnum\exposant>0\relax \num{\the\pileb}\ifnum\exposant>1 ^{\num{\the\exposant}}\fi\times% - %\pilea=\anp\relax \fi \bnp=\numexpr\bnp+1\relax% \pileb=\bnp\relax% - \exposant=0\relax + \exposant=0\relax% \fi% - } + }% \num{\the\pileb}\ifnum\exposant>1^{\num{\the\exposant}}\fi% - } -} + }% +}% \newcommand{\PremierLong}[1]{% %#1 : le nombre entier à tester \ensuremath{% \newcount\anpl\newcount\bnpl\newcount\cnpl% - \newcount\pilebl + \newcount\pilebl% \anpl=#1\relax% \bnpl=2\relax% \pilebl=2\relax% @@ -3564,7 +3889,7 @@ vardef Positions(expr Step)= \else% \bnpl=\numexpr\bnpl+1\relax% \pilebl=\bnpl\relax% - \fi% + \fi% } } } @@ -3635,9 +3960,9 @@ vardef Positions(expr Step)= }% } -%%%%%%%%%%%%%%%%%%% +%%% % Simplification -%%%%%%%%%%%%%%%%%%% +%%% \makeatletter%by christian Tellechea % Calcul du PGCD de #1 et #2 \newcount\cnt@a\newcount\cnt@b\newcount\pgcd @@ -3675,6 +4000,11 @@ vardef Positions(expr Step)= \numerateur=\valabsnum \denominateur=\valabsdeno \fi + \else + \ifnum\the\denominateur<0\relax + \numerateur=-\valabsnum + \denominateur=\valabsdeno + \fi \fi \ifnum\number#2=0\relax \text{\bfseries(???)} @@ -3718,6 +4048,17 @@ vardef Positions(expr Step)= \else \valabsdeno=\number#2 \fi + \ifnum\the\numerateur<0\relax + \ifnum\the\denominateur<0\relax + \numerateur=\valabsnum + \denominateur=\valabsdeno + \fi + \else + \ifnum\the\denominateur<0\relax + \numerateur=-\valabsnum + \denominateur=\valabsdeno + \fi + \fi \ifnum\number#2=0\relax \ensuremath{\text{\bfseries(???)}} \else @@ -3743,49 +4084,50 @@ vardef Positions(expr Step)= \fi } +\newcount\anpdc\newcount\bnpdc\newcount\cnpdc\newcount\dnpdc% +\newcount\DivCom \newcommand\DiviseurCommun[2]{% % #1 : le premier nombre entier - % #2 : le deuxième nombre entier - \newcount\anpdc\newcount\bnpdc\newcount\cnpdc% + % #2 : le deuxième nombre entier + % nombre 1 vaut #1 - Nombre 2 vaut #2 \anpdc=#1% \cnpdc=#2% \bnpdc=2\relax% - \whiledo{\bnpdc<\anpdc}{% - \modulo{\the\anpdc}{\the\bnpdc}{}% + \dnpdc=\numexpr#1+1\relax% + \DivCom=1\relax% + \whiledo{\bnpdc<\dnpdc}{% + \modulo{\the\anpdc}{\the\bnpdc}\relax \ifnum\remainder=0% - \modulo{\the\cnpdc}{\the\bnpdc}{} + \modulo{\the\cnpdc}{\the\bnpdc} \ifnum\remainder=0% - \xdef\DivCom{\the\bnpdc}% + \DivCom=\bnpdc% \bnpdc=\anpdc% \else% - \xdef\DivCom{1}% - \bnpdc=\numexpr\bnpdc+1% - \fi% + \DivCom=1% + \fi \else% - \xdef\DivCom{1}% - \bnpdc=\numexpr\bnpdc+1% + \DivCom=1% \fi + \bnpdc=\numexpr\bnpdc+1\relax% }% } \newcommand\LongueSimplification[2]{% - \DiviseurCommun{#1}{#2}% \xdef\NumerateurDiv{#1}% \xdef\DenominateurDiv{#2}% + \DiviseurCommun{#1}{#2}% \ensuremath{% - \whiledo{\DivCom > 1}{% - \xdef\DivComa{\DivCom}\xdef\MulComa{\fpeval{\NumerateurDiv/\DivComa}} - \xdef\DivComb{\DivCom}\xdef\MulComb{\fpeval{\DenominateurDiv/\DivComb}} - \frac{\num{\DivComa}\times\num{\MulComa}}{\num{\DivComb}\times\num{\MulComb}}=\frac{\num{\MulComa}}{\num{\MulComb}}% - \xdef\NumerateurDiv{\MulComa}% - \xdef\DenominateurDiv{\MulComb}% + \whiledo{\DivCom>1}{% + \frac{\num{\fpeval{\NumerateurDiv/\the\DivCom}}\times\num{\the\DivCom}}{\num{\fpeval{\DenominateurDiv/\the\DivCom}}\times\num{\the\DivCom}}=\frac{\num{\fpeval{\NumerateurDiv/\DivCom}}}{\num{\fpeval{\DenominateurDiv/\DivCom}}}% + \xdef\NumerateurDiv{\fpeval{\NumerateurDiv/\DivCom}}% + \xdef\DenominateurDiv{\fpeval{\DenominateurDiv/\DivCom}}% \DiviseurCommun{\NumerateurDiv}{\DenominateurDiv}% \xintifboolexpr{\DivCom>1}{=}{}% - } - } -} + }% + }% +}% -\setKVdefault[ClesSimplification]{Details=false,All=false,Longue=false,Fleches=false} +\setKVdefault[ClesSimplification]{Details=false,All=false,Longue=false,Fleches=false,Contraire=0} \newcounter{NbFrac}% \setcounter{NbFrac}{0}% @@ -3814,17 +4156,23 @@ vardef Positions(expr Step)= \draw[out=-45,in=-135,-stealth,transform canvas={yshift=-0.25em}] (pic cs:B-\theNbFrac) to node[midway,below]{\Listeb[1,2]}(pic cs:D-\theNbFrac);% \end{tikzpicture}% }{% - \ifboolKV[ClesSimplification]{Longue}{% - \LongueSimplification{#2}{#3}% + \xintifboolexpr{\useKV[ClesSimplification]{Contraire}>1}{% + \ensuremath{% + \frac{\num{#2}}{\num{#3}}=\frac{\num{#2}\times\num{\useKV[ClesSimplification]{Contraire}}}{\num{#3}\times\num{\useKV[ClesSimplification]{Contraire}}}=\frac{\num{\fpeval{\useKV[ClesSimplification]{Contraire}*#2}}}{\num{\fpeval{\useKV[ClesSimplification]{Contraire}*#3}}}% + }% }{% - \ifboolKV[ClesSimplification]{Details}{\SSimpli{#2}{#3}}{\ifboolKV[ClesSimplification]{All}{\ensuremath{\SSimpli{#2}{#3}=\SSimplifie{#2}{#3}}}{\SSimplifie{#2}{#3}}}% + \ifboolKV[ClesSimplification]{Longue}{% + \LongueSimplification{#2}{#3}% + }{% + \ifboolKV[ClesSimplification]{Details}{\SSimpli{#2}{#3}}{\ifboolKV[ClesSimplification]{All}{\ensuremath{\SSimpli{#2}{#3}=\SSimplifie{#2}{#3}}}{\SSimplifie{#2}{#3}}}% + }% }% }% }% -%%%%%%%%%%%%%%%%%%%%% -%%% Thales -%%%%%%%%%%%%%%%%%%%%% +%%% +% Thales +%%% \newcount\ppcm \newcommand\PPCM[2]{% @@ -3832,10 +4180,10 @@ vardef Positions(expr Step)= \ppcm=\numexpr#1*#2/\pgcd\relax } -\setKVdefault[ClesThales]{Calcul=true,Droites=false,Propor=false,Segment=false,Figure=false,Figurecroisee=false,Precision=2,Entier=false,Unite=cm,Reciproque=false,Produit=false,ChoixCalcul=0,Simplification,Redaction=false,Remediation=false} +\setKVdefault[ClesThales]{Calcul=true,Droites=false,Propor=false,Segment=false,Figure=false,FigureSeule=false,Figurecroisee=false,FigurecroiseeSeule=false,Angle=0,Precision=2,Entier=false,Unite=cm,Reciproque=false,Produit=false,ChoixCalcul=0,Simplification,Redaction=false,Remediation=false} %On définit la figure à utiliser -\def\MPFigThales#1#2#3#4#5{ +\def\MPFigThales#1#2#3#4#5#6{ % #1 Premier sommet % #2 Deuxième sommet % #3 Troisième sommet @@ -3855,15 +4203,10 @@ vardef Positions(expr Step)= O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour éventuellement moins de lassitude :) - numeric Angle; - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); - % On définit le centre du cercle inscrit - %(I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C]; - %(I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C]; - %on dessine à main levée :) + A:=A rotatedabout(O,#6); + B:=B rotatedabout(O,#6); + C:=C rotatedabout(O,#6); + % on dessine à main levée :) path cotes[]; cotes1=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; cotes2=B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; @@ -3909,14 +4252,10 @@ vardef Positions(expr Step)= O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour éventuellement moins de lassitude :) - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); - % On définit le centre du cercle inscrit - %(I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C]; - %(I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C]; - %on dessine à main levée :) + A:=A rotatedabout(O,#6); + B:=B rotatedabout(O,#6); + C:=C rotatedabout(O,#6); + % on dessine à main levée :) path cotes[]; cotes1=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; cotes2=B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; @@ -3953,7 +4292,7 @@ vardef Positions(expr Step)= } %On définit la figure à utiliser -\def\MPFigReciThales#1#2#3#4#5{ +\def\MPFigReciThales#1#2#3#4#5#6{ % #1 Premier sommet % #2 Deuxième sommet % #3 Troisième sommet @@ -3973,15 +4312,10 @@ vardef Positions(expr Step)= O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour éventuellement moins de lassitude :) - numeric Angle; - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); - % On définit le centre du cercle inscrit - %(I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C]; - %(I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C]; - %on dessine à main levée :) + A:=A rotatedabout(O,#6); + B:=B rotatedabout(O,#6); + C:=C rotatedabout(O,#6); + % on dessine à main levée :) path cotes[]; cotes1=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; cotes2=B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; @@ -4015,14 +4349,10 @@ vardef Positions(expr Step)= O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour éventuellement moins de lassitude :) - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); - % On définit le centre du cercle inscrit - %(I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C]; - %(I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C]; - %on dessine à main levée :) + A:=A rotatedabout(O,#6); + B:=B rotatedabout(O,#6); + C:=C rotatedabout(O,#6); + % on dessine à main levée :) path cotes[]; cotes1=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; cotes2=B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; @@ -4042,24 +4372,12 @@ vardef Positions(expr Step)= label(btex #5 etex,1.1[B,N]); fill (fullcircle scaled 0.75mm) shifted (cotes1 intersectionpoint cotes4); fill (fullcircle scaled 0.75mm) shifted (cotes3 intersectionpoint cotes4); -% pair I,J,K; -% I=1/2[M,N]; -% J=1/2[B,C]; -% K=1/2[I,J]; -% path cd; -% cd=(fullcircle scaled 6mm) shifted K; -% drawoptions(withcolor 0.75*white); -% drawarrow reverse((I{dir(210+angle(I-J))}..{dir(150+angle(I-J))}K) cutafter cd); -% drawarrow reverse((J{dir(210+angle(J-I))}..{dir(150+angle(J-I))}K) cutafter cd); -% draw cd; -% label(btex $//$ etex ,K); -% drawoptions(); \end{mpost} \fi } %On définit la deuxième figure à utiliser -\def\MPFigThalesCroisee#1#2#3#4#5{% +\def\MPFigThalesCroisee#1#2#3#4#5#6{% % #1 Premier sommet % #2 Deuxième sommet % #3 Troisième sommet @@ -4079,11 +4397,9 @@ vardef Positions(expr Step)= B=A rotatedabout(O,130); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On tourne pour éventuellement moins de lassitude :) - numeric Angle; - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); + A:=A rotatedabout(O,#6); + B:=B rotatedabout(O,#6); + C:=C rotatedabout(O,#6); % on dessine à main levée :) M=1.4[B,A]; N=1.4[C,A]; @@ -4102,7 +4418,6 @@ vardef Positions(expr Step)= (I-C) rotated ((angle(A-C)-angle(M-C))/2) shifted C=whatever[A,C]; (I-M) rotated ((angle(C-M)-angle(A-M))/2) shifted M=whatever[M,C]; %on labelise - %label(btex #1 etex,1.15[1/2[B,C],A]); label(btex #1 etex,I); label(btex #2 etex,1.2[M,B]); label(btex #3 etex,1.2[N,C]); @@ -4136,10 +4451,9 @@ vardef Positions(expr Step)= B=A rotatedabout(O,130); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On tourne pour éventuellement moins de lassitude :) - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); + A:=A rotatedabout(O,#6); + B:=B rotatedabout(O,#6); + C:=C rotatedabout(O,#6); % on dessine à main levée :) M=1.4[B,A]; N=1.4[C,A]; @@ -4158,7 +4472,6 @@ vardef Positions(expr Step)= (I-C) rotated ((angle(A-C)-angle(M-C))/2) shifted C=whatever[A,C]; (I-M) rotated ((angle(C-M)-angle(A-M))/2) shifted M=whatever[M,C]; %on labelise - %label(btex #1 etex,1.15[1/2[B,C],A]); label(btex #1 etex,I); label(btex #2 etex,1.2[M,B]); label(btex #3 etex,1.2[N,C]); @@ -4183,7 +4496,7 @@ vardef Positions(expr Step)= } %On définit la deuxième figure à utiliser -\def\MPFigReciThalesCroisee#1#2#3#4#5{% +\def\MPFigReciThalesCroisee#1#2#3#4#5#6{% % #1 Premier sommet % #2 Deuxième sommet % #3 Troisième sommet @@ -4203,11 +4516,9 @@ vardef Positions(expr Step)= B=A rotatedabout(O,130); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On tourne pour éventuellement moins de lassitude :) - numeric Angle; - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); + A:=A rotatedabout(O,#6); + B:=B rotatedabout(O,#6); + C:=C rotatedabout(O,#6); % on dessine à main levée :) M=1.4[B,A]; N=1.4[C,A]; @@ -4226,7 +4537,6 @@ vardef Positions(expr Step)= (I-C) rotated ((angle(A-C)-angle(M-C))/2) shifted C=whatever[A,C]; (I-M) rotated ((angle(C-M)-angle(A-M))/2) shifted M=whatever[M,C]; %on labelise - %label(btex #1 etex,1.15[1/2[B,C],A]); label(btex #1 etex,I); label(btex #2 etex,1.2[M,B]); label(btex #3 etex,1.2[N,C]); @@ -4250,10 +4560,9 @@ vardef Positions(expr Step)= B=A rotatedabout(O,130); C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]); % On tourne pour éventuellement moins de lassitude :) - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); + A:=A rotatedabout(O,#6); + B:=B rotatedabout(O,#6); + C:=C rotatedabout(O,#6); % on dessine à main levée :) M=1.4[B,A]; N=1.4[C,A]; @@ -4272,7 +4581,6 @@ vardef Positions(expr Step)= (I-C) rotated ((angle(A-C)-angle(M-C))/2) shifted C=whatever[A,C]; (I-M) rotated ((angle(C-M)-angle(A-M))/2) shifted M=whatever[M,C]; %on labelise - %label(btex #1 etex,1.15[1/2[B,C],A]); label(btex #1 etex,I); label(btex #2 etex,1.2[M,B]); label(btex #3 etex,1.2[N,C]); @@ -4291,7 +4599,7 @@ vardef Positions(expr Step)= \useKVdefault[ClesThales]% \setKV[ClesThales]{#1}% \ifboolKV[ClesThales]{Droites}{% - Les droites $(#3#5)$ et $(#4#6)$ sont sécantes en $#2$.% + Les droites \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$(#3#5)$} et \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$(#4#6)$} sont sécantes en \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$#2$}.% }{% Dans le triangle \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$#2#3#4$}, \ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{$#5$} est un point \ifboolKV[ClesThales]{Segment}{du segment}{de la droite} @@ -4869,23 +5177,31 @@ vardef Positions(expr Step)= \newcommand{\TThales}[8][]{% \setKV[ClesThales]{#1}% - \ifboolKV[ClesThales]{Figure}{% - \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% - \begin{multicols}{2}% - {\em La figure est donnée à titre indicatif.}% - \[\MPFigThales\NomA\NomB\NomC\NomM\NomN\]% - \par\columnbreak\par% - \ifboolKV[ClesThales]{Entier}{\TThalesCalculsE[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}{\TThalesCalculsD[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}% - \end{multicols}% - }{\ifboolKV[ClesThales]{Figurecroisee}{% - \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% - \begin{multicols}{2}% - {\em La figure est donnée à titre indicatif.}% - \[\MPFigThalesCroisee\NomA\NomB\NomC\NomM\NomN\]% - \par\columnbreak\par% - \ifboolKV[ClesThales]{Entier}{\TThalesCalculsE[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}{\TThalesCalculsD[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}% - \end{multicols}% - }{\ifboolKV[ClesThales]{Entier}{\TThalesCalculsE[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}{\TThalesCalculsD[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}}% + \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% + \ifboolKV[ClesThales]{FigureSeule}{% + \MPFigThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% + }{\ifboolKV[ClesThales]{FigurecroiseeSeule}{% + \MPFigThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% + }{% + \ifboolKV[ClesThales]{Figure}{% + \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% + \begin{multicols}{2}% + {\em La figure est donnée à titre indicatif.}% + \[\MPFigThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]% + \par\columnbreak\par% + \ifboolKV[ClesThales]{Entier}{\TThalesCalculsE[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}{\TThalesCalculsD[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}% + \end{multicols}% + }{\ifboolKV[ClesThales]{Figurecroisee}{% + \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% + \begin{multicols}{2}% + {\em La figure est donnée à titre indicatif.}% + \[\MPFigThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]% + \par\columnbreak\par% + \ifboolKV[ClesThales]{Entier}{\TThalesCalculsE[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}{\TThalesCalculsD[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}% + \end{multicols}% + }{\ifboolKV[ClesThales]{Entier}{\TThalesCalculsE[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}{\TThalesCalculsD[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}}}% + }% + }% }% }% %%%% @@ -4984,31 +5300,40 @@ vardef Positions(expr Step)= % #4 longueur AB % #5 longueur AF % #6 longueur AC - \ifboolKV[ClesThales]{Figure}{% + \ifboolKV[ClesThales]{FigureSeule}{% \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% - \begin{multicols}{2} - {\em La figure est donnée à titre indicatif.} - \[\MPFigReciThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}\] - \par\columnbreak\par - \ReciThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par - \ReciThalesCalculs[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8} - \end{multicols} - }{\ifboolKV[ClesThales]{Figurecroisee}{% - \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN] - \begin{minipage}{0.4\linewidth} - {\em La figure est donnée à titre indicatif.} - \[\MPFigReciThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}\] - \end{minipage} - \hfill - \begin{minipage}{0.55\linewidth} - \ReciThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par - \ReciThalesCalculs[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8} - \end{minipage}\\% - }{\ReciThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par - \ReciThalesCalculs[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8} - } - } -} + \MPFigReciThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% + }{\ifboolKV[ClesThales]{FigurecroiseeSeule}{% + \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% + \MPFigReciThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% + }{% + \ifboolKV[ClesThales]{Figure}{% + \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% + \begin{multicols}{2} + {\em La figure est donnée à titre indicatif.} + \[\MPFigReciThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\] + \par\columnbreak\par + \ReciThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par + \ReciThalesCalculs[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8} + \end{multicols} + }{\ifboolKV[ClesThales]{Figurecroisee}{% + \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN] + \begin{minipage}{0.4\linewidth} + {\em La figure est donnée à titre indicatif.} + \[\MPFigReciThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\] + \end{minipage} + \hfill + \begin{minipage}{0.55\linewidth} + \ReciThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par + \ReciThalesCalculs[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}% + \end{minipage}\\% + }{\ReciThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par + \ReciThalesCalculs[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}% + }% + }% + }% + }% +}% \newcommand{\Thales}[8][]{% \useKVdefault[ClesThales]% @@ -5016,18 +5341,48 @@ vardef Positions(expr Step)= \ifboolKV[ClesThales]{Reciproque}{% \ReciproqueThales[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}% }{% - \ifboolKV[ClesThales]{Redaction}{% - \TTThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}% + \ifboolKV[ClesThales]{FigureSeule}{% + \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% + \MPFigThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% }{% - \TThales[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}% - } + \ifboolKV[ClesThales]{FigurecroiseeSeule}{% + \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% + \MPFigThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}% + }{% + \ifboolKV[ClesThales]{Redaction}{% + \ifboolKV[ClesThales]{Figure}{% + \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% + \begin{multicols}{2} + {\em La figure est donnée à titre indicatif.}% + \[\MPFigThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]% + \par\columnbreak\par% + \TTThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}% + \end{multicols}% + }{% + \ifboolKV[ClesThales]{Figurecroisee}{% + \StrMid{#2}{1}{1}[\NomA]\StrMid{#2}{2}{2}[\NomB]\StrMid{#2}{3}{3}[\NomC]\StrMid{#2}{4}{4}[\NomM]\StrMid{#2}{5}{5}[\NomN]% + \begin{multicols}{2} + {\em La figure est donnée à titre indicatif.}% + \[\MPFigThalesCroisee{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}{\useKV[ClesThales]{Angle}}\]% + \par\columnbreak\par% + \TTThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}% + \end{multicols} + }{% + \TTThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}% + } + } + }{% + \TThales[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}% + }% + }% + }% }% }% -%%%%%%%%%%%%%%%% -%% Trigonométrie -%%%%%%%%%%%%%%%% -\def\MPFigTrigo#1#2#3#4#5#6#7{% +%%% +% Trigonométrie +%%% +\def\MPFigTrigo#1#2#3#4#5#6#7#8{% \ifluatex \mplibcodeinherit{enable} \mplibforcehmode @@ -5042,11 +5397,9 @@ vardef Positions(expr Step)= O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour éventuellement moins de lassitude :) - numeric Angle; - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); + A:=A rotatedabout(O,#8); + B:=B rotatedabout(O,#8); + C:=C rotatedabout(O,#8); % On définit le centre du cercle inscrit (I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C]; (I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C]; @@ -5065,8 +5418,6 @@ vardef Positions(expr Step)= picture MAngle; MAngle=image( draw (cc shifted A); - % draw (cc shifted B); - % draw (cc shifted C); ); draw MAngle; clip currentpicture to triangle; @@ -5084,15 +5435,15 @@ vardef Positions(expr Step)= else: if angle(1/2[A,C]-B)>0: if #6=0: - label(btex ? etex rotated angle(C-A),1.1[B,1/2[A,C]]); + label(btex ? etex,1.1[B,1/2[A,C]]); else: - label(btex \num{#6} etex rotated angle(C-A),1.1[B,1/2[A,C]]); + label(btex \num{#6} etex,1.1[B,1/2[A,C]]); fi; else: if #6=0: - label(btex ? etex rotated angle(A-C),1.1[B,1/2[A,C]]); + label(btex ? etex,1.1[B,1/2[A,C]]); else: - label(btex \num{#6} etex rotated angle(A-C),1.1[B,1/2[A,C]]); + label(btex \num{#6} etex,1.1[B,1/2[A,C]]); fi; fi; fi; @@ -5100,15 +5451,15 @@ vardef Positions(expr Step)= else: if angle(1/2[B,C]-A)>0: if #4=0: - label(btex ? etex rotated(angle(B-C)),1/2[B,C]-decalage*(unitvector(A-B))); + label(btex ? etex,1/2[B,C]-decalage*(unitvector(A-B))); else: - label(btex \num{#4} etex rotated(angle(B-C)),1/2[B,C]-decalage*(unitvector(A-B))); + label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B))); fi; else: if #4=0: - label(btex ? etex rotated(angle(C-B)),1/2[B,C]-decalage*(unitvector(A-B))); + label(btex ? etex,1/2[B,C]-decalage*(unitvector(A-B))); else: - label(btex \num{#4} etex rotated(angle(C-B)),1/2[B,C]-decalage*(unitvector(A-B))); + label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B))); fi; fi; fi; @@ -5116,15 +5467,15 @@ vardef Positions(expr Step)= else: if angle(1/2[A,B]-C)>0: if #5=0: - label(btex ? etex rotated angle(A-B),1/2[A,B]-decalage*(unitvector(C-B))); + label(btex ? etex,1/2[A,B]-decalage*(unitvector(C-B))); else: - label(btex \num{#5} etex rotated angle(A-B),1/2[A,B]-decalage*(unitvector(C-B))); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); fi; else: if #5=0: - label(btex ? etex rotated angle(B-A),1/2[A,B]-decalage*(unitvector(C-B))); + label(btex ? etex,1/2[A,B]-decalage*(unitvector(C-B))); else: - label(btex \num{#5} etex rotated angle(B-A),1/2[A,B]-decalage*(unitvector(C-B))); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); fi; fi; fi; @@ -5142,10 +5493,9 @@ vardef Positions(expr Step)= O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour éventuellement moins de lassitude :) - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); + A:=A rotatedabout(O,#8); + B:=B rotatedabout(O,#8); + C:=C rotatedabout(O,#8); % On définit le centre du cercle inscrit (I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C]; (I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C]; @@ -5231,7 +5581,7 @@ vardef Positions(expr Step)= \fi } -\def\MPFigTrigoAngle#1#2#3#4#5#6{% +\def\MPFigTrigoAngle#1#2#3#4#5#6#7{% % #1 A % #2 B % #3 C @@ -5252,12 +5602,10 @@ vardef Positions(expr Step)= O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour éventuellement moins de lassitude :) - numeric Anglelua; - Anglelua=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Anglelua); - B:=B rotatedabout(O,Anglelua); - C:=C rotatedabout(O,Anglelua); - % On définit le centre du cercle inscrit + A:=A rotatedabout(O,#7); + B:=B rotatedabout(O,#7); + C:=C rotatedabout(O,#7); + % On définit le centre du cercle inscrit (I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C]; (I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C]; %on dessine à main levée :) @@ -5275,34 +5623,32 @@ vardef Positions(expr Step)= picture MAngle; MAngle=image( draw (cc shifted A); -% draw (cc shifted B); -% draw (cc shifted C); ); draw MAngle; clip currentpicture to triangle; draw A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; draw B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; draw C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; - %on labelise + % on labelise label(btex #1 etex,1.15[O,A]); label(btex #2 etex,1.15[O,B]); label(btex #3 etex,1.15[O,C]); label(btex ? etex,A+0.95u*unitvector(I-A)); decalage:=3mm; if angle(1/2[A,C]-B)>0: - label(btex \num{#6} etex rotated angle(C-A),1.1[B,1/2[A,C]]); + label(btex \num{#6} etex,1.1[B,1/2[A,C]]); else: - label(btex \num{#6} etex rotated angle(A-C),1.1[B,1/2[A,C]]); + label(btex \num{#6} etex,1.1[B,1/2[A,C]]); fi; if angle(1/2[B,C]-A)>0: - label(btex \num{#4} etex rotated(angle(B-C)),1/2[B,C]-decalage*(unitvector(A-B))); + label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B))); else: - label(btex \num{#4} etex rotated(angle(C-B)),1/2[B,C]-decalage*(unitvector(A-B))); + label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B))); fi; if angle(1/2[A,B]-C)>0: - label(btex \num{#5} etex rotated angle(A-B),1/2[A,B]-decalage*(unitvector(C-B))); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); else: - label(btex \num{#5} etex rotated angle(B-A),1/2[A,B]-decalage*(unitvector(C-B))); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); fi; \end{mplibcode} \mplibcodeinherit{disable} @@ -5318,10 +5664,9 @@ vardef Positions(expr Step)= O - .5[A,B] = whatever * (B-A) rotated 90; O - .5[B,C] = whatever * (C-B) rotated 90; % On tourne pour éventuellement moins de lassitude :) - Angle=uniformdeviate(180);%Caractère aléatoire - A:=A rotatedabout(O,Angle); - B:=B rotatedabout(O,Angle); - C:=C rotatedabout(O,Angle); + A:=A rotatedabout(O,#7); + B:=B rotatedabout(O,#7); + C:=C rotatedabout(O,#7); % On définit le centre du cercle inscrit (I-C) rotated ((angle(A-C)-angle(B-C))/2) shifted C=whatever[A,C]; (I-B) rotated ((angle(C-B)-angle(A-B))/2) shifted B=whatever[B,C]; @@ -5340,8 +5685,6 @@ vardef Positions(expr Step)= picture MAngle; MAngle=image( draw (cc shifted A); -% draw (cc shifted B); -% draw (cc shifted C); ); draw MAngle; clip currentpicture to triangle; @@ -5355,25 +5698,25 @@ vardef Positions(expr Step)= label(btex ? etex,A+0.95u*unitvector(I-A)); decalage:=3mm; if angle(1/2[A,C]-B)>0: - label(btex \num{#6} etex rotated angle(C-A),1.1[B,1/2[A,C]]); + label(btex \num{#6} etex,1.1[B,1/2[A,C]]); else: - label(btex \num{#6} etex rotated angle(A-C),1.1[B,1/2[A,C]]); + label(btex \num{#6} etex,1.1[B,1/2[A,C]]); fi; if angle(1/2[B,C]-A)>0: - label(btex \num{#4} etex rotated(angle(B-C)),1/2[B,C]-decalage*(unitvector(A-B))); + label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B))); else: - label(btex \num{#4} etex rotated(angle(C-B)),1/2[B,C]-decalage*(unitvector(A-B))); + label(btex \num{#4} etex,1/2[B,C]-decalage*(unitvector(A-B))); fi; if angle(1/2[A,B]-C)>0: - label(btex \num{#5} etex rotated angle(A-B),1/2[A,B]-decalage*(unitvector(C-B))); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); else: - label(btex \num{#5} etex rotated angle(B-A),1/2[A,B]-decalage*(unitvector(C-B))); + label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); fi; \end{mpost} \fi } -\setKVdefault[ClesTrigo]{Angle=false,Propor=false,Figure=false,Precision=2,Unite=cm,Sinus=false,Cosinus=false,Tangente=false}% +\setKVdefault[ClesTrigo]{Angle=0,Propor=false,Figure=false,FigureSeule=false,Precision=2,Unite=cm,Sinus=false,Cosinus=false,Tangente=false}% \newcommand\TrigoCalculs[5][]{% \setKV[ClesTrigo]{#1}% @@ -5381,18 +5724,19 @@ vardef Positions(expr Step)= % #2 Nom du triangle ABC, rectangle en B, angle connu ou pas : BAC % #3 Longueur % #4 Longueur - %#5 angle + % #5 angle % On définit les points \StrMid{#2}{1}{1}[\NomA]% \StrMid{#2}{2}{2}[\NomB]% \StrMid{#2}{3}{3}[\NomC]% - Dans le triangle $\NomA\NomB\NomC$, rectangle en $\NomB$, on a : + Dans le triangle $\NomA\NomB\NomC$, rectangle en $\NomB$, on a :% \ifboolKV[ClesTrigo]{Cosinus}{% \ifx\bla#3\bla%on calcule le côté adjacent - \ifboolKV[ClesTrigo]{Propor}{% - \begin{align*} - \NomA\NomC\times\cos(\widehat{\NomB\NomA\NomC})&=\NomA\NomB\\ - \num{#4}\times\cos(\ang{#5})&=\NomA\NomB\\ + \xdef\ResultatTrigo{\fpeval{round(\fpeval{#4*cosd(#5)},\useKV[ClesTrigo]{Precision})}}% + \ifboolKV[ClesTrigo]{Propor}{% + \begin{align*} + \NomA\NomC\times\cos(\widehat{\NomB\NomA\NomC})&=\NomA\NomB\\ + \num{#4}\times\cos(\ang{#5})&=\NomA\NomB\\ \num{\fpeval{round(\fpeval{#4*cosd(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}&\IfInteger{\fpeval{round(\fpeval{#4*cosd(#5)},2)}}{=}{\approx}\NomA\NomB% \end{align*}% }{% @@ -5400,12 +5744,12 @@ vardef Positions(expr Step)= \cos(\widehat{\NomB\NomA\NomC})&=\frac{\NomA\NomB}{\NomA\NomC}\\ \cos(\ang{#5})&=\frac{\NomA\NomB}{\num{#4}}\\ \num{#4}\times\cos(\ang{#5})&=\NomA\NomB\\ - \num{\fpeval{round(\fpeval{#4*cosd(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}&\IfInteger{\fpeval{round(\fpeval{#4*cosd(#5)},2)}}{=}{\approx}\NomA\NomB% - \end{align*}% + \num{\fpeval{round(\fpeval{#4*cosd(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}&\IfInteger{\fpeval{round(\fpeval{#4*cosd(#5)},2)}}{=}{\approx}\NomA\NomB + \end{align*} }% - \xdef\ResultatTrigo{\fpeval{round(\fpeval{#4*cosd(#5)},\useKV[ClesTrigo]{Precision})}}% - \else + \else% \ifx\bla#4\bla%on calcule l'hypothénuse + \xdef\ResultatTrigo{\fpeval{round(\fpeval{#3/cosd(#5)},\useKV[ClesTrigo]{Precision})}}% \ifboolKV[ClesTrigo]{Propor}{% \begin{align*} \NomA\NomC\times\cos(\widehat{\NomB\NomA\NomC})&=\NomA\NomB\\ @@ -5421,8 +5765,8 @@ vardef Positions(expr Step)= \NomA\NomC&\IfInteger{\fpeval{round(\fpeval{#3/cosd(#5)},2)}}{=}{\approx}\num{\fpeval{round(\fpeval{#3/cosd(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}% \end{align*}% }% - \xdef\ResultatTrigo{\fpeval{round(\fpeval{#3/cosd(#5)},\useKV[ClesTrigo]{Precision})}}% \else%on calcule l'angle + \xdef\ResultatTrigo{\fpeval{round(\fpeval{acosd(#3/#4)})}}% \ifboolKV[ClesTrigo]{Propor}{% \begin{align*} \NomA\NomC\times\cos(\widehat{\NomB\NomA\NomC})&=\NomA\NomB\\ @@ -5437,12 +5781,12 @@ vardef Positions(expr Step)= \widehat{\NomB\NomA\NomC}&\IfInteger{\fpeval{round(\fpeval{acosd(#3/#4)},2)}}{=}{\approx}\ang{\fpeval{round(\fpeval{acosd(#3/#4)})}}% \end{align*}% }% - \xdef\ResultatTrigo{\fpeval{round(\fpeval{acosd(#3/#4)})}}% - \fi - \fi - }{} + \fi% + \fi% + }{}% \ifboolKV[ClesTrigo]{Sinus}{% \ifx\bla#3\bla%on calcule le côté opposé + \xdef\ResultatTrigo{\fpeval{round(\fpeval{#4*sind(#5)},\useKV[ClesTrigo]{Precision})}}% \ifboolKV[ClesTrigo]{Propor}{% \begin{align*} \NomA\NomC\times\sin(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\ @@ -5457,26 +5801,26 @@ vardef Positions(expr Step)= \num{\fpeval{round(\fpeval{#4*sind(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}&\IfInteger{\fpeval{round(\fpeval{#4*sind(#5)},2)}}{=}{\approx}\NomB\NomC% \end{align*}% }% - \xdef\ResultatTrigo{\fpeval{round(\fpeval{#4*sind(#5)},\useKV[ClesTrigo]{Precision})}}% \else \ifx\bla#4\bla%on calcule l'hypothénuse + \xdef\ResultatTrigo{\fpeval{round(\fpeval{#3/sind(#5)},\useKV[ClesTrigo]{Precision})}}% \ifboolKV[ClesTrigo]{Propor}{% - \begin{align*} - \NomA\NomC\times\sin(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\ - \NomA\NomC\times\sin(\ang{#5})&=\num{#3}\\ - \NomA\NomC&=\frac{\num{#3}}{\sin(\ang{#5})}\\ - \NomA\NomC&\IfInteger{\fpeval{round(\fpeval{#3/sind(#5)},2)}}{=}{\approx}\num{\fpeval{round(\fpeval{#3/sind(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}% - \end{align*}% - }{ - \begin{align*} - \sin(\widehat{\NomB\NomA\NomC})&=\frac{\NomB\NomC}{\NomA\NomC}\\ - \sin(\ang{#5})&=\frac{\num{#3}}{\NomA\NomC}\\ - \NomA\NomC&=\frac{\num{#3}}{\sin(\ang{#5})}\\ - \NomA\NomC&\IfInteger{\fpeval{round(\fpeval{#3/sind(#5)},2)}}{=}{\approx}\num{\fpeval{round(\fpeval{#3/sind(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}% - \end{align*}% - }% - \xdef\ResultatTrigo{\fpeval{round(\fpeval{#3/sind(#5)},\useKV[ClesTrigo]{Precision})}}% - \else%on calcule l'angle + \begin{align*} + \NomA\NomC\times\sin(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\ + \NomA\NomC\times\sin(\ang{#5})&=\num{#3}\\ + \NomA\NomC&=\frac{\num{#3}}{\sin(\ang{#5})}\\ + \NomA\NomC&\IfInteger{\fpeval{round(\fpeval{#3/sind(#5)},2)}}{=}{\approx}\num{\fpeval{round(\fpeval{#3/sind(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}% + \end{align*}% + }{% + \begin{align*} + \sin(\widehat{\NomB\NomA\NomC})&=\frac{\NomB\NomC}{\NomA\NomC}\\ + \sin(\ang{#5})&=\frac{\num{#3}}{\NomA\NomC}\\ + \NomA\NomC&=\frac{\num{#3}}{\sin(\ang{#5})}\\ + \NomA\NomC&\IfInteger{\fpeval{round(\fpeval{#3/sind(#5)},2)}}{=}{\approx}\num{\fpeval{round(\fpeval{#3/sind(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}% + \end{align*}% + }% + \else%on calcule l'angle + \xdef\ResultatTrigo{\fpeval{round(\fpeval{asind(#3/#4)})}}% \ifboolKV[ClesTrigo]{Propor}{% \begin{align*} \NomA\NomC\times\sin(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\ @@ -5491,12 +5835,12 @@ vardef Positions(expr Step)= \widehat{\NomB\NomA\NomC}&\IfInteger{\fpeval{round(\fpeval{asind(#3/#4)},2)}}{=}{\approx}\ang{\fpeval{round(\fpeval{asind(#3/#4)})}}% \end{align*}% }% - \xdef\ResultatTrigo{\fpeval{round(\fpeval{asind(#3/#4)})}}% - \fi - \fi - }{} + \fi% + \fi% + }{}% \ifboolKV[ClesTrigo]{Tangente}{% \ifx\bla#3\bla%on calcule le côté opposé + \xdef\ResultatTrigo{\fpeval{round(\fpeval{#4*tand(#5)},\useKV[ClesTrigo]{Precision})}}% \ifboolKV[ClesTrigo]{Propor}{% \begin{align*} \NomA\NomB\times\tan(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\% @@ -5511,26 +5855,26 @@ vardef Positions(expr Step)= \num{\fpeval{round(\fpeval{#4*tand(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}&\IfInteger{\fpeval{round(\fpeval{#4*tand(#5)},2)}}{=}{\approx}\NomB\NomC% \end{align*}% }% - \xdef\ResultatTrigo{\fpeval{round(\fpeval{#4*tand(#5)},\useKV[ClesTrigo]{Precision})}}% \else \ifx\bla#4\bla%on calcule l'adjacent + \xdef\ResultatTrigo{\fpeval{round(\fpeval{#3/tand(#5)},\useKV[ClesTrigo]{Precision})}}% \ifboolKV[ClesTrigo]{Propor}{% - \begin{align*} - \NomA\NomB\times\tan(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\ - \NomA\NomB\times\tan(\ang{#5})&=\num{#3}\\ - \NomA\NomB&=\frac{\num{#3}}{\tan(\ang{#5})}\\ - \NomA\NomB&\IfInteger{\fpeval{round(\fpeval{#3/tand(#5)},2)}}{=}{\approx}\num{\fpeval{round(\fpeval{#3/tand(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}% - \end{align*}% - }{ - \begin{align*} - \tan(\widehat{\NomB\NomA\NomC})&=\frac{\NomB\NomC}{\NomA\NomB}\\ - \tan(\ang{#5})&=\frac{\num{#3}}{\NomA\NomB}\\ - \NomA\NomB&=\frac{\num{#3}}{\tan(\ang{#5})}\\ - \NomA\NomB&\IfInteger{\fpeval{round(\fpeval{#3/tand(#5)},2)}}{=}{\approx}\num{\fpeval{round(\fpeval{#3/tand(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}% - \end{align*}% - }% - \xdef\ResultatTrigo{\fpeval{round(\fpeval{#3/tand(#5)},\useKV[ClesTrigo]{Precision})}}% + \begin{align*} + \NomA\NomB\times\tan(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\ + \NomA\NomB\times\tan(\ang{#5})&=\num{#3}\\ + \NomA\NomB&=\frac{\num{#3}}{\tan(\ang{#5})}\\ + \NomA\NomB&\IfInteger{\fpeval{round(\fpeval{#3/tand(#5)},2)}}{=}{\approx}\num{\fpeval{round(\fpeval{#3/tand(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}% + \end{align*}% + }{% + \begin{align*} + \tan(\widehat{\NomB\NomA\NomC})&=\frac{\NomB\NomC}{\NomA\NomB}\\ + \tan(\ang{#5})&=\frac{\num{#3}}{\NomA\NomB}\\ + \NomA\NomB&=\frac{\num{#3}}{\tan(\ang{#5})}\\ + \NomA\NomB&\IfInteger{\fpeval{round(\fpeval{#3/tand(#5)},2)}}{=}{\approx}\num{\fpeval{round(\fpeval{#3/tand(#5)},\useKV[ClesTrigo]{Precision})}}~\text{\useKV[ClesTrigo]{Unite}}% + \end{align*}% + }% \else%on calcule l'angle + \xdef\ResultatTrigo{\fpeval{round(\fpeval{atand(#3/#4)})}}% \ifboolKV[ClesTrigo]{Propor}{% \begin{align*} \NomA\NomB\times\tan(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\ @@ -5538,18 +5882,17 @@ vardef Positions(expr Step)= \tan(\widehat{\NomB\NomA\NomC})&=\frac{\num{#3}}{\num{#4}}\\ \widehat{\NomB\NomA\NomC}&\IfInteger{\fpeval{round(\fpeval{atand(#3/#4)},2)}}{=}{\approx}\ang{\fpeval{round(\fpeval{atand(#3/#4)})}}% \end{align*}% - }{ + }{% \begin{align*} \tan(\widehat{\NomB\NomA\NomC})&=\frac{\NomB\NomC}{\NomA\NomB}\\ \tan(\widehat{\NomB\NomA\NomC})&=\frac{\num{#3}}{\num{#4}}\\ \widehat{\NomB\NomA\NomC}&\IfInteger{\fpeval{round(\fpeval{atand(#3/#4)},2)}}{=}{\approx}\ang{\fpeval{round(\fpeval{atand(#3/#4)})}}% \end{align*}% }% - \xdef\ResultatTrigo{\fpeval{round(\fpeval{atand(#3/#4)})}}% - \fi - \fi - }{} -} + \fi% + \fi% + }{}% +}% \newcommand\Trigo[5][]{% \useKVdefault[ClesTrigo]% @@ -5557,77 +5900,114 @@ vardef Positions(expr Step)= % #1 Clés % #2 Nom du triangle ABC, rectangle en B, angle connu ou pas : BAC % #3 Longueur - % #4 Longueur ou angle en fonction du calcul à faire. Si longueur, #3<#4 + % #4 Longueur + % #5 angle % On définit les points \StrMid{#2}{1}{1}[\NomA]% \StrMid{#2}{2}{2}[\NomB]% \StrMid{#2}{3}{3}[\NomC]% % On rédige - \ifboolKV[ClesTrigo]{Figure}{% - \begin{multicols}{2}% - {\em La figure est donnée à titre indicatif.}% - \ifboolKV[ClesTrigo]{Angle}{%figure pour calculer un angle - \ifboolKV[ClesTrigo]{Cosinus}{% - \begin{center} - \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{}{#3}{#4} - \end{center} - }{}% - \ifboolKV[ClesTrigo]{Sinus}{% - \begin{center} - \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{#3}{}{#4} - \end{center} - }{}% - \ifboolKV[ClesTrigo]{Tangente}{% - \begin{center} - \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{#3}{#4}{} - \end{center} - }{}% - }{%figure pour calculer une longueur - \ifboolKV[ClesTrigo]{Cosinus}{% - \ifx#3\bla\bla%adjacent inconnu - \begin{center} - \MPFigTrigo{\NomA}{\NomB}{\NomC}{-1}{0}{#4}{#5} + \ifboolKV[ClesTrigo]{FigureSeule}{% + \ifx#5\bla\bla% + \ifboolKV[ClesTrigo]{Cosinus}{% + \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{}{#3}{#4}{\useKV[ClesTrigo]{Angle}} + }{}% + \ifboolKV[ClesTrigo]{Sinus}{% + \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{#3}{}{#4}{\useKV[ClesTrigo]{Angle}} + }{}% + \ifboolKV[ClesTrigo]{Tangente}{% + \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{#3}{#4}{}{\useKV[ClesTrigo]{Angle}} + }{}% + \else%}{%figure pour calculer une longueur + \ifboolKV[ClesTrigo]{Cosinus}{% + \ifx#3\bla\bla%adjacent inconnu + \MPFigTrigo{\NomA}{\NomB}{\NomC}{-1}{0}{#4}{#5}{\useKV[ClesTrigo]{Angle}} + \else + \MPFigTrigo{\NomA}{\NomB}{\NomC}{-1}{#3}{0}{#5}{\useKV[ClesTrigo]{Angle}} + \fi + }{}% + \ifboolKV[ClesTrigo]{Sinus}{% + \ifx#3\bla\bla%adjacent inconnu + \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{-1}{#4}{#5}{\useKV[ClesTrigo]{Angle}} + \else + \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{-1}{0}{#5}{\useKV[ClesTrigo]{Angle}} + \fi + }{}% + \ifboolKV[ClesTrigo]{Tangente}{% + \ifx#3\bla\bla%adjacent inconnu + \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{#4}{-1}{#5}{\useKV[ClesTrigo]{Angle}} + \else% + \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{0}{-1}{#5}{\useKV[ClesTrigo]{Angle}} + \fi% + }{}% + \fi% + }{% + \ifboolKV[ClesTrigo]{Figure}{% + \begin{multicols}{2}% + {\em La figure est donnée à titre indicatif.}% + \ifx#5\bla\bla% + \ifboolKV[ClesTrigo]{Cosinus}{% + \begin{center} + \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{}{#3}{#4}{\useKV[ClesTrigo]{Angle}} + \end{center} + }{}% + \ifboolKV[ClesTrigo]{Sinus}{% + \begin{center} + \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{#3}{}{#4}{\useKV[ClesTrigo]{Angle}} + \end{center} + }{}% + \ifboolKV[ClesTrigo]{Tangente}{% + \begin{center} + \MPFigTrigoAngle{\NomA}{\NomB}{\NomC}{#3}{#4}{}{\useKV[ClesTrigo]{Angle}} + \end{center} + }{}% + \else%}{%figure pour calculer une longueur + \ifboolKV[ClesTrigo]{Cosinus}{% + \ifx#3\bla\bla%adjacent inconnu + \begin{center} + \MPFigTrigo{\NomA}{\NomB}{\NomC}{-1}{0}{#4}{#5}{\useKV[ClesTrigo]{Angle}} \end{center} \else \begin{center} - \MPFigTrigo{\NomA}{\NomB}{\NomC}{-1}{#3}{0}{#5} + \MPFigTrigo{\NomA}{\NomB}{\NomC}{-1}{#3}{0}{#5}{\useKV[ClesTrigo]{Angle}} \end{center} \fi }{}% \ifboolKV[ClesTrigo]{Sinus}{% \ifx#3\bla\bla%adjacent inconnu \begin{center} - \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{-1}{#4}{#5} + \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{-1}{#4}{#5}{\useKV[ClesTrigo]{Angle}} \end{center} \else \begin{center} - \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{-1}{0}{#5} + \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{-1}{0}{#5}{\useKV[ClesTrigo]{Angle}} \end{center} \fi }{}% \ifboolKV[ClesTrigo]{Tangente}{% \ifx#3\bla\bla%adjacent inconnu \begin{center} - \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{#4}{-1}{#5} + \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{#4}{-1}{#5}{\useKV[ClesTrigo]{Angle}} \end{center} \else% \begin{center} - \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{0}{-1}{#5} + \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{0}{-1}{#5}{\useKV[ClesTrigo]{Angle}} \end{center} \fi% }{}% - }% - \par\columnbreak\par - \TrigoCalculs{#2}{#3}{#4}{#5}% - \end{multicols} - }{% - \TrigoCalculs{#2}{#3}{#4}{#5}% + \fi% + \par\columnbreak\par + \TrigoCalculs[#1]{#2}{#3}{#4}{#5}% + \end{multicols} + }{% + \TrigoCalculs[#1]{#2}{#3}{#4}{#5}% + }% }% }% -%%%%%%%%%%%%%%% -%% Statistiques -%%%%%%%%%%%%%%% +%%% +% Statistiques +%%% \newcommand\NbDonnees{} \newcommand\SommeDonnees{}% \newcommand\EffectifTotal{}% @@ -5638,104 +6018,183 @@ vardef Positions(expr Step)= \newcommand\DonneeMin{}% \newcommand\EffectifMax{}% -\setKVdefault[ClesStat]{Tableau=false,Frequence=false,EffectifTotal=false,Etendue=false,Moyenne=false,SET=false,Mediane=false,Total=false,Concret=false,Unite={},Largeur=1cm,Precision=2,Donnee=Valeurs,Effectif=Effectif(s),Origine=0,Angle=false,SemiAngle=false,Qualitatif=false,TableauVide=false,Graphique=false,Batons=true,Unitex=0.5,Unitey=0.5,Rayon=3cm,AffichageAngle=false,Liste=false,ECC=false,Coupure=10,ColorTab=gray!15} +\setKVdefault[ClesStat]{ColVide=0,EffVide=false,% +FreqVide=false,AngVide=false,ECCVide=false,TotalVide=false,Sondage=false,% +Tableau=false,Stretch=1,Frequence=false,EffectifTotal=false,% +Etendue=false,Moyenne=false,SET=false,Mediane=false,Total=false,Concret=false,% +Unite={},Largeur=1cm,Precision=2,Donnee=Valeurs,Effectif=Effectif,Origine=0,Angle=false,SemiAngle=false,Qualitatif=false,TableauVide=false,Graphique=false,Batons=true,Unitex=0.5,Unitey=0.5,Rayon=3cm,AffichageAngle=false,Liste=false,ECC=false,Coupure=10,CouleurTab=gray!15,ListeCouleurs={white},Hachures=false,Inverse=false,AbscisseRotation=false} % La construction du tableau \def\addtotok#1#2{#1\expandafter{\the#1#2}} \newtoks\tabtoksa\newtoks\tabtoksb\newtoks\tabtoksc -\def\updatetoks#1/#2\nil{\addtotok\tabtoksa{&\num{#1}}\addtotok\tabtoksb{&\num{#2}}} -\def\buildtab{% +\def\updatetoks#1/#2\nil{\addtotok\tabtoksa{\ifboolKV[ClesStat]{Qualitatif}{}{&\num{#1}}}\addtotok\tabtoksb{&\num{#2}}} +\def\buildtab{% %%Tableau sans total \tabtoksa{\useKV[ClesStat]{Donnee}}\tabtoksb{\useKV[ClesStat]{Effectif}}% \foreachitem\compteur\in\ListeComplete{\expandafter\updatetoks\compteur\nil}% \[% - \begin{tabular}{|>{\columncolor{\useKV[ClesStat]{ColorTab}}}c|*{\number\numexpr\ListeCompletelen}{>{\centering\arraybackslash}p{\useKV[ClesStat]{Largeur}}|}}% + %\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{\ListeComplete[##1,2]}% + \renewcommand{\arraystretch}{\useKV[ClesStat]{Stretch}}% + \begin{tabular}{|>{\columncolor{\useKV[ClesStat]{CouleurTab}}}c|*{\number\numexpr\ListeCompletelen}{>{\centering\arraybackslash}p{\useKV[ClesStat]{Largeur}}|}}% \hline% - \rowcolor{\useKV[ClesStat]{ColorTab}}\the\tabtoksa\\\hline% - \the\tabtoksb\\\hline% - \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculFrequence{##1}}}\\\hline}{}% - \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculAngle{##1}}}\\\hline}{}% - \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\CalculSemiAngle{##1}}\\\hline}{}% - \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculECC{##1}}}\\\hline}{}% - \end{tabular} + \rowcolor{\useKV[ClesStat]{CouleurTab}}\the\tabtoksa\\\hline% + \ifnum\number\numexpr\useKV[ClesStat]{ColVide}<1% + \ifboolKV[ClesStat]{EffVide}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&}}{\the\tabtoksb}\\\hline% + \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculAngle{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculSemiAngle{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}\\\hline}{}% + \end{tabular} + \else% + \ifnum\number\numexpr\useKV[ClesStat]{ColVide}>\ListeCompletelen% + \ifboolKV[ClesStat]{EffVide}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&}}{\the\tabtoksb}\\\hline% + \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculAngle{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculSemiAngle{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}\\\hline}{}% + \end{tabular} + \else% + \ifnum\number\numexpr\useKV[ClesStat]{ColVide}=1% + \ifboolKV[ClesStat]{EffVide}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&}}{\useKV[ClesStat]{Effectif}&\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{&\ListeComplete[##1,2]}}\\\hline% + \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)&\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})&\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculAngle{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})&\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculSemiAngle{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{ECC}{E.C.C.&\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}\\\hline}{}% + \end{tabular} + \else% + \ifnum\number\numexpr\useKV[ClesStat]{ColVide}=\ListeCompletelen% + \ifboolKV[ClesStat]{EffVide}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&}}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen-1}}\do{&\ListeComplete[##1,2]}}&\\\hline% + \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}&\\\hline}{}% + \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculAngle{##1}}}}&\\\hline}{}% + \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculSemiAngle{##1}}}}&\\\hline}{}% + \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}&\\\hline}{}% + \end{tabular} + \else% + \ifboolKV[ClesStat]{EffVide}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&}}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\number\numexpr\useKV[ClesStat]{ColVide}-1}}\do{&\ListeComplete[##1,2]}&\xintFor* ##1 in {\xintSeq {\number\numexpr\useKV[ClesStat]{ColVide}+1}{\ListeCompletelen}}\do{&\ListeComplete[##1,2]}}\\\hline% + \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\number\numexpr\useKV[ClesStat]{ColVide}-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}&\xintFor* ##1 in {\xintSeq {\number\numexpr\useKV[ClesStat]{ColVide}+1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\number\numexpr\useKV[ClesStat]{ColVide}-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculAngle{##1}}}}&\xintFor* ##1 in {\xintSeq {\number\numexpr\useKV[ClesStat]{ColVide}+1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculAngle{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\number\numexpr\useKV[ClesStat]{ColVide}-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculSemiAngle{##1}}}}&\xintFor* ##1 in {\xintSeq {\number\numexpr\useKV[ClesStat]{ColVide}+1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculSemiAngle{##1}}}}\\\hline}{}% + \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\number\numexpr\useKV[ClesStat]{ColVide}-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}&\xintFor* ##1 in {\xintSeq {\number\numexpr\useKV[ClesStat]{ColVide}+1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}\\\hline}{}% + \end{tabular} + \fi% + \fi% + \fi% + \fi% + \renewcommand{\arraystretch}{1}% \] } -\def\buildtabt{% +\def\buildtabt{% %%Tableau avec total \tabtoksa{\useKV[ClesStat]{Donnee}}\tabtoksb{\useKV[ClesStat]{Effectif}}% \foreachitem\compteur\in\ListeComplete{\expandafter\updatetoks\compteur\nil}% - \[% - \begin{tabular}{|>{\columncolor{\useKV[ClesStat]{ColorTab}}}c|*{\number\numexpr\ListeCompletelen+1}{>{\centering\arraybackslash}p{\useKV[ClesStat]{Largeur}}|}}% + \[% + \renewcommand{\arraystretch}{\useKV[ClesStat]{Stretch}}% + \begin{tabular}{|>{\columncolor{\useKV[ClesStat]{CouleurTab}}}c|*{\number\numexpr\ListeCompletelen+1}{>{\centering\arraybackslash}p{\useKV[ClesStat]{Largeur}}|}}% \hline% - \rowcolor{\useKV[ClesStat]{ColorTab}}\the\tabtoksa&Total\\\hline% - \the\tabtoksb&\ifboolKV[ClesStat]{TableauVide}{}{\num{\EffectifTotal}}% - \\\hline% - \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculFrequence{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{100}\\\hline}{}% - \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculAngle{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{360}\\\hline}{}% - \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculSemiAngle{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{180}\\\hline}{}% - \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculECC{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{\num{\EffectifTotal}}\\\hline}{}% + \rowcolor{\useKV[ClesStat]{CouleurTab}}\the\tabtoksa&Total\\\hline% + \ifnum\number\numexpr\useKV[ClesStat]{ColVide}<1% + \ifboolKV[ClesStat]{EffVide}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen+1}}\do{&}}{\the\tabtoksb&\ifboolKV[ClesStat]{TotalVide}{}{\num{\EffectifTotal}}}\\\hline% + \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{100}}}\\\hline}{}% + \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculAngle{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{360}}}\\\hline}{}% + \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculSemiAngle{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{180}}}\\\hline}{}% + \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\num{\EffectifTotal}}}}\\\hline}{}% \end{tabular} - \] -} - -\def\updatetoksq#1/#2\nil{\addtotok\tabtoksa{}\addtotok\tabtoksb{&\num{#2}}} -\def\buildtabq{% - \tabtoksa{\useKV[ClesStat]{Donnee}}\tabtoksb{\useKV[ClesStat]{Effectif}}% - \foreachitem\compteur\in\ListeComplete{\expandafter\updatetoksq\compteur\nil}% - \[% - \begin{tabular}{|>{\columncolor{\useKV[ClesStat]{ColorTab}}}c|*{\number\numexpr\ListeCompletelen}{>{\centering\arraybackslash}p{\useKV[ClesStat]{Largeur}}|}}% - \hline% - \rowcolor{\useKV[ClesStat]{ColorTab}}\the\tabtoksa\\\hline% - \the\tabtoksb\\\hline% - \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculFrequence{##1}}}\\\hline}{}% - \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculAngle{##1}}}\\\hline}{}% - \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculSemiAngle{##1}}}\\\hline}{}% - \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculECC{##1}}}\\\hline}{}% + \else% + \ifnum\number\numexpr\useKV[ClesStat]{ColVide}>\ListeCompletelen% + \ifboolKV[ClesStat]{EffVide}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen+1}}\do{&}}{\the\tabtoksb&\ifboolKV[ClesStat]{TotalVide}{}{\num{\EffectifTotal}}}\\\hline% + \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{100}}}\\\hline}{}% + \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculAngle{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{360}}}\\\hline}{}% + \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculSemiAngle{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{180}}}\\\hline}{}% + \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\num{\EffectifTotal}}}}\\\hline}{}% \end{tabular} - \] -} - -\def\buildtabqt{% - \tabtoksa{\useKV[ClesStat]{Donnee}}\tabtoksb{\useKV[ClesStat]{Effectif}}% - \foreachitem\compteur\in\ListeComplete{\expandafter\updatetoksq\compteur\nil}% - \[% - \begin{tabular}{|>{\columncolor{\useKV[ClesStat]{ColorTab}}}c|*{\number\numexpr\ListeCompletelen+1}{>{\centering\arraybackslash}p{\useKV[ClesStat]{Largeur}}|}}% - \hline% - \rowcolor{\useKV[ClesStat]{ColorTab}}\the\tabtoksa&Total\\\hline% - \the\tabtoksb&\num{\EffectifTotal}\\\hline% - \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculFrequence{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{100}\\\hline}{}% - \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculAngle{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{360}\\\hline}{}% - \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculSemiAngle{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{180}\\\hline}{}% - \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculECC{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{\num{\EffectifTotal}}\\\hline}{}% + \else% + \ifnum\number\numexpr\useKV[ClesStat]{ColVide}=1% + \ifboolKV[ClesStat]{EffVide}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen+1}}\do{&}}{\useKV[ClesStat]{Effectif}&\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{&\ListeComplete[##1,2]}&\ifboolKV[ClesStat]{TotalVide}{}{\num{\EffectifTotal}}}\\\hline% + \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)&\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{100}}}\\\hline}{}% + \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})&\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculAngle{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{360}}}\\\hline}{}% + \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})&\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculSemiAngle{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{180}}}\\\hline}{}% + \ifboolKV[ClesStat]{ECC}{E.C.C.&\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\num{\EffectifTotal}}}}\\\hline}{}% \end{tabular} + \else% + \ifnum\number\numexpr\useKV[ClesStat]{ColVide}=\ListeCompletelen% + \ifboolKV[ClesStat]{EffVide}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen+1}}\do{&}}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen-1}}\do{&\ListeComplete[##1,2]}&&\ifboolKV[ClesStat]{TotalVide}{}{\num{\EffectifTotal}}}\\\hline% + \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}&&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{100}}}\\\hline}{}% + \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculAngle{##1}}}}&&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{360}}}\\\hline}{}% + \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculSemiAngle{##1}}}}&&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{180}}}\\\hline}{}% + \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}&&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\num{\EffectifTotal}}}}\\\hline}{}% + \end{tabular} + \else% + \ifboolKV[ClesStat]{EffVide}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen+1}}\do{&}}{\useKV[ClesStat]{Effectif}\xintFor* ##1 in {\xintSeq {1}{\number\numexpr\useKV[ClesStat]{ColVide}-1}}\do{&\ListeComplete[##1,2]}&\xintFor* ##1 in {\xintSeq {\number\numexpr\useKV[ClesStat]{ColVide}+1}{\ListeCompletelen}}\do{&\ListeComplete[##1,2]}&\ifboolKV[ClesStat]{TotalVide}{}{\num{\EffectifTotal}}}\\\hline% + \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\number\numexpr\useKV[ClesStat]{ColVide}-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}&\xintFor* ##1 in {\xintSeq {\number\numexpr\useKV[ClesStat]{ColVide}+1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{\CalculFrequence{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{FreqVide}{}{100}}}\\\hline}{}% + \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\number\numexpr\useKV[ClesStat]{ColVide}-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculAngle{##1}}}}&\xintFor* ##1 in {\xintSeq {\number\numexpr\useKV[ClesStat]{ColVide}+1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculAngle{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{360}}}\\\hline}{}% + \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\number\numexpr\useKV[ClesStat]{ColVide}-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculSemiAngle{##1}}}}&\xintFor* ##1 in {\xintSeq {\number\numexpr\useKV[ClesStat]{ColVide}+1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{\CalculSemiAngle{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{AngVide}{}{180}}}\\\hline}{}% + \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\number\numexpr\useKV[ClesStat]{ColVide}-1}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}&\xintFor* ##1 in {\xintSeq {\number\numexpr\useKV[ClesStat]{ColVide}+1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\CalculECC{##1}}}}&\ifboolKV[ClesStat]{TotalVide}{}{\ifboolKV[ClesStat]{TableauVide}{}{\ifboolKV[ClesStat]{ECCVide}{}{\num{\EffectifTotal}}}}\\\hline}{}% + \end{tabular} + \fi% + \fi% + \fi% + \fi% + \renewcommand{\arraystretch}{1}% \] } % Pour construire le diagramme en bâtons \def\Updatetoks#1/#2\nil{\addtotok\toklistepoint{(#1,#2),}} -\def\buildgraph{% - \newtoks\toklistepoint +\newcommand\buildgraph[1][]{% + \newtoks\toklistepoint \foreachitem\compteur\in\ListeComplete{\expandafter\Updatetoks\compteur\nil}% - \[\MPStat{\useKV[ClesStat]{Unitex}}{\useKV[ClesStat]{Unitey}}{\the\toklistepoint}{\useKV[ClesStat]{Donnee}}{\useKV[ClesStat]{Effectif}}{\useKV[ClesStat]{Origine}}\]% + \[\MPStat[#1]{\useKV[ClesStat]{Unitex}}{\useKV[ClesStat]{Unitey}}{\the\toklistepoint}{\useKV[ClesStat]{Donnee}}{\useKV[ClesStat]{Effectif}}{\useKV[ClesStat]{Origine}}{\useKV[ClesStat]{AbscisseRotation}}\]% }% % Pour construire le diagramme en bâtons qualitatif \def\Updatetoksq#1/#2\nil{\addtotok\toklistepointq{"#1",#2,}} -\def\buildgraphq{% +\newcommand\buildgraphq[1][]{% \newtoks\toklistepointq - \toklistepointq{} \foreachitem\compteur\in\ListeComplete{\expandafter\Updatetoksq\compteur\nil} - \[\MPStatQ{2*\useKV[ClesStat]{Unitex}}{0.5*\useKV[ClesStat]{Unitey}}{\the\toklistepointq}{\useKV[ClesStat]{Donnee}}{\useKV[ClesStat]{Effectif}}{\useKV[ClesStat]{Origine}}\] + \[\MPStatQ[#1]{2*\useKV[ClesStat]{Unitex}}{0.5*\useKV[ClesStat]{Unitey}}{\the\toklistepointq}{\useKV[ClesStat]{Donnee}}{\useKV[ClesStat]{Effectif}}{\useKV[ClesStat]{Origine}}{\useKV[ClesStat]{AbscisseRotation}}\] } + +\def\UpdateCoul#1\nil{\addtotok\toklistecouleur{#1,}}% + % Pour construire le diagramme circulaire qualitatif \def\buildgraphcq#1{% \newtoks\toklistepointq% \toklistepointq{}% + \newtoks\toklistecouleur% + \toklistecouleur{}% + % \foreachitem\compteur\in\ListeComplete{\expandafter\Updatetoksq\compteur\nil}% + \xdef\ListeAvantCouleurs{\useKV[ClesStat]{ListeCouleurs}}% + \readlist*\ListeCouleur{\ListeAvantCouleurs}% + \foreachitem\couleur\in\ListeCouleur{\expandafter\UpdateCoul\couleur\nil}% \ifboolKV[ClesStat]{AffichageAngle}{% - \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{1}\]% + \ifboolKV[ClesStat]{Hachures}{% + \ifboolKV[ClesStat]{Inverse}{% + \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{1}{\the\toklistecouleur}{1}{1}\]% + }{% + \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{1}{\the\toklistecouleur}{1}{0}\]% + }% + }{% + \ifboolKV[ClesStat]{Inverse}{% + \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{1}{\the\toklistecouleur}{0}{1}\]% + }{% + \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{1}{\the\toklistecouleur}{0}{0}\]% + }% + }% }{% - \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{0}\]% + \ifboolKV[ClesStat]{Hachures}{% + \ifboolKV[ClesStat]{Inverse}{% + \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{0}{\the\toklistecouleur}{1}{1}\]% + }{% + \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{0}{\the\toklistecouleur}{1}{0}\]% + }% + }{% + \ifboolKV[ClesStat]{Inverse}{% + \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{0}{\the\toklistecouleur}{0}{1}\]% + }{% + \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{0}{\the\toklistecouleur}{0}{0}\]% + }% + }% }% }% @@ -5767,92 +6226,103 @@ vardef Positions(expr Step)= \num{\TotalECC}% } -% la construction du graphique -\def\MPStat#1#2#3#4#5#6{% +% la construction du graphique en bâtons pour quantitatif +\newcommand\MPStat[8][]{% \ifluatex \mplibforcehmode \begin{mplibcode} maxx:=0; maxy:=0; - unitex:=#1*cm; - unitey:=#2*cm; + unitex:=#2*cm; + unitey:=#3*cm; pair A[],B[],P[]; n:=0; vardef toto(text t)= for p_=t: if pair p_: n:=n+1; - P[n]=((xpart(p_)-(#6))*unitex,ypart(p_)*unitey); + P[n]=((xpart(p_)-(#7))*unitex,ypart(p_)*unitey); if xpart(p_)>maxx: - maxx:=xpart(p_)-(#6); + maxx:=xpart(p_)-(#7); fi; if ypart(p_)>maxy: maxy:=ypart(p_); fi; - A[n]=unitex*(xpart(p_)-(#6),0); + A[n]=unitex*(xpart(p_)-(#7),0); B[n]=unitey*(0,ypart(p_)); + if (#8): + label.bot(TEX("\num{"&decimal(xpart(p_))&"}") rotated 90,A[n]); + else : label.bot(TEX("\num{"&decimal(xpart(p_))&"}"),A[n]); + fi; label.lft(TEX("\num{"&decimal(ypart(p_))&"}"),B[n]); fi; endfor; enddef; - toto(#3); + toto(#4); for k=1 upto n: draw A[k]--P[k] withpen pencircle scaled 2bp; draw B[k]--P[k] dashed evenly; endfor; drawarrow (0,0)--unitex*(maxx+1,0); drawarrow (0,0)--unitey*(0,maxy+1); - label.lrt(btex #4 etex,unitex*(maxx+1,0)); - label.urt(btex #5 etex,unitey*(0,maxy+1)); + label.lrt(btex #5 etex,unitex*(maxx+1,0)); + label.urt(btex #6 etex,unitey*(0,maxy+1)); \end{mplibcode} \else + \mpxcommands{% + \setKV[ClesStat]{#1}% + } \begin{mpost} maxx:=0; maxy:=0; - unitex:=#1*cm; - unitey:=#2*cm; + unitex:=#2*cm; + unitey:=#3*cm; pair A[],B[],P[]; n:=0; vardef toto(text t)= for p_=t: if pair p_: n:=n+1; - P[n]=((xpart(p_)-(#6))*unitex,ypart(p_)*unitey); + P[n]=((xpart(p_)-(#7))*unitex,ypart(p_)*unitey); if xpart(p_)>maxx: - maxx:=xpart(p_)-(#6); + maxx:=xpart(p_)-(#7); fi; if ypart(p_)>maxy: maxy:=ypart(p_); fi; - A[n]=unitex*(xpart(p_)-(#6),0); + A[n]=unitex*(xpart(p_)-(#7),0); B[n]=unitey*(0,ypart(p_)); + if (#8): + label.bot(LATEX("\num{"&decimal(xpart(p_))&"}") rotated 90,A[n]); + else : label.bot(LATEX("\num{"&decimal(xpart(p_))&"}"),A[n]); + fi; label.lft(LATEX("\num{"&decimal(ypart(p_))&"}"),B[n]); fi; endfor; enddef; - toto(#3); + toto(#4); for k=1 upto n: draw A[k]--P[k] withpen pencircle scaled 2bp; draw B[k]--P[k] dashed evenly; endfor; drawarrow (0,0)--unitex*(maxx+1,0); drawarrow (0,0)--unitey*(0,maxy+1); - label.lrt(btex #4 etex,unitex*(maxx+1,0)); - label.urt(btex #5 etex,unitey*(0,maxy+1)); + label.lrt(\btex \useKV[ClesStat]{Donnee} etex,unitex*(maxx+1,0)); + label.urt(\btex \useKV[ClesStat]{Effectif} etex,unitey*(0,maxy+1)); \end{mpost} \fi } -% la construction du graphique qualitatif -\def\MPStatQ#1#2#3#4#5#6{% +% la construction du graphique en bâtons pour qualitatif +\newcommand\MPStatQ[8][]{% \ifluatex \mplibforcehmode \begin{mplibcode} maxy:=0; - unitex:=#1*cm; - unitey:=#2*cm; + unitex:=#2*cm; + unitey:=#3*cm; pair A[],B[],P[]; n:=0; vardef toto(text t)= @@ -5867,25 +6337,32 @@ vardef Positions(expr Step)= n:=n+1; else: A[n]=unitex*(n+1,0); + if (#8): label.bot(TEX(p_) rotated 90,A[n]); + else : + label.bot(TEX(p_),A[n]); + fi; fi; endfor; enddef; - toto(#3); + toto(#4); for k=0 upto n-1: draw A[k]--P[k] withpen pencircle scaled 2bp; draw B[k]--P[k] dashed evenly; endfor; drawarrow (0,0)--unitex*(n+1,0); drawarrow (0,0)--unitey*(0,maxy+1); - label.lrt(btex #4 etex,unitex*(n+1,0)); - label.urt(btex #5 etex,unitey*(0,maxy+1)); + label.lrt(btex #5 etex,unitex*(n+1,0)); + label.urt(btex #6 etex,unitey*(0,maxy+1)); \end{mplibcode} \else + \mpxcommands{% + \setKV[ClesStat]{#1}% + } \begin{mpost} maxy:=0; - unitex:=#1*cm; - unitey:=#2*cm; + unitex:=#2*cm; + unitey:=#3*cm; pair A[],B[],P[]; n:=0; vardef toto(text t)= @@ -5900,25 +6377,29 @@ vardef Positions(expr Step)= n:=n+1; else: A[n]=unitex*(n+1,0); + if (#8): label.bot(LATEX(p_) rotated 90,A[n]); + else : + label.bot(LATEX(p_),A[n]); + fi; fi; endfor; enddef; - toto(#3); + toto(#4); for k=0 upto n-1: draw A[k]--P[k] withpen pencircle scaled 2bp; draw B[k]--P[k] dashed evenly; endfor; drawarrow (0,0)--unitex*(n+1,0); drawarrow (0,0)--unitey*(0,maxy+1); - label.lrt(btex #4 etex,unitex*(n+1,0)); - label.urt(btex #5 etex,unitey*(0,maxy+1)); + label.lrt(\btex \useKV[ClesStat]{Donnee} etex,unitex*(n+1,0)); + label.urt(\btex \useKV[ClesStat]{Effectif} etex,unitey*(0,maxy+1)); \end{mpost} \fi } % la construction du graphique qualitatif -\def\MPStatCirculaireQ#1#2#3#4{% +\def\MPStatCirculaireQ#1#2#3#4#5#6#7{% \ifluatex \mplibforcehmode \begin{mplibcode} @@ -5930,13 +6411,20 @@ vardef Positions(expr Step)= ang[0]:=0; path cc; cc=(fullcircle scaled (2*#1)); - if #3=360: - draw cc; + % on récupère les couleurs + color Col[]; + n:=0; + for p_=#5: + n:=n+1; + Col[n]=p_; + endfor; + if #7=0: + A[0]=point(0) of cc; else: - draw (subpath(0,length cc/2) of cc)--cycle; + A[0]=point(180) of cc; fi; - A[0]=point(0) of cc; vardef toto(text t)= + n:=0; for p_=t: if numeric p_: n:=n+1; @@ -5951,28 +6439,65 @@ vardef Positions(expr Step)= for p_=t: if numeric p_: n:=n+1; + if #7=0: A[n]=A[n-1] rotatedabout(O,p_*(#3/total[N])); - draw A[n-1]--O--A[n]; + else: + A[n]=A[n-1] rotatedabout(O,-p_*(#3/total[N])); + fi; + %hachure ou pas ? + if #6=0: + fill (O--if #7=0:arccercle(A[n-1],A[n],O) else: + arccercle(A[n],A[n-1],O) fi--cycle) withcolor if unknown Col[n]: white else:Col[n] fi; + else: + draw + hachurage((O--if #7=0:arccercle(A[n-1],A[n],O) + else:arccercle(A[n],A[n-1],O) fi--cycle),p_*(#3/total[N]) if + (n mod 2)=0: +90 else: -90 fi,0.25,if (n mod 2)=0 : 0 else: 1 fi) + if #4=1: withcolor 0.5white fi; + fi; + draw A[n-1]--O--A[n] if #6=1: withpen pencircle scaled2 fi; % Affichage des angles associés if #4=1: if round(p_*(#3/total[N]))>15: if (n mod 2)=0: - marque_a:=0.9*20 + marque_a:=3.1*20 + else: + marque_a:=3.1*20/0.9 + fi; + if #6=1: + if #7=0: + undraw + Codeangle(A[n-1],O,A[n],0,(((TEX("\ang{"&decimal(round(p_*(#3/total[N])))&"}"))))); + else: + undraw + Codeangle(A[n],O,A[n-1],0,(((TEX("\ang{"&decimal(round(p_*(#3/total[N])))&"}"))))); + fi; + fill cercles(w shifted(marque_ang*unitvector(w-O)),3mm) withcolor + blanc; + fi; + if #7=0: + draw + Codeangle(A[n-1],O,A[n],0,(((TEX("\ang{"&decimal(round(p_*(#3/total[N])))&"}"))))); else: - marque_a:=1.1*20/0.9 + draw + Codeangle(A[n],O,A[n-1],0,(((TEX("\ang{"&decimal(round(p_*(#3/total[N])))&"}"))))); fi; - draw Codeangle(A[n-1],O,A[n],0,(((TEX("\ang{"&decimal(round(p_*(#3/total[N])))&"}")) scaled 0.5))); fi; fi; % fi; endfor; + if #3=360: + draw cc if #6=1: withpen pencircle scaled2 fi; + else: + draw (subpath(0,length cc/2) of cc)--cycle if #6=1: withpen pencircle scaled2 fi;; + fi; n:=0; path cd[]; for p_=t: if string p_: n:=n+1; - C[n]=A[n-1] rotatedabout(O,(ang[n]-ang[n-1])/2); + C[n]=A[n-1] rotatedabout(O,if #7=1:-1* fi(ang[n]-ang[n-1])/2); draw 0.95[O,C[n]]--1.05[O,C[n]]; C[n]:=1.05[O,C[n]]; if (xpart(C[n])>xpart(O)) and (ypart(C[n])>ypart(O)): @@ -6002,7 +6527,7 @@ vardef Positions(expr Step)= toto(#2); \end{mplibcode} \else - \begin{mpost}[mpsettings={input PfC-Geometrie;}] + \begin{mpost}%[mpsettings={input PfC-Geometrie;}] pair A[],O,B[],C[],D[]; O=(0,0); n:=0; @@ -6011,13 +6536,20 @@ vardef Positions(expr Step)= ang[0]:=0; path cc; cc=(fullcircle scaled (2*#1)); - if #3=360: - draw cc; + % on récupère les couleurs + color Col[]; + n:=0; + for p_=#5: + n:=n+1; + Col[n]=p_; + endfor; + if #7=0: + A[0]=point(0) of cc; else: - draw (subpath(0,length cc/2) of cc)--cycle; + A[0]=point(180) of cc; fi; - A[0]=point(0) of cc; vardef toto(text t)= + n:=0; for p_=t: if numeric p_: n:=n+1; @@ -6032,28 +6564,65 @@ vardef Positions(expr Step)= for p_=t: if numeric p_: n:=n+1; + if #7=0: A[n]=A[n-1] rotatedabout(O,p_*(#3/total[N])); - draw A[n-1]--O--A[n]; + else: + A[n]=A[n-1] rotatedabout(O,-p_*(#3/total[N])); + fi; + %hachure ou pas ? + if #6=0: + fill (O--if #7=0:arccercle(A[n-1],A[n],O) else: + arccercle(A[n],A[n-1],O) fi--cycle) withcolor if unknown Col[n]: white else:Col[n] fi; + else: + draw + hachurage((O--if #7=0:arccercle(A[n-1],A[n],O) + else:arccercle(A[n],A[n-1],O) fi--cycle),p_*(#3/total[N]) if + (n mod 2)=0: +90 else: -90 fi,0.25,if (n mod 2)=0 : 0 else: 1 fi) + if #4=1: withcolor 0.5white fi; + fi; + draw A[n-1]--O--A[n] if #6=1: withpen pencircle scaled2 fi; % Affichage des angles associés if #4=1: if round(p_*(#3/total[N]))>15: if (n mod 2)=0: - marque_a:=0.9*20 + marque_a:=3.1*20 + else: + marque_a:=3.1*20/0.9 + fi; + if #6=1: + if #7=0: + undraw + Codeangle(A[n-1],O,A[n],0,(((LATEX("\ang{"&decimal(round(p_*(#3/total[N])))&"}"))))); + else: + undraw + Codeangle(A[n],O,A[n-1],0,(((LATEX("\ang{"&decimal(round(p_*(#3/total[N])))&"}"))))); + fi; + fill cercles(w shifted(marque_ang*unitvector(w-O)),3mm) withcolor + blanc; + fi; + if #7=0: + draw + Codeangle(A[n-1],O,A[n],0,(((LATEX("\ang{"&decimal(round(p_*(#3/total[N])))&"}"))))); else: - marque_a:=1.1*20/0.9 + draw + Codeangle(A[n],O,A[n-1],0,(((LATEX("\ang{"&decimal(round(p_*(#3/total[N])))&"}"))))); fi; - draw Codeangle(A[n-1],O,A[n],0,(((LATEX("\ang{"&decimal(round(p_*(#3/total[N])))&"}")) scaled 0.5))); fi; fi; % fi; endfor; + if #3=360: + draw cc if #6=1: withpen pencircle scaled2 fi; + else: + draw (subpath(0,length cc/2) of cc)--cycle if #6=1: withpen pencircle scaled2 fi;; + fi; n:=0; path cd[]; for p_=t: if string p_: n:=n+1; - C[n]=A[n-1] rotatedabout(O,(ang[n]-ang[n-1])/2); + C[n]=A[n-1] rotatedabout(O,if #7=1:-1* fi(ang[n]-ang[n-1])/2); draw 0.95[O,C[n]]--1.05[O,C[n]]; C[n]:=1.05[O,C[n]]; if (xpart(C[n])>xpart(O)) and (ypart(C[n])>ypart(O)): @@ -6089,8 +6658,16 @@ vardef Positions(expr Step)= \DTLgnewdb{mtdb}% \dtlexpandnewvalue% \newcount\nbdonnees% - - +% +\def\AjoutListEEaa#1\nil{\addtotok\tabtoksEEa{#1,}}% +\def\AjoutListEEab#1\nil{\addtotok\tabtoksEEa{#1/}}% +\def\AjoutListEEb#1\nil{\addtotok\tabtoksEEb{#1,}}% +\def\AjoutListEEx#1\nil{\addtotok\tabtoksEE{#1,}}% +\def\AjoutListEEy#1\nil{\addtotok\tabtoksEE{#1/}}% + +\DTLgnewdb{mtdbEE}% +\DTLgnewdb{mtdbEEqual}% +% \newcommand\Stat[2][]{% \useKVdefault[ClesStat]% \setKV[ClesStat]{#1}% @@ -6104,11 +6681,89 @@ vardef Positions(expr Step)= }% \readlist*\ListeComplete{\foo}% \setKV[ClesStat]{Qualitatif}% + }{ + \ifboolKV[ClesStat]{Sondage}{% + \setsepchar{,}\ignoreemptyitems% + \readlist*\Liste{#2}% + % "liste vide" + \newtoks\tabtoksEEa% + \tabtoksEEa{}% + % + % "liste vide" + \newtoks\tabtoksEEb% + \tabtoksEEb{}% + % + \readlist*\ListeSansDoublonsEE{999}% %% Pour ne pas avoir une liste vide + % + \newcount\cmptEE% + \newcount\PasNumEE% %% Permettra de savoir si ce sondage est qualitatif ou quantitatif + \PasNumEE=0\relax% + \DTLcleardb{mtdbEE}% + % on range les resultats du sondage par ordre croissant. + \foreachitem\x\in\Liste{% + \DTLnewrow{mtdbEE}% + \DTLnewdbentry{mtdbEE}{Numeric}{\x}% + }% + \dtlsort{Numeric}{mtdbEE}{\dtlicompare}% + \DTLforeach{mtdbEE}{\nba=Numeric}{% + \IfDecimal{\nba}{}{\PasNumEE=\numexpr\PasNumEE+1\relax}% + \cmptEE=0\relax% + \foreachitem\nbb\in\ListeSansDoublonsEE{% + \ifthenelse{\equal{\nba}{\nbb}}{\cmptEE=\numexpr\cmptEE+1\relax}{}% + }% + \ifthenelse{\equal{\the\cmptEE}{0}}{% + \expandafter\AjoutListEEb\nba\nil% + \xdef\listEEa{\the\tabtoksEEb}% + \ignoreemptyitems% + \setsepchar{,}% + \readlist*\ListeSansDoublonsEE\listEEa% %%% Enlève tous les élements + %%% identiques de Liste + }{}% + }% + \foreachitem\nba\in\ListeSansDoublonsEE{% + \cmptEE=0\relax% + \DTLforeach{mtdbEE}{\nbb=Numeric}{% + \ifthenelse{\equal{\nba}{\nbb}}{\cmptEE=\numexpr\cmptEE+1\relax}{}% + }% + \expandafter\AjoutListEEab\nba\nil% + \expandafter\AjoutListEEaa\the\cmptEE\nil% %%% Compte tous les élements + %%% identiques de Liste + }% + \xdef\listEEb{\the\tabtoksEEa} + \ignoreemptyitems% + \setsepchar[*]{,*/} + \readlist*\ListeComplete\listEEb% + % + \ifthenelse{\equal{\the\PasNumEE}{0}}{\setKV[ClesStat]{Quantitatif}}{\setKV[ClesStat]{Qualitatif}}% }{% + \ifboolKV[ClesStat]{Qualitatif}{% % % on lit la liste écrite sous la forme valeur/effectif \setsepchar[*]{,*/}\ignoreemptyitems% \readlist*\ListeComplete{#2}% - } + }{% Dans le qualitatif, on trie d'abord les valeurs. + \setsepchar[*]{,*/}\ignoreemptyitems% + \readlist*\ListeInitiale{#2}% +% "liste vide" + \newtoks\tabtoksEE% + \tabtoksEE{}% + \DTLcleardb{mtdbEEqual}% + \foreachitem\x\in\ListeInitiale{% + \DTLnewrow{mtdbEEqual}% + \itemtomacro\ListeInitiale[\xcnt,1]\x% + \DTLnewdbentry{mtdbEEqual}{Val}{\x}% + \itemtomacro\ListeInitiale[\xcnt,2]\y% + \DTLnewdbentry{mtdbEEqual}{Eff}{\y}% + }% + \dtlsort{Val}{mtdbEEqual}{\dtlicompare}% + \DTLforeach{mtdbEEqual}{\Val=Val,\Eff=Eff}{% + \expandafter\AjoutListEEy\Val\nil% + \expandafter\AjoutListEEx\Eff\nil% + } + \xdef\listEE{\the\tabtoksEE} + \ignoreemptyitems% + \setsepchar[*]{,*/} + \readlist*\ListeComplete\listEE% + }}} % on crée la base de données des valeurs dans le cas qualitatif \DTLcleardb{mtdb}% % on les trie pour la médiane dans le cas qualitatif % Touhami / Texnique.fr @@ -6134,14 +6789,20 @@ vardef Positions(expr Step)= % %% celui de la somme des données \foreachitem\don\in\ListeComplete{\xdef\SommeDonnees{\fpeval{\SommeDonnees+\ListeComplete[\doncnt,2]}}}% % %% celui de l'effectif total - \xdef\EffectifTotal{\SommeDonnees}% \ifboolKV[ClesStat]{EffectifTotal}{% - L'effectif total est \num{\ListeCompletelen}.\par - }{} + \ifboolKV[ClesStat]{Liste}{L'effectif total de la série est + \num{\ListeCompletelen}.\par}{ + \foreachitem\don\in\ListeComplete{\xdef\EffectifTotal{\fpeval{\EffectifTotal+\ListeComplete[\doncnt,2]}}}% + L'effectif total de la série est : \[\ListeComplete[1,2]\xintFor* ##1 in + {\xintSeq {2}{\ListeCompletelen}}\do{% + +\ListeComplete[##1,2]}=\num{\EffectifTotal}\]} + }{}% + \xdef\EffectifTotal{\SommeDonnees}% % %% celui de la moyenne - \xdef\Moyenne{\fpeval{\SommeDonnees/\ListeCompletelen}}% + \xdef\Moyenne{\fpeval{\SommeDonnees/\ListeCompletelen}}% \ifboolKV[ClesStat]{Moyenne}{% - La somme des données est :% + \ifboolKV[ClesStat]{Liste}{% + La somme des données de la série est :% \xintifboolexpr{\ListeCompletelen<\useKV[ClesStat]{Coupure}}{% \[ \num{\ListeComplete[1,2]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{% @@ -6155,15 +6816,15 @@ vardef Positions(expr Step)= }=\num{\SommeDonnees}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}% \]% }% - \ifboolKV[ClesStat]{SET}{}{L'effectif total est \num{\ListeCompletelen}.\\}% - Donc la moyenne est égale à :% + \ifboolKV[ClesStat]{SET}{}{Le nombre de données de la série est \num{\ListeCompletelen}.\\}% + Donc la moyenne de la série est égale à :% \[\frac{\num{\SommeDonnees}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}}{\num{\ListeCompletelen}}%\IfInteger{\fpeval{round(\fpeval{\SommeDonnees/\ListeCompletelen},\useKV[ClesStat]{Precision})}}{=}{\approx} \opdiv*{\SommeDonnees}{\ListeCompletelen}{resultatmoy}{restemoy}% \opround{resultatmoy}{\useKV[ClesStat]{Precision}}{resultatmoy1}% \opcmp{resultatmoy}{resultatmoy1}\ifopeq=\else\approx\fi% \num{\fpeval{round(\fpeval{\SommeDonnees/\ListeCompletelen},\useKV[ClesStat]{Precision})}}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}.}{.}% \]% - }{}% + }{Pas de moyenne possible pour une série de données à caractère qualitatif.}}{}% % % %% celui de l'étendue \xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{% \xintifboolexpr{\ListeComplete[##1,2]>\DonneeMax}{% @@ -6175,11 +6836,12 @@ vardef Positions(expr Step)= }% \xdef\EffectifMax{\DonneeMax}% \xdef\Etendue{\fpeval{\DonneeMax-\DonneeMin}}% - \ifboolKV[ClesStat]{Etendue}{L'étendue est égale à $\num{\DonneeMax}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}-\num{\DonneeMin}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}=\num{\Etendue}$\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}% - }{}% + \ifboolKV[ClesStat]{Etendue}{% + \ifboolKV[ClesStat]{Liste}{% + L'étendue de la série est égale à $\num{\DonneeMax}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}-\num{\DonneeMin}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}=\num{\Etendue}$\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}% + }{Pas d'étendue possible pour une série de données à caractère qualitatif.}}{}% \ifboolKV[ClesStat]{Mediane}{% - %%%%%%%%%%%%%%%%%%%%%%%% - + \ifboolKV[ClesStat]{Liste}{% On range les données par ordre croissant :% \nbdonnees=0% \xintifboolexpr{\ListeCompletelen<\useKV[ClesStat]{Coupure}}{% @@ -6198,35 +6860,38 @@ vardef Positions(expr Step)= \newcount\meda% \ifodd\number\ListeCompletelen%odd impair \med=\fpeval{(\ListeCompletelen+1)/2}\relax% - L'effectif total est \num{\ListeCompletelen}. Or, $\num{\ListeCompletelen}=\num{\fpeval{\med-1}}+1+\num{\fpeval{\med-1}}$.\\ + L'effectif total de la série est \num{\ListeCompletelen}. Or, $\num{\ListeCompletelen}=\num{\fpeval{\med-1}}+1+\num{\fpeval{\med-1}}$.\\ \else% pair \med=\fpeval{\ListeCompletelen/2}\relax \meda=\numexpr\med+1\relax - L'effectif total est \num{\ListeCompletelen}. Or, $\num{\ListeCompletelen}=\num{\the\med}+\num{\the\med}$.\\ + L'effectif total de la série est \num{\ListeCompletelen}. Or, $\num{\ListeCompletelen}=\num{\the\med}+\num{\the\med}$.\\ \fi% \newcount\k% \k=0% \DTLforeach{mtdb}{\numeroDonnee=Numeric}{\k=\numexpr\k+1\relax% \ifnum\k=\med %La médiane vaut \numeroDonnee\fi \ifodd\number\ListeCompletelen% - La médiane est la \the\med\ieme{} donnée.\\Donc la médiane est \num{\numeroDonnee}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}% + La médiane de la série est la \the\med\ieme{} donnée.\\Donc la médiane de la série est \num{\numeroDonnee}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}% \else% La \the\med\ieme{} donnée est \num{\numeroDonnee}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}\xdef\Mediane{\numeroDonnee} % \fi \fi \ifnum\k=\meda - La \the\meda\ieme{} donnée est \num{\numeroDonnee}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.} Donc la médiane est \xdef\Mediane{\fpeval{(\Mediane+\numeroDonnee)/2}}\num{\Mediane}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.} + La \the\meda\ieme{} donnée est \num{\numeroDonnee}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.} Donc la médiane de la série est \xdef\Mediane{\fpeval{(\Mediane+\numeroDonnee)/2}}\num{\Mediane}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.} \fi } %%%%%%%%%%%%%%%%%%%%%%%% - }{} - % construction du tableau - \ifboolKV[ClesStat]{Tableau}{\ifboolKV[ClesStat]{Total}{\buildtabqt}{\buildtabq}}{} - % Construction du graphique ?? + }{Pas de médiane possible pour une série de données à caractère qualitatif.}}{} + % Construction du tableau + \ifboolKV[ClesStat]{Tableau}{% + \ifboolKV[ClesStat]{Liste}{Pas de tableau possible avec la clé Liste.\\Utilisez plutôt la clé Sondage si vous voulez un tableau avec cette liste.}{% + \ifboolKV[ClesStat]{Total}{\buildtabt}{\buildtab}}}% + {}% + % Construction du graphique \ifboolKV[ClesStat]{Graphique}{% - \ifboolKV[ClesStat]{Angle}{\buildgraphcq{360}}{\ifboolKV[ClesStat]{SemiAngle}{\buildgraphcq{180}}{}} - \ifboolKV[ClesStat]{Batons}{\buildgraphq}{} - }{} + \ifboolKV[ClesStat]{Liste}{Pas de graphique possible avec la clé Liste.\\Utilisez plutôt la clé Sondage si vous voulez un graphique avec cette liste.}{% + \ifboolKV[ClesStat]{Angle}{\buildgraphcq{360}}{\ifboolKV[ClesStat]{SemiAngle}{\buildgraphcq{180}}{\buildgraphq[#1]}}% + }}{} }{%%%%%%%%%%%%%%%%%%%%%Début quantitatif % % on effectue les calculs % %% celui de la somme des données @@ -6247,12 +6912,12 @@ vardef Positions(expr Step)= % %% celui de la moyenne \xdef\Moyenne{\fpeval{\SommeDonnees/\EffectifTotal}}% \ifboolKV[ClesStat]{EffectifTotal}{% - L'effectif total est : \[\ListeComplete[1,2]\xintFor* ##1 in + L'effectif total de la série est : \[\ListeComplete[1,2]\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{% +\ListeComplete[##1,2]}=\num{\EffectifTotal}\] }{}% \ifboolKV[ClesStat]{Moyenne}{% - La somme des données est :% + La somme des données de la série est :% \xintifboolexpr{\ListeCompletelen<\useKV[ClesStat]{Coupure}}{% \[ \ifnum\ListeComplete[1,2]=1\else\num{\ListeComplete[1,2]}\times\fi\num{\ListeComplete[1,1]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{% @@ -6268,7 +6933,7 @@ vardef Positions(expr Step)= }=\num{\SommeDonnees}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{} \] } - \ifboolKV[ClesStat]{SET}{}{L'effectif total est :% + \ifboolKV[ClesStat]{SET}{}{L'effectif total de la série est :% \ifboolKV[ClesStat]{Liste}{ \num{\EffectifTotal}\\}{% \[\num{\ListeComplete[1,2]}\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{% +\num{\ListeComplete[##1,2]} @@ -6276,7 +6941,7 @@ vardef Positions(expr Step)= \]% }% } - Donc la moyenne est égale à :% + Donc la moyenne de la série est égale à :% \[\frac{\num{\SommeDonnees}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}}{\num{\EffectifTotal}}% \opdiv*{\SommeDonnees}{\EffectifTotal}{resultatmoy}{restemoy}% \opround{resultatmoy}{\useKV[ClesStat]{Precision}}{resultatmoy1}% @@ -6287,7 +6952,7 @@ vardef Positions(expr Step)= }{}% % % Affichage des réponses. % %% pour l'étendue - \ifboolKV[ClesStat]{Etendue}{L'étendue est égale à $\num{\ListeComplete[\ListeCompletelen,1]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}-\num{\ListeComplete[1,1]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}=\num{\Etendue}$\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}}{}% + \ifboolKV[ClesStat]{Etendue}{L'étendue de la série est égale à $\num{\ListeComplete[\ListeCompletelen,1]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}-\num{\ListeComplete[1,1]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}=\num{\Etendue}$\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}}{}% % %% pour la médiane \ifboolKV[ClesStat]{Mediane}{% @@ -6295,11 +6960,11 @@ vardef Positions(expr Step)= \newcount\meda% \ifodd\number\EffectifTotal%odd impair \med=\fpeval{(\EffectifTotal+1)/2}\relax% - L'effectif total est \num{\EffectifTotal}. Or, $\num{\EffectifTotal}=\num{\fpeval{\med-1}}+1+\num{\fpeval{\med-1}}$. % + L'effectif total de la série est \num{\EffectifTotal}. Or, $\num{\EffectifTotal}=\num{\fpeval{\med-1}}+1+\num{\fpeval{\med-1}}$. % \else% pair \med=\fpeval{\EffectifTotal/2}\relax% \meda=\numexpr\med+1\relax% - L'effectif total est \num{\EffectifTotal}. Or, $\num{\EffectifTotal}=\num{\fpeval{\med}}+\num{\fpeval{\med}}$. % + L'effectif total de la série est \num{\EffectifTotal}. Or, $\num{\EffectifTotal}=\num{\fpeval{\med}}+\num{\fpeval{\med}}$. % \fi% \newcount\k% \k=0% @@ -6308,13 +6973,13 @@ vardef Positions(expr Step)= \k=\numexpr\k+1\relax% \ifnum\k=\med% \ifodd\number\EffectifTotal% - La médiane est la \the\med\ieme{} donnée. Donc la médiane est \num{\ListeComplete[##1,1]}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}% + La médiane de la série est la \the\med\ieme{} donnée. Donc la médiane de la série est \num{\ListeComplete[##1,1]}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}% \else% La \the\med\ieme{} donnée est \num{\ListeComplete[##1,1]}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}. }{. }\xdef\Mediane{\ListeComplete[##1,1]}% \fi% \fi% \ifnum\k=\meda% - La \the\meda\ieme{} valeur est \num{\ListeComplete[##1,1]}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}\\Donc la médiane est \xdef\Mediane{\fpeval{(\Mediane+\ListeComplete[##1,1])/2}}\num{\Mediane}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}% + La \the\meda\ieme{} valeur est \num{\ListeComplete[##1,1]}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}\\Donc la médiane de la série est \xdef\Mediane{\fpeval{(\Mediane+\ListeComplete[##1,1])/2}}\num{\Mediane}\ifboolKV[ClesStat]{Concret}{~\useKV[ClesStat]{Unite}.}{.}% \fi% }% }% @@ -6322,13 +6987,15 @@ vardef Positions(expr Step)= % Construction de tableau \ifboolKV[ClesStat]{Tableau}{\ifboolKV[ClesStat]{Total}{\buildtabt}{\buildtab}}{}% % Construction du graphique ?? - \ifboolKV[ClesStat]{Graphique}{\buildgraph}{}% + \ifboolKV[ClesStat]{Graphique}{% + \ifboolKV[ClesStat]{Angle}{\buildgraphcq{360}}{\ifboolKV[ClesStat]{SemiAngle}{\buildgraphcq{180}}{\buildgraph[#1]}} + }{}% }% }% -%%%%%%%%%%%%% -%%% Radar -%%%%%%%%%%%%% +%%% +% Radar +%%% \setKVdefault[ClesRadar]{Rayon=3cm,Reference=20,MoyenneClasse=false,Disciplines=false,Pas=5} \newtoks\toklisteradara%pour la moyenne de l'élève @@ -6359,12 +7026,17 @@ vardef Positions(expr Step)= p:=0; for p_=#2: p:=p+1; - if N[p]>180: - label(TEX(p_) - rotated(90+N[p]),1.15[O,pointarc(cc,N[p])]); - else: - label(TEX(p_) - rotated(-90+N[p]),1.15[O,pointarc(cc,N[p])]); + if (N[p]<90) or (N[p]=90): + label.urt(TEX(p_),1.025[O,pointarc(cc,N[p])]); + fi; + if ((N[p]>90) and (N[p]<180)) or (N[p]=180): + label.ulft(TEX(p_),1.025[O,pointarc(cc,N[p])]); + fi; + if (N[p]>180) and (N[p]<270): + label.llft(TEX(p_),1.025[O,pointarc(cc,N[p])]); + fi; + if (N[p]>270) or (N[p]=270): + label.lrt(TEX(p_),1.025[O,pointarc(cc,N[p])]); fi; endfor; % tracé des pas: @@ -6376,7 +7048,7 @@ vardef Positions(expr Step)= trace pointarc(cc,N[1]) for l=2 upto n: --pointarc(cc,N[l]) endfor --cycle; % etiquettage des pas - dotlabel.top(btex \tiny #4 etex rotated -90,pointarc(cc,0)); + dotlabel.urt(btex \tiny #4 etex,pointarc(cc,0)); dotlabel.urt(btex \tiny #3 etex,(1/pas)[O,pointarc(cc,0)]); % tracé des résultats élèves pair El[]; @@ -6414,12 +7086,17 @@ vardef Positions(expr Step)= p:=0; for p_=#2: p:=p+1; - if N[p]>180: - label(LATEX(p_) - rotated(90+N[p]),1.15[O,pointarc(cc,N[p])]); - else: - label(LATEX(p_) - rotated(-90+N[p]),1.15[O,pointarc(cc,N[p])]); + if (N[p]<90) or (N[p]=90): + label.urt(TEX(p_),1.025[O,pointarc(cc,N[p])]); + fi; + if ((N[p]>90) and (N[p]<180)) or (N[p]=180): + label.ulft(TEX(p_),1.025[O,pointarc(cc,N[p])]); + fi; + if (N[p]>180) and (N[p]<270): + label.llft(TEX(p_),1.025[O,pointarc(cc,N[p])]); + fi; + if (N[p]>270) or (N[p]=270): + label.lrt(TEX(p_),1.025[O,pointarc(cc,N[p])]); fi; endfor; % tracé des pas: @@ -6460,6 +7137,7 @@ vardef Positions(expr Step)= \useKVdefault[ClesRadar]% \setKV[ClesRadar]{#1}% \ignoreemptyitems% + \setsepchar[*]{,}% \readlist*\ListeRadar{#2}% \toklisteradara{}% \foreachitem\compteur\in\ListeRadar{\expandafter\UpdateRadara\compteur\nil}% @@ -6474,9 +7152,9 @@ vardef Positions(expr Step)= \MPRadar{\useKV[ClesRadar]{Rayon}}{\the\toklisteradarb}{\useKV[ClesRadar]{Pas}}{\useKV[ClesRadar]{Reference}}{\the\toklisteradara}{\the\toklisteradarc}% } -%%%%%%%%%%%% +%%% % Barres de niveaux -%%%%%%%%%%%% +%%% \setKVdefault[ClesBarre]{Niveau=false,LimiteI=25,LimiteF=50,LimiteS=75,TexteOrigine=0,TexteReference=100,CouleurGraduation=white,CouleurFond=gray!50,CouleurBarre=black,Graduation=false,Nom=Défaut,Pas=10,CouleurI=red,CouleurF=orange,CouleurS=yellow,CouleurM=green} \newlength{\barrewidth} @@ -6537,10 +7215,10 @@ vardef Positions(expr Step)= } } -%%%%%%%%%%%%%%% -%%% Equations -%%%%%%%%%%%%%%% -\setKVdefault[ClesEquation]{Ecart=0.5,Fleches=false,FlecheDiv=false,Laurent=false,Decomposition=false,Terme=false,Composition=false,Symbole=false,Entier=false,Lettre=x,Solution=false,Bloc=false,Simplification=false,CouleurTerme=black,CouleurCompo=black,CouleurSous=red,CouleurSymbole=orange,Verification=false,Nombre=0,Egalite=false,Produit=false,Facteurs=false,Carre=false,Pose=false,Equivalence=false} +%%% +% Equations +%%% +\setKVdefault[ClesEquation]{Ecart=0.5,Fleches=false,FlecheDiv=false,Laurent=false,Decomposition=false,Terme=false,Composition=false,Symbole=false,Entier=false,Lettre=x,Solution=false,LettreSol=true,Bloc=false,Simplification=false,CouleurTerme=black,CouleurCompo=black,CouleurSous=red,CouleurSymbole=orange,Verification=false,Nombre=0,Egalite=false,Produit=false,Facteurs=false,Carre=false,Exact=false,Pose=false,Equivalence=false} \newcommand\rightcomment[4]% {\begin{tikzpicture}[remember picture,overlay] @@ -6552,7 +7230,6 @@ vardef Positions(expr Step)= \end{tikzpicture}% } - \newcommand\leftcomment[4]% {\begin{tikzpicture}[remember picture,overlay] \draw[Cfleches,-stealth] @@ -6659,9 +7336,9 @@ vardef Positions(expr Step)= \definecolor{Cfleches}{RGB}{100,100,100}% -\input{PfC-EquationSoustraction1}% +\input{PfC-EquationSoustraction2}% \input{PfC-EquationTerme1}% -\input{PfC-EquationComposition1}% +\input{PfC-EquationComposition2}% \input{PfC-EquationPose1}% \input{PfC-EquationSymbole1}% \input{PfC-EquationLaurent1} @@ -6716,12 +7393,12 @@ vardef Positions(expr Step)= Comme \num{#2} est positif, alors l'équation $\useKV[ClesEquation]{Lettre}^2=\num{#2}$ a deux solutions :% \begin{align*} \useKV[ClesEquation]{Lettre}&=\sqrt{\num{#2}}&&\text{et}&\useKV[ClesEquation]{Lettre}&=-\sqrt{\num{#2}}%\\ - \ifboolKV[ClesEquation]{Entier}{\\% + \ifboolKV[ClesEquation]{Exact}{\\% \useKV[ClesEquation]{Lettre}&=\num{\fpeval{sqrt(#2)}}&&\text{et}&\useKV[ClesEquation]{Lettre}&=-\num{\fpeval{sqrt(#2)}}}{}% \end{align*} - } - } -} + }% + }% +}% \newcommand\ResolEquationProduit[5][]{% \setKV[ClesEquation]{#1}% @@ -6782,9 +7459,8 @@ vardef Positions(expr Step)= } \end{align*} }% - - \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#3=0}{\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}{(\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}})}\xintifboolexpr{#5=0}{\times\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}{(\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}})}=0$ a deux solutions : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$ et \opdiv*{\Coeffd}{\Coeffc}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffd}{\Coeffc}}{\frac{\num{\Coeffd}}{\num{\Coeffc}}}\fi$. - }{} + \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#3=0}{\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}{(\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}})}\xintifboolexpr{#5=0}{\times\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}{(\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}})}=0$ a deux solutions : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$ et \opdiv*{\Coeffd}{\Coeffc}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffd}{\Coeffc}}{\frac{\num{\Coeffd}}{\num{\Coeffc}}}\fi$. + }{}% } \newcommand\Verification[5][]{% @@ -6802,10 +7478,10 @@ vardef Positions(expr Step)= }{\xintifboolexpr{\Testa=\Testb}{Comme $\num{\Testa}=\num{\Testb}$, alors $\useKV[ClesEquation]{Lettre}=\num{\useKV[ClesEquation]{Nombre}}$ est bien }{Comme $\num{\Testa}\not=\num{\Testb}$, alors $\useKV[ClesEquation]{Lettre}=\num{\useKV[ClesEquation]{Nombre}}$ n'est pas }une solution de l'équation $\xintifboolexpr{#2=0}{\num{#3}}{\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3=0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}}=\xintifboolexpr{#4=0}{\num{#5}}{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5=0}{}{\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}}}$.} } -%%%%%%%%%%%%%%%%%%%% -%%% Proportionnalité -%%%%%%%%%%%%%%%%%%%% -\setKVdefault[ClesPropor]{GrandeurA=Grandeur A,GrandeurB=Grandeur B,Largeur=1cm,Math=false,Stretch=1,ColorFill=white,ColorTab=gray!15}%Tableau=false : +%%% +% Proportionnalité +%%% +\setKVdefault[ClesPropor]{GrandeurA=Grandeur A,GrandeurB=Grandeur B,Largeur=1cm,Math=false,Stretch=1,ColorFill=white,CouleurTab=gray!15}%Tableau=false : %inutile ? \def\Updatetoksmath#1/#2\nil{\addtotok\tabtoksa{}\addtotok\tabtoksb{}}% @@ -6819,7 +7495,7 @@ vardef Positions(expr Step)= }% \xdef\LongListe{\ListeValeurlen}% \renewcommand{\arraystretch}{\useKV[ClesPropor]{Stretch}}% - \begin{tabular}{|>{\columncolor{\useKV[ClesPropor]{ColorTab}}}c|*{\number\numexpr\ListeValeurlen}{>{\centering\arraybackslash}p{\useKV[ClesPropor]{Largeur}}|}}% + \begin{tabular}{|>{\columncolor{\useKV[ClesPropor]{CouleurTab}}}c|*{\number\numexpr\ListeValeurlen}{>{\centering\arraybackslash}p{\useKV[ClesPropor]{Largeur}}|}}% \multicolumn{1}{c}{\TikzPHD\setcounter{NbPropor}{1}}\xintFor* ##1 in {\xintSeq {1}{\ListeValeurlen}}\do{&\multicolumn{1}{c}{\TikzPH}}\\% \hhline{*{\number\numexpr\ListeValeurlen+1}{-}}% \the\tabtoksa\\% @@ -6839,9 +7515,15 @@ vardef Positions(expr Step)= }% \newcommand{\TikzPHD}{% - \setbox1=\hbox{\useKV[ClesPropor]{GrandeurA}} - \tikz[remember picture,overlay]{% - \coordinate[name=ProporHD,xshift=-0.5*\the\wd1,yshift=-\the\dp\strutbox*\arraystretch];}% + \setbox1=\hbox{\useKV[ClesPropor]{GrandeurA}}% + \setbox2=\hbox{\useKV[ClesPropor]{GrandeurB}}% + \xintifboolexpr{\wd1>\wd2}{% + \tikz[remember picture,overlay]{% + \coordinate[name=ProporHD,xshift=-0.5\wd1,yshift=-\the\dp\strutbox*\arraystretch];}% + }{% + \tikz[remember picture,overlay]{% + \coordinate[name=ProporHD,xshift=-0.5\wd2,yshift=-\the\dp\strutbox*\arraystretch];}% + } }% \newcommand{\TikzPB}{% @@ -6851,20 +7533,26 @@ vardef Positions(expr Step)= }% \newcommand{\TikzPBD}{% - \setbox1=\hbox{\useKV[ClesPropor]{GrandeurA}} - \tikz[remember picture, overlay]{% - \coordinate[name=ProporBD,xshift=-0.5*\the\wd1,yshift=\the\ht\strutbox*\arraystretch];}% + \setbox1=\hbox{\useKV[ClesPropor]{GrandeurA}}% + \setbox2=\hbox{\useKV[ClesPropor]{GrandeurB}}% + \xintifboolexpr{\wd1>\wd2}{% + \tikz[remember picture, overlay]{% + \coordinate[name=ProporBD,xshift=-0.5*\the\wd1,yshift=\the\ht\strutbox*\arraystretch];}% + }{% + \tikz[remember picture, overlay]{% + \coordinate[name=ProporBD,xshift=-0.5*\the\wd2,yshift=\the\ht\strutbox*\arraystretch];}% + } \stepcounter{NbPropor}% }% \newcommand\FlechesPH[3]{% \ifnum#1<#2\relax% \begin{tikzpicture}[remember picture,overlay]% - \draw[-stealth,out=50,in=130] (ProporH-#1) to node[inner sep=0pt, inner xsep=1pt,fill=\colorfill, pos=0.65, sloped]{#3}(ProporH-#2);% + \draw[-stealth,out=50,in=130] (ProporH-#1) to node[inner sep=0pt, inner xsep=1pt,fill=\colorfill, pos=0.5, sloped]{#3}(ProporH-#2);% \end{tikzpicture}% \else% \begin{tikzpicture}[remember picture,overlay]% - \draw[-stealth,out=130,in=50] (ProporH-#1) to node[inner sep=0pt, inner xsep=1pt,fill=\colorfill, pos=0.65, sloped]{#3}(ProporH-#2);% + \draw[-stealth,out=130,in=50] (ProporH-#1) to node[inner sep=0pt, inner xsep=1pt,fill=\colorfill, pos=0.5, sloped]{#3}(ProporH-#2);% \end{tikzpicture}% \fi% }% @@ -6872,11 +7560,11 @@ vardef Positions(expr Step)= \newcommand\FlechesPB[3]{% \ifnum\number#1<\number#2\relax% \begin{tikzpicture}[remember picture,overlay]% - \draw[-stealth,out=-50,in=-130] (ProporB-#1) to node[inner sep=0pt, inner xsep=1pt,fill=\colorfill, pos=0.65, sloped]{#3}(ProporB-#2);% + \draw[-stealth,out=-50,in=-130] (ProporB-#1) to node[inner sep=0pt, inner xsep=1pt,fill=\colorfill, pos=0.5, sloped]{#3}(ProporB-#2);% \end{tikzpicture}% \else% \begin{tikzpicture}[remember picture,overlay]% - \draw[-stealth,out=-130,in=-50] (ProporB-#1) to node[inner sep=0pt, inner xsep=1pt,fill=\colorfill, pos=0.65, sloped]{#3}(ProporB-#2);% + \draw[-stealth,out=-130,in=-50] (ProporB-#1) to node[inner sep=0pt, inner xsep=1pt,fill=\colorfill, pos=0.5, sloped]{#3}(ProporB-#2);% \end{tikzpicture}% \fi% } @@ -6902,14 +7590,13 @@ vardef Positions(expr Step)= \end{tikzpicture}% }% -\newcommand\FlecheCoefDebut[2][1.25\tabcolsep]{% +\newcommand\FlecheCoefDebut[2][\tabcolsep+\arrayrulewidth]{% \begin{tikzpicture}[remember picture, overlay]% \node[] (Noeud1) at ($(ProporHD)!0.1!(ProporBD)$) {};% \node[] (Noeud2) at ($(ProporHD)!0.9!(ProporBD)$) {};% \coordinate[left of=Noeud1,node distance=#1] (noeud1);% \coordinate[left of=Noeud2,node distance=#1] (noeud2);% \draw[-stealth,out=160,in=-160] (noeud2) to node[midway,left,inner sep=1pt]{#2}(noeud1);% - %\draw[red](ProporHD) to (ProporBD); \end{tikzpicture}% }% @@ -6945,26 +7632,26 @@ vardef Positions(expr Step)= \end{tikzpicture} } -%%%%%%%%%%% -%% Application : pourcentage -%%%%%%%%%%% -\setKVdefault[ClesPourcentage]{Appliquer,Calculer=false,Augmenter=false,Reduire=false,Fractionnaire=false,Decimal,Formule=false,Unite=g,Concret=false,GrandeurA=Grandeur A,GrandeurB=Total,MotReduction=diminution,AideTableau=false,ColorFill=white,ColorTab=gray!15} +%%% +% Application : pourcentage +%%% +\setKVdefault[ClesPourcentage]{Appliquer,Calculer=false,Augmenter=false,Reduire=false,Fractionnaire=false,Decimal,Formule=false,Unite=g,Concret=false,GrandeurA=Grandeur A,GrandeurB=Total,MotReduction=diminution,AideTableau=false,ColorFill=white,CouleurTab=gray!15} \newcommand\Pourcentage[3][]{% \useKVdefault[ClesPourcentage]% \setKV[ClesPourcentage]{#1}% \ifboolKV[ClesPourcentage]{Reduire}{% \ifboolKV[ClesPourcentage]{Formule}{% - Réduire une quantité de \num{#2}~\%, cela revient à multiplier cette quantitié par $1-\dfrac{\num{#2}}{100}$. Par conséquent, si on réduit \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{} de \num{#2}~\%, cela donne : + Réduire une quantité de \num{#2}~\%, cela revient à multiplier cette quantité par $1-\dfrac{\num{#2}}{100}$. Par conséquent, si on réduit \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{} de \num{#2}~\%, cela donne : \[\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\left(1-\frac{\num{#2}}{100}\right)=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times(1-\num{\fpeval{#2/100}})=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\num{\fpeval{(1-#2/100)}}=\num{\fpeval{#3*(1-#2/100)}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\] }{% Calculons ce que représente la \useKV[ClesPourcentage]{MotReduction} de \num{#2}~\%. \ifboolKV[ClesPourcentage]{AideTableau}{% \xdef\NomA{\useKV[ClesPourcentage]{GrandeurA}}% \xdef\NomB{\useKV[ClesPourcentage]{GrandeurB}}% - \xdef\NomColorTab{\useKV[ClesPourcentage]{ColorTab}}% + \xdef\NomCouleurTab{\useKV[ClesPourcentage]{CouleurTab}}% \begin{center} - \Propor[GrandeurA=\NomA,GrandeurB=\NomB,ColorTab=\NomColorTab]{/#3,#2/100} + \Propor[GrandeurA=\NomA,GrandeurB=\NomB,CouleurTab=\NomCouleurTab]{/#3,#2/100} \end{center} \FlecheCoefInv{\tiny$\times\num{\fpeval{#2/100}}$}% On obtient une \useKV[ClesPourcentage]{MotReduction} de $\num{\fpeval{#2/100}}\times\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\num{\fpeval{#3*#2/100}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}. Donc un total de $\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}-\num{\fpeval{#3*#2/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\num{\fpeval{#3*(1-#2/100)}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}.% @@ -6975,16 +7662,16 @@ vardef Positions(expr Step)= }{% \ifboolKV[ClesPourcentage]{Augmenter}{% \ifboolKV[ClesPourcentage]{Formule}{% - Augmenter de \num{#2}~\% une quantité, cela revient à multiplier cette quantitié par $1+\dfrac{\num{#2}}{100}$. Par conséquent, si on augmente \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{} de \num{#2}~\%, cela donne : + Augmenter de \num{#2}~\% une quantité, cela revient à multiplier cette quantité par $1+\dfrac{\num{#2}}{100}$. Par conséquent, si on augmente \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{} de \num{#2}~\%, cela donne : \[\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\left(1+\frac{\num{#2}}{100}\right)=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times(1+\num{\fpeval{#2/100}})=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\num{\fpeval{(1+#2/100)}}=\num{\fpeval{#3*(1+#2/100)}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\] }{% Calculons ce que représente l'augmentation de \num{#2}~\%. % \ifboolKV[ClesPourcentage]{AideTableau}{% \xdef\NomA{\useKV[ClesPourcentage]{GrandeurA}}% \xdef\NomB{\useKV[ClesPourcentage]{GrandeurB}}% - \xdef\NomColorTab{\useKV[ClesPourcentage]{ColorTab}}% + \xdef\NomCouleurTab{\useKV[ClesPourcentage]{CouleurTab}}% \begin{center}% - \Propor[GrandeurA=\NomA,GrandeurB=\NomB,ColorTab=\NomColorTab]{/#3,#2/100}% + \Propor[GrandeurA=\NomA,GrandeurB=\NomB,CouleurTab=\NomCouleurTab]{/#3,#2/100}% \end{center}% \FlecheCoefInv{\tiny$\times\num{\fpeval{#2/100}}$}% On obtient une augmentation de $\num{\fpeval{#2/100}}\times\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\num{\fpeval{#3*#2/100}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}.\\Donc un total de $\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}+\num{\fpeval{#3*#2/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\num{\fpeval{#3*(1+#2/100)}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}.% @@ -6996,8 +7683,8 @@ vardef Positions(expr Step)= \ifboolKV[ClesPourcentage]{Calculer}{% \xdef\NomA{\useKV[ClesPourcentage]{GrandeurA}}% \xdef\NomB{\useKV[ClesPourcentage]{GrandeurB}}% - \xdef\NomColorTab{\useKV[ClesPourcentage]{ColorTab}}% - \Propor[GrandeurA=\NomA,GrandeurB=\NomB,ColorTab=\NomColorTab]{#2/#3,/100}% + \xdef\NomCouleurTab{\useKV[ClesPourcentage]{CouleurTab}}% + \Propor[GrandeurA=\NomA,GrandeurB=\NomB,CouleurTab=\NomCouleurTab]{#2/#3,/100}% \xdef\colorfill{\useKV[ClesPourcentage]{ColorFill}}% \FlechesPB{2}{1}{\scriptsize$\times\num{\fpeval{#3/100}}$}% \FlechesPH{1}{2}{\scriptsize$\div\num{\fpeval{#3/100}}$}% @@ -7010,10 +7697,10 @@ vardef Positions(expr Step)= }% }% -%%%%%%%%%%%%% -%Lien : ratio -%%%%%%%%%%%%% -\setKVdefault[ClesRatio]{Figure=false,Longueur=5cm,TexteTotal=quantité,TextePart=part,Tableau=false,GrandeurA=Grandeur A,GrandeurB=Part(s),Largeur=1cm,Stretch=1,Nom=false,CouleurUn=gris,CouleurDeux=0.5gris+0.5blanc,CouleurTrois=white,ColorTab=gray!15} +%%% +% Lien : ratio +%%% +\setKVdefault[ClesRatio]{Figure=false,Longueur=5cm,TexteTotal=quantité,TextePart=part,Tableau=false,GrandeurA=Grandeur A,GrandeurB=Part(s),Largeur=1cm,Stretch=1,Nom=false,CouleurUn=gris,CouleurDeux=0.5gris+0.5blanc,CouleurTrois=white,CouleurTab=gray!15} \newcommand\MPTest[9][]{% % #2 : Longueur de la barre unité @@ -7098,12 +7785,11 @@ vardef Positions(expr Step)= fi; \end{mplibcode} \else - \usempxpackage{simplekv} \mpxcommands{% \setKVdefault[ClesRatio]{TexteTotal=quantité,TextePart=part} \setKV[ClesRatio]{#1} } - \begin{mpost}[mpsettings={input PfC-Geometrie;}] + \begin{mpost} vardef RatioTrois(expr long)(text t)=%longueur de la barre / quantité à partager / textepart :) / t le ratio pair A,B,C,D; A=u*(1,1); @@ -7189,7 +7875,7 @@ vardef Positions(expr Step)= \foreachitem\compteur\in\ListeRatio{\expandafter\updateratiotoks\compteur\nil}% \xdef\LongListe{\ListeRatiolen}% \renewcommand{\arraystretch}{\useKV[ClesRatio]{Stretch}}% - \begin{tabular}{|>{\columncolor{\useKV[ClesRatio]{ColorTab}}}c|*{\number\numexpr\ListeRatiolen}{>{\centering\arraybackslash}p{\useKV[ClesRatio]{Largeur}}|}l} + \begin{tabular}{|>{\columncolor{\useKV[ClesRatio]{CouleurTab}}}c|*{\number\numexpr\ListeRatiolen}{>{\centering\arraybackslash}p{\useKV[ClesRatio]{Largeur}}|}l} \ifboolKV[ClesRatio]{Nom}{% \hhline{~*{\number\numexpr\ListeRatiolen}{-}} \multicolumn{1}{c|}{}\the\tabtoksc\\ @@ -7245,7 +7931,7 @@ vardef Positions(expr Step)= \foreachitem\compteur\in\ListeRatio{\expandafter\UpdateRatio\compteur\nil}% \itemtomacro\ListeRatio[1]\NbUn \itemtomacro\ListeRatio[2]\NbDeux - \xintifboolexpr{\ListeRatiolen>2}{\itemtomacro\ListeRatio[3]\NbTrois}{\newcommand\NbTrois{}} + \xintifboolexpr{\ListeRatiolen>2}{\itemtomacro\ListeRatio[3]\NbTrois}{\xdef\NbTrois{}} \MPTest[#1]{\useKV[ClesRatio]{Longueur}}{\NbUn}{\NbDeux}{\NbTrois}{\the\toklisteratio}{\useKV[ClesRatio]{CouleurUn}}{\useKV[ClesRatio]{CouleurDeux}}{\useKV[ClesRatio]{CouleurTrois}}% }{% \ifboolKV[ClesRatio]{Tableau}{% @@ -7256,9 +7942,9 @@ vardef Positions(expr Step)= }% }% -%%%%%%%%%%%%%%% -%% Cartes Mentales -%%%%%%%%%%%%%%% +%%% +% Cartes Mentales +%%% \setKVdefault[ClesMentales]{Nom={Bulle}, Largeur=5cm, Ancre={0,0},Pointilles=false,CTrace=black,CFond=white,Epaisseur=1pt,Rayon=1}% \newenvironment{Mind}{\begin{tikzpicture}}{\end{tikzpicture}}% @@ -7282,9 +7968,9 @@ vardef Positions(expr Step)= } } -%%%%%%%%%%%% +%%% % Pptés des droites (6eme) -%%%%%%%%%%% +%%% \setKVdefault[ClesDroites]{Brouillon=false,CitePropriete=false,Num=1,Figure=false,Remediation=false} \newcommand\Redaction[4][]{% @@ -7320,7 +8006,7 @@ vardef Positions(expr Step)= Comme les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont parallèles, alors la droite $(\hbox to2em{\dotfill})$ qui est perpendiculaire à $(\hbox to2em{\dotfill})$ est également perpendiculaire à la droite $(\hbox to2em{\dotfill})$. } } - }%%%%%%%%%%%%%%%%%%%%% + }% }{% \xintifboolexpr{\useKV[ClesDroites]{Num}=1}{% \ifboolKV[ClesDroites]{CitePropriete}{% @@ -7351,11 +8037,11 @@ vardef Positions(expr Step)= Donc les droites $(#2)$ et $(#3)$ sont perpendiculaires. }{% Comme les droites $(#2)$ et $(#4)$ sont parallèles, alors la droite $(#3)$ qui est perpendiculaire à $(#4)$ est également perpendiculaire à la droite $(#2)$. - } - } - } - } -} + }% + }% + }% + }% +}% \newcommand\Brouillon[4][]{% \setlength{\abovedisplayskip}{0pt} @@ -7417,10 +8103,10 @@ vardef Positions(expr Step)= \end{array} \right\}(#2)\perp(#3) \] - } - } - } -} + }% + }% + }% +}% \def\MPFigureDroite#1#2{% \ifluatex @@ -7626,11 +8312,10 @@ vardef Positions(expr Step)= }% }% -%%%%%%%%%%%%%%%%%%%% -%%% Fonction Affine -%%%%%%%%%%%%%%%%%%%% -\setKVdefault[ClesAffine]{Nom=f,Variable=x,Ligne=false,Image=false,Antecedent=false,Graphique=false,Retrouve=false,ProgCalcul=false,Unitex=1,Unitey=1,VoirCoef=false,ACoef=0,Redaction=false,Ecriture=false,Definition=false}%ACoefficient=false - %: inutile ? +%%% +% Fonction Affine +%%% +\setKVdefault[ClesAffine]{Nom=f,Variable=x,Ligne=false,Image=false,Antecedent=false,Graphique=false,Retrouve=false,ProgCalcul=false,Unitex=1,Unitey=1,VoirCoef=false,ACoef=0,Redaction=false,Ecriture=false,Definition=false}%ACoefficient=false%: inutile ? \newcommand\FonctionAffine[5][]{% % #1 nombre ou abscisse premier point @@ -7641,7 +8326,7 @@ vardef Positions(expr Step)= \setKV[ClesAffine]{#1}% \ifboolKV[ClesAffine]{Image}{% \ifboolKV[ClesAffine]{Ligne}{% - \ensuremath{\useKV[ClesAffine]{Nom}(\num{#2})=\num{#3}\times\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{\num{#4}}}=\num{\fpeval{#2*#3}}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{\num{#4}}}\xintifboolexpr{#4=0}{}{=\num{\fpeval{#2*#3+#4}}}}% + \ensuremath{\useKV[ClesAffine]{Nom}(\num{#2})=\num{#3}\times\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{-\num{\fpeval{0-#4}}}}=\num{\fpeval{#2*#3}}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{-\num{\fpeval{0-#4}}}}\xintifboolexpr{#4=0}{}{=\num{\fpeval{#2*#3+#4}}}}% }{% \ifboolKV[ClesAffine]{ProgCalcul}{% \begin{align*} @@ -7650,8 +8335,8 @@ vardef Positions(expr Step)= \end{align*} }{% \begin{align*} - \useKV[ClesAffine]{Nom}(\num{#2})&=\num{#3}\times\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{\num{#4}}}\\ - \useKV[ClesAffine]{Nom}(\num{#2})&=\num{\fpeval{#3*#2}}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{\num{#4}}}%\\ + \useKV[ClesAffine]{Nom}(\num{#2})&=\num{#3}\times\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{-\num{\fpeval{0-#4}}}}\\ + \useKV[ClesAffine]{Nom}(\num{#2})&=\num{\fpeval{#3*#2}}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{-\num{\fpeval{0-#4}}}}%\\ \xintifboolexpr{#4=0}{}{\\ \useKV[ClesAffine]{Nom}(\num{#2})&=\num{\fpeval{#3*#2+#4}}%\\ } @@ -7669,17 +8354,20 @@ vardef Positions(expr Step)= \useKV[ClesAffine]{Nom}&:\frac{\num{\fpeval{#2-#4}}}{\num{#3}}\stackrel{\div\xintifboolexpr{#3<0}{(\num{#3})}{\num{#3}}}{\longleftarrow}\num{\fpeval{#2-#4}}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{\stackrel{-\num{#4}}{\longleftarrow}}{\stackrel{+\num{\fpeval{0-#4}}}{\longleftarrow}}\num{#2}} \end{align*} }{% - On cherche l'antécédent de $\num{#2}$ par la fonction $\useKV[ClesAffine]{Nom}$, c'est-à-dire le nombre $\useKV[ClesAffine]{Variable}$ tel que $\useKV[ClesAffine]{Nom}(\useKV[ClesAffine]{Variable})=\num{#2}$. Or, la fonction $\useKV[ClesAffine]{Nom}$ est définie par : - \begin{align*} - \useKV[ClesAffine]{Nom}&:\useKV[ClesAffine]{Variable}\stackrel{\times\xintifboolexpr{#3<0}{(\num{#3})}{\num{#3}}}{\longrightarrow}\num{#3}\useKV[ClesAffine]{Variable}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{\stackrel{+\num{#4}}{\longrightarrow}}{\stackrel{\num{#4}}{\longrightarrow}}\num{#3}\useKV[ClesAffine]{Variable}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{\num{#4}}}} - \end{align*} + On cherche l'antécédent de $\num{#2}$ par la fonction + $\useKV[ClesAffine]{Nom}$, c'est-à-dire le nombre + $\useKV[ClesAffine]{Variable}$ tel que + $\useKV[ClesAffine]{Nom}(\useKV[ClesAffine]{Variable})=\num{#2}$. Or, + la fonction $\useKV[ClesAffine]{Nom}$ est définie par : \[% + \useKV[ClesAffine]{Nom}(\useKV[ClesAffine]{Variable})=\xintifboolexpr{#3=0}{}{\num{#3}\useKV[ClesAffine]{Variable}}\xintifboolexpr{#3=0}{\num{#4}}{\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{-\num{\fpeval{0-#4}}}}} + \] Par conséquent, on a : \begin{align*} - \num{#3}\useKV[ClesAffine]{Variable}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{\num{#4}}}&=\num{#2}\\ - \xintifboolexpr{#4=0}{\useKV[ClesAffine]{Variable}\uppercase{&}=\frac{\num{#2}}{\num{#3}} - }{\num{#3}\useKV[ClesAffine]{Variable}&=\num{\fpeval{#2-#4}}\\ - \useKV[ClesAffine]{Variable}&=\frac{\num{\fpeval{#2-#4}}}{\num{#3}} - } + \num{#3}\useKV[ClesAffine]{Variable}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{+\num{#4}}{-\num{\fpeval{0-#4}}}}&=\num{#2}\\ + \xintifboolexpr{#4=0}{\useKV[ClesAffine]{Variable}\uppercase{&}=\frac{\num{#2}}{\num{#3}}%\\ + }{\num{#3}\useKV[ClesAffine]{Variable}&=\num{\fpeval{#2-#4}}\\ + \useKV[ClesAffine]{Variable}&=\frac{\num{\fpeval{#2-#4}}}{\num{#3}}%\\ + } \end{align*} }% }{% @@ -7716,16 +8404,15 @@ vardef Positions(expr Step)= \ifboolKV[ClesAffine]{Redaction}{% \xintifboolexpr{#2=0}{Comme la fonction $\useKV[ClesAffine]{Nom}$ est une fonction constante, alors sa représentation graphique est une droite parallèle à l'axe des abscisses passant par le point de coordonnées $(0;\num{#3})$.}% - {\xintifboolexpr{#3=0}{Comme la fonction - $\useKV[ClesAffine]{Nom}$ est une fonction linéaire, alors sa représentation graphique est une droite passant par l'origine du repère.\\Je choisis $\useKV[ClesAffine]{Variable}=\num{#4}$. Son image est \xdef\NomFonctionA{\useKV[ClesAffine]{Nom}}\FonctionAffine[Nom=\NomFonctionA,Image,Ligne]{#4}{#2}{#3}{#5}. On place le point de coordonnées $(\num{#4};\num{\fpeval{#2*#4+#3}})$. + {\xintifboolexpr{#3=0}{Comme la fonction $\useKV[ClesAffine]{Nom}$ est une fonction linéaire, alors sa représentation graphique est une droite passant par l'origine du repère.\\Je choisis $\useKV[ClesAffine]{Variable}=\num{#4}$. Son image est \xdef\NomFonctionA{\useKV[ClesAffine]{Nom}}\FonctionAffine[Nom=\NomFonctionA,Image,Ligne]{#4}{#2}{#3}{#5}. On place le point de coordonnées $(\num{#4};\num{\fpeval{#2*#4+#3}})$. }{% - Comme $\useKV[ClesAffine]{Nom}$ est une fonction affine, alors sa représentation graphique est une droite.\\Je choisis $\useKV[ClesAffine]{Variable}=\num{#4}$. Son image est \xdef\NomFonction{\useKV[ClesAffine]{Nom}}\FonctionAffine[Nom=\NomFonction,Image,Ligne]{#4}{#2}{#3}{#5}. On place le point de coordonnées $(\num{#4};\num{\fpeval{#2*#4+#3}})$.\\Je choisis $\useKV[ClesAffine]{Variable}=\num{#5}$. Son image est \FonctionAffine[Nom=\NomFonction,Image,Ligne]{#5}{#2}{#3}{#4}. On place le point de coordonnées $(\num{#5};\num{\fpeval{#2*#5+#3}})$.% + Comme $\useKV[ClesAffine]{Nom}$ est une fonction affine, alors sa représentation graphique est une droite.\\Je choisis $\useKV[ClesAffine]{Variable}=\num{#4}$. Son image est \xdef\NomVariable{\useKV[ClesAffine]{Variable}}\xdef\NomFonction{\useKV[ClesAffine]{Nom}}\FonctionAffine[Nom=\NomFonction,Image,Ligne]{#4}{#2}{#3}{#5}. On place le point de coordonnées $(\num{#4};\num{\fpeval{#2*#4+#3}})$.\\Je choisis \setKV[ClesAffine]{Variable=\NomVariable}$\useKV[ClesAffine]{Variable}=\num{#5}$. Son image est \FonctionAffine[Nom=\NomFonction,Image,Ligne]{#5}{#2}{#3}{#4}. On place le point de coordonnées $(\num{#5};\num{\fpeval{#2*#5+#3}})$.% }% }% }% {}% - \ifboolKV[ClesAffine]{Ecriture}{\ensuremath{\useKV[ClesAffine]{Nom}(\useKV[ClesAffine]{Variable})=\xintifboolexpr{#2=0}{}{\num{#2}\useKV[ClesAffine]{Variable}}\xintifboolexpr{#2=0}{\num{#3}}{\xintifboolexpr{#3=0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{\num{#3}}}}}}{}% - \ifboolKV[ClesAffine]{Definition}{\ensuremath{\useKV[ClesAffine]{Nom}:\useKV[ClesAffine]{Variable}\mapsto\xintifboolexpr{#2=0}{}{\num{#2}\useKV[ClesAffine]{Variable}}\xintifboolexpr{#2=0}{\num{#3}}{\xintifboolexpr{#3=0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{\num{#3}}}}}}{}% + \ifboolKV[ClesAffine]{Ecriture}{\ensuremath{\useKV[ClesAffine]{Nom}(\useKV[ClesAffine]{Variable})=\xintifboolexpr{#2=0}{}{\num{#2}\useKV[ClesAffine]{Variable}}\xintifboolexpr{#2=0}{\num{#3}}{\xintifboolexpr{#3=0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}}}}{}% + \ifboolKV[ClesAffine]{Definition}{\ensuremath{\useKV[ClesAffine]{Nom}:\useKV[ClesAffine]{Variable}\mapsto\xintifboolexpr{#2=0}{}{\num{#2}\useKV[ClesAffine]{Variable}}\xintifboolexpr{#2=0}{\num{#3}}{\xintifboolexpr{#3=0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}}}}{}% }% \def\MPFonctionAffine#1#2#3#4#5#6#7{% @@ -7987,56 +8674,254 @@ vardef Positions(expr Step)= } -%%%%%%%%%%%%%%% +%%% % Fonction -%%%%%%%%%%%%%%% -\setKVdefault[ClesFonction]{Nom=f,Variable=x,Calcul=x,Tableau=false,Largeur=5mm,Ecriture=false,Definition=false} - -\newcommand{\Fonction}[2][]{% - \useKVdefault[ClesFonction] - \setKV[ClesFonction]{#1} - \ignoreemptyitems% - \readlist*\ListeFonction{#2} - \StrSubstitute{\useKV[ClesFonction]{Calcul}}{\useKV[ClesFonction]{Variable}}{\i}[\temp]% - - \StrSubstitute{\useKV[ClesFonction]{Calcul}}{**}{^}[\tempa]% - \StrSubstitute{\tempa}{*}{}[\tempab]% - \ifboolKV[ClesFonction]{Ecriture}{% - \ensuremath{\useKV[ClesFonction]{Nom}(\useKV[ClesFonction]{Variable})=\tempab} - }{}% - \ifboolKV[ClesFonction]{Definition}{% - \ensuremath{\useKV[ClesFonction]{Nom}:\useKV[ClesFonction]{Variable}\mapsto\tempab} - }{}% - \ifboolKV[ClesFonction]{Tableau}{% - \buildtabfonction% - }{} -} +%%% +\setKVdefault[ClesFonction]{Nom=f,Variable=x,Calcul=x,Tableau=false,Largeur=5mm,Ecriture=false,Definition=false,Points=false,Tangentes=false,PasX=1,PasY=1,UniteX=1,UniteY=1,Prolonge=false} -\def\buildtabfonction{%\\ - \[% - \begin{array}{|>{\columncolor{gray!15}}c|*{\number\numexpr\ListeFonctionlen}{>{\centering\arraybackslash}p{\useKV[ClesFonction]{Largeur}}|}}% - \hline - \useKV[ClesFonction]{Variable}\xintFor* ##1 in {\xintSeq {1}{\ListeFonctionlen}}\do{&\num{\ListeFonction[##1]}}\\ - \hline - \useKV[ClesFonction]{Nom}(\useKV[ClesFonction]{Variable})\xintFor* ##1 in {\xintSeq {1}{\ListeFonctionlen}}\do{& \StrSubstitute{\useKV[ClesFonction]{Calcul}}{\useKV[ClesFonction]{Variable}}{\ListeFonction[##1]}[\tempab]\num{\fpeval{\tempab}}} - \\\hline - \end{array} - \] -} +\newtoks\toklistePtsFn%pour la discipline -%%%%%%% -%% Formules -%%%%%% -\setKVdefault[ClesFormule]{Perimetre=false,Aire=false,Volume=false,Surface=carré,Solide=pavé droit,Figure=false,Angle=0,Ancre={(0,0)},Largeur=5cm} +\def\UpdatePtsFn#1/#2/#3/#4\nil{\addtotok\toklistePtsFn{#1,(#2,#3),#4,}}% +\def\UpdatePtsFN#1/#2/#3/#4\nil{\addtotok\toklistePtsFn{(#2,#3),}}% -\def\MPFigureCarre{% +\def\MPCourbePoints#1#2#3#4#5#6{% + % #1 la liste des points + % #2: pas en x + % #3: pas en y + % #4: unité en x + % #5: unité en y + % #6 : prolongement avant et après les premier et dernier points ? \ifluatex - \mplibforcehmode + \mplibforcehmode \begin{mplibcode} - drawoptions( dashed dashpattern(on1cm)); - pair A,B,C,D; - A=u*(1,1); - B-A=u*(2,0); + x.u:=#2; + y.u:=#3; + X.u:=#4; + Y.u:=#5; + numeric dirav[],dirap[]; + pair Fn[],Gn[]; + n=0; + for p_=#1: + Gn[n]=p_; + Fn[n]=cm*(X.u*xpart(p_),Y.u*ypart(p_)); + n:=n+1; + endfor; + N:=(n-1); + MinX=999; + MaxX=-999; + MinY=999; + MaxY=-999; + for k=0 upto N: + if xpart(Gn[k])MaxX: + MaxX:=xpart(Gn[k]); + fi; + if ypart(Gn[k])MaxY: + MaxY:=ypart(Gn[k]); + fi; + endfor; + if #6=0: + for k=MinY-1 step y.u until MaxY+1: + draw cm*((MinX-1)*X.u,k*Y.u)--cm*((MaxX+1)*X.u,k*Y.u) withcolor 0.75white; + endfor; + for k=MinX-1 step x.u until MaxX+1: + draw cm*(k*X.u,(MinY-1)*Y.u)--cm*(k*X.u,(MaxY+1)*Y.u) withcolor 0.75white; + endfor; + else: + for k=MinY-1 step y.u until MaxY+1: + draw cm*((MinX)*X.u,k*Y.u)--cm*((MaxX)*X.u,k*Y.u) withcolor 0.75white; + endfor; + for k=MinX step x.u until MaxX: + draw cm*(k*X.u,(MinY-1)*Y.u)--cm*(k*X.u,(MaxY+1)*Y.u) withcolor 0.75white; + endfor; + fi; + if #6=0: + for k=0 upto N: + fill cercles(Fn[k],0.5mm); + endfor; + else: + for k=1 upto N-1: + fill cercles(Fn[k],0.5mm); + endfor; + fi; + if #6=0: + drawarrow (0,(MinY-1)*Y.u*cm)--(0,(MaxY+1)*Y.u*cm); + drawarrow ((MinX-1)*X.u*cm,0)--((MaxX+1)*X.u*cm,0); + else: + drawarrow (0,(MinY-1)*Y.u*cm)--(0,(MaxY+1)*Y.u*cm); + drawarrow ((MinX)*X.u*cm,0)--((MaxX)*X.u*cm,0); + fi; + label.llft(btex O etex,(0,0)); + dotlabel.bot(btex 1 etex,cm*X.u*(1,0)); + dotlabel.lft(btex 1 etex,cm*Y.u*(0,1)); + draw Fn[0] + for k=1 upto N: + ..Fn[k] + endfor; + \end{mplibcode} + \fi +} + +\def\MPCourbe#1#2#3#4#5#6{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + x.u:=#2; + y.u:=#3; + X.u:=#4; + Y.u:=#5; + numeric dirav[],dirap[]; + pair Fn[],Gn[]; + n=0; + for p_=#1: + if (n mod 3)=0: + dirav[n div 3]=p_; + fi; + if (n mod 3)=1: + Gn[n div 3]=p_; + Fn[n div 3]=cm*(X.u*xpart(p_),Y.u*ypart(p_)); + fi; + if (n mod 3)=2: + dirap[n div 3]=p_; + fi; + n:=n+1; + endfor; + N:=(n-1) div 3; + MinX=999; + MaxX=-999; + MinY=999; + MaxY=-999; + for k=0 upto N: + if xpart(Gn[k])MaxX: + MaxX:=xpart(Gn[k]); + fi; + if ypart(Gn[k])MaxY: + MaxY:=ypart(Gn[k]); + fi; + endfor; + if #6=0: + for k=MinY-1 step y.u until MaxY+1: + draw cm*((MinX-1)*X.u,k*Y.u)--cm*((MaxX+1)*X.u,k*Y.u) withcolor 0.75white; + endfor; + for k=MinX-1 step x.u until MaxX+1: + draw cm*(k*X.u,(MinY-1)*Y.u)--cm*(k*X.u,(MaxY+1)*Y.u) withcolor 0.75white; + endfor; + else: + for k=MinY-1 step y.u until MaxY+1: + draw cm*((MinX)*X.u,k*Y.u)--cm*((MaxX)*X.u,k*Y.u) withcolor 0.75white; + endfor; + for k=MinX step x.u until MaxX: + draw cm*(k*X.u,(MinY-1)*Y.u)--cm*(k*X.u,(MaxY+1)*Y.u) withcolor 0.75white; + endfor; + fi; + if #6=0: + for k=0 upto N: + fill cercles(Fn[k],0.5mm); + endfor; + else: + for k=1 upto N-1: + fill cercles(Fn[k],0.5mm); + endfor; + fi; + if #6=0: + drawarrow (0,(MinY-1)*Y.u*cm)--(0,(MaxY+1)*Y.u*cm); + drawarrow ((MinX-1)*X.u*cm,0)--((MaxX+1)*X.u*cm,0); + else: + drawarrow (0,(MinY-1)*Y.u*cm)--(0,(MaxY+1)*Y.u*cm); + drawarrow ((MinX)*X.u*cm,0)--((MaxX)*X.u*cm,0); + fi; + label.llft(btex O etex,(0,0)); + dotlabel.bot(btex 1 etex,cm*X.u*(1,0)); + dotlabel.lft(btex 1 etex,cm*Y.u*(0,1)); + draw Fn[0]{dir dirap[0]} + for k=1 upto (N-1): + ..{dir dirav[k]}Fn[k]{dir dirap[k]} + endfor + ..{dir dirav[N]}Fn[N]; + \end{mplibcode} + \fi +} + +\newcommand{\Fonction}[2][]{% + \useKVdefault[ClesFonction] + \setKV[ClesFonction]{#1} + \ifboolKV[ClesFonction]{Points}{% + \toklistePtsFn{}% + \setsepchar[*]{,*/}%\ignoreemptyitems% + \readlist*\ListePoints{#2}% + \ifboolKV[ClesFonction]{Tangentes}{% + \foreachitem\compteur\in\ListePoints{% + \expandafter\UpdatePtsFn\compteur\nil% + }% + \ifboolKV[ClesFonction]{Prolonge}{% + \MPCourbe{\the\toklistePtsFn}{\useKV[ClesFonction]{PasX}}{\useKV[ClesFonction]{PasY}}{\useKV[ClesFonction]{UniteX}}{\useKV[ClesFonction]{UniteY}}{1}% + }{% + \MPCourbe{\the\toklistePtsFn}{\useKV[ClesFonction]{PasX}}{\useKV[ClesFonction]{PasY}}{\useKV[ClesFonction]{UniteX}}{\useKV[ClesFonction]{UniteY}}{0}% + }% + }{% + \foreachitem\compteur\in\ListePoints{% + \expandafter\UpdatePtsFN\compteur\nil% + }% + \ifboolKV[ClesFonction]{Prolonge}{% + \MPCourbePoints{\the\toklistePtsFn}{\useKV[ClesFonction]{PasX}}{\useKV[ClesFonction]{PasY}}{\useKV[ClesFonction]{UniteX}}{\useKV[ClesFonction]{UniteY}}{1}% + }{% + \MPCourbePoints{\the\toklistePtsFn}{\useKV[ClesFonction]{PasX}}{\useKV[ClesFonction]{PasY}}{\useKV[ClesFonction]{UniteX}}{\useKV[ClesFonction]{UniteY}}{0}% + }% + }% + }{% + \ignoreemptyitems% + \readlist*\ListeFonction{#2} + \StrSubstitute{\useKV[ClesFonction]{Calcul}}{\useKV[ClesFonction]{Variable}}{\i}[\temp]% + \StrSubstitute{\useKV[ClesFonction]{Calcul}}{**}{^}[\tempa]% + \StrSubstitute{\tempa}{*}{}[\tempab]% + \ifboolKV[ClesFonction]{Ecriture}{% + \ensuremath{\useKV[ClesFonction]{Nom}(\useKV[ClesFonction]{Variable})=\tempab} + }{}% + \ifboolKV[ClesFonction]{Definition}{% + \ensuremath{\useKV[ClesFonction]{Nom}:\useKV[ClesFonction]{Variable}\mapsto\tempab} + }{}% + \ifboolKV[ClesFonction]{Tableau}{% + \buildtabfonction% + }{}% + }% +}% + +\def\buildtabfonction{%\\ + \[% + \begin{array}{|>{\columncolor{gray!15}}c|*{\number\numexpr\ListeFonctionlen}{>{\centering\arraybackslash}p{\useKV[ClesFonction]{Largeur}}|}}% + \hline + \useKV[ClesFonction]{Variable}\xintFor* ##1 in {\xintSeq {1}{\ListeFonctionlen}}\do{&\num{\ListeFonction[##1]}}\\ + \hline + \useKV[ClesFonction]{Nom}(\useKV[ClesFonction]{Variable})\xintFor* ##1 in {\xintSeq {1}{\ListeFonctionlen}}\do{& \StrSubstitute{\useKV[ClesFonction]{Calcul}}{\useKV[ClesFonction]{Variable}}{(\ListeFonction[##1])}[\tempab]\num{\fpeval{\tempab}}} + \\\hline + \end{array} + \] +} + +%%% +% Formules +%%% +\setKVdefault[ClesFormule]{Perimetre=false,Aire=false,Volume=false,Surface=carré,Solide=pavé,Angle=0,Ancre={(0,0)},Largeur=5cm,Couleur=white} + +\def\MPFigureCarre{% + \ifluatex + \mplibforcehmode + \begin{mplibcode} + drawoptions( dashed dashpattern(on1cm)); + pair A,B,C,D; + A=u*(1,1); + B-A=u*(2,0); C=rotation(A,B,-90); D-C=A-B; draw polygone(A,B,C,D); @@ -8496,7 +9381,6 @@ vardef Positions(expr Step)= \mplibforcehmode \begin{mplibcode} drawoptions( dashed dashpattern(on1cm)); - % Figure(-10u,-10u,10u,10u); u:=0.5cm; z0=(-0.5,0)*u; z1=(2.5,0.5)*u; @@ -8788,7 +9672,6 @@ vardef Positions(expr Step)= \mplibforcehmode \begin{mplibcode} drawoptions( dashed dashpattern(on1cm)); - % Figure(-5u,-5u,5u,5u); pair A,B,C,H,I,J; A=u*(0.5,1); B-A=u*(1.4,0); @@ -8866,12 +9749,13 @@ vardef Positions(expr Step)= } \newcommand\Formule[1][]{% - \useKVdefault[ClesFormule] - \setKV[ClesFormule]{#1} - \setlength{\RoundedBoxWidth}{\useKV[ClesFormule]{Largeur}} + \useKVdefault[ClesFormule]% + \setKV[ClesFormule]{#1}% + \setlength{\RoundedBoxWidth}{\useKV[ClesFormule]{Largeur}}% + \xdef\ColorFill{\useKV[ClesFormule]{Couleur}}% \ifboolKV[ClesFormule]{Perimetre}{% \begin{tikzpicture}[remember picture, overlay] - \node[draw,dashed,rounded corners,rotate={\useKV[ClesFormule]{Angle}}] (test) at \useKV[ClesFormule]{Ancre} {\begin{minipage}{\RoundedBoxWidth}% + \node[draw,fill=\ColorFill,dashed,rounded corners,rotate={\useKV[ClesFormule]{Angle}}] (test) at \useKV[ClesFormule]{Ancre} {\begin{minipage}{\RoundedBoxWidth}% \IfStrEqCase{\useKV[ClesFormule]{Surface}}{% {carré}{\begin{center} \MPFigureCarre\par @@ -8883,7 +9767,7 @@ vardef Positions(expr Step)= Périmètre d'un polygone : \par$\text{Somme des côtés}$ \end{center} }% - {rectangle}{ + {rectangle}{% \begin{center} \MPFigureRectangle\par Périmètre d'un rectangle : \par$2\times(L+\ell)$ @@ -8907,7 +9791,7 @@ vardef Positions(expr Step)= Périmètre d'un cercle : \par$\pi\times\text{diamètre}$ \end{center} }% - {parallélogramme}{ + {parallélogramme}{% \begin{center} \MPFigureParallelogramme\par Périmètre d'un parallélogramme : \par Somme des côtés @@ -8917,7 +9801,7 @@ vardef Positions(expr Step)= \end{tikzpicture} }{\ifboolKV[ClesFormule]{Aire}{% \begin{tikzpicture}[remember picture, overlay] - \node[draw,dashed,rounded corners=2,rotate={\useKV[ClesFormule]{Angle}}] (test) at \useKV[ClesFormule]{Ancre} {\begin{minipage}{\RoundedBoxWidth}% + \node[draw,fill=\ColorFill,dashed,rounded corners=2,rotate={\useKV[ClesFormule]{Angle}}] (test) at \useKV[ClesFormule]{Ancre} {\begin{minipage}{\RoundedBoxWidth}% \IfStrEqCase{\useKV[ClesFormule]{Surface}}{% {carré}{\begin{center} \MPFigureCarre\par @@ -8963,7 +9847,7 @@ vardef Positions(expr Step)= \end{tikzpicture} }{%Volume \begin{tikzpicture}[remember picture, overlay] - \node[draw,dashed,rounded corners=2,rotate={\useKV[ClesFormule]{Angle}}] (test) at \useKV[ClesFormule]{Ancre} {\begin{minipage}{\RoundedBoxWidth}% + \node[draw,fill=\ColorFill,dashed,rounded corners=2,rotate={\useKV[ClesFormule]{Angle}}] (test) at \useKV[ClesFormule]{Ancre} {\begin{minipage}{\RoundedBoxWidth}% \IfStrEqCase{\useKV[ClesFormule]{Solide}}{% {boule}{\begin{center} \MPFigureSphere\par @@ -9012,10 +9896,10 @@ vardef Positions(expr Step)= } } -%%%%%%%%%% -%%% Proba -%%%%%%%%%% -\setKVdefault[ClesProba]{Echelle=false,Arbre=false,Branche=2,Angle=60,Rayon=0.25,LongueurEchelle=5,Affichage=0,Grille=0} +%%% +% Proba +%%% +\setKVdefault[ClesProba]{Echelle=false,Arbre=false,Branche=2,Angle=60,Rayon=0.25,LongueurEchelle=5,Affichage=0,Grille=1} \def\Updatetoksproba#1/#2\nil{\addtotok\toklistepointproba{"#1","\footnotesize #2",}} \def\Updatetoksprobaechelle#1/#2/#3\nil{\addtotok\toklistepointproba{#1,#2,"#3",}} @@ -9091,7 +9975,7 @@ vardef Positions(expr Step)= dotlabel.top("",C[k]); fi; if (#3>2): - label.bot(TEX("$\frac{"&decimal(num)&"}{"&decimal(deno)&"}$"),C[k]-u*(0,0.5));%Le \noexpand est nécessaire pour éviter un problème à la compilation, dû à l'expansion du \frac par gmp. + label.bot(TEX("$\frac{"&decimal(num)&"}{"&decimal(deno)&"}$"),C[k]-u*(0,0.5)); fi; k:=k+1; fi; @@ -9271,10 +10155,10 @@ vardef Positions(expr Step)= } } -%%%%%%%%%%%%%% -%%%Reperage -%%%%%%%%%%%%%% -\setKVdefault[ClesReperage]{Unitex=1,Pasx=1,Unitey=1,Pasy=1,Unitez=1,Pasz=1,DemiDroite=false,Droite=false,Plan=false,Trace=false,ListeSegment={},Espace=false,Sphere=false,AffichageNom=false,AffichageCoord=false,ValeurUnitex=1,ValeurUnitey=1,ValeurOrigine=0,EchelleEspace=50,CouleurCoord=black} +%%% +% Reperage +%%% +\setKVdefault[ClesReperage]{Unitex=1,Pasx=1,Unitey=1,Pasy=1,Unitez=1,Pasz=1,DemiDroite=false,Droite=false,Plan=false,Trace=false,ListeSegment={},Espace=false,Sphere=false,AffichageNom=false,AffichageGrad=false,AffichageAbs=0,AffichageCoord=false,LectureCoord=false,ValeurUnitex=1,ValeurUnitey=1,ValeurOrigine=0,NomOrigine=O,EchelleEspace=50,CouleurCoord=black} % ValeurOrigine permet de faire des morceaux de demi-droite graduée en passant par droite :) \def\Updatetoksdroite#1/#2\nil{\addtotok\toklistepointdroite{#1,"#2",}} @@ -9565,46 +10449,44 @@ vardef Positions(expr Step)= }% % Pour construire le repère du plan -\def\buildrepere{% +\def\buildreperenew{% \toklistepointrepere{}% \foreachitem\compteur\in\ListePointRepere{\expandafter\Updatetoksrepere\compteur\nil}% \ifboolKV[ClesReperage]{Trace}{% \[\MPPlanTrace{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\useKV[ClesReperage]{Unitey}}{\useKV[ClesReperage]{Pasy}}{\the\toklistepointrepere}{2}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurUnitey}}{\useKV[ClesReperage]{ListeSegment}}\]% }{% - \ifboolKV[ClesReperage]{AffichageNom}{% - \ifboolKV[ClesReperage]{AffichageCoord}{% - \[\MPPlan{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\useKV[ClesReperage]{Unitey}}{\useKV[ClesReperage]{Pasy}}{\the\toklistepointrepere}{3}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurUnitey}}\]% - }{% - \[\MPPlan{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\useKV[ClesReperage]{Unitey}}{\useKV[ClesReperage]{Pasy}}{\the\toklistepointrepere}{2}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurUnitey}}\]% - } - }{% - \ifboolKV[ClesReperage]{AffichageCoord}{% - \[\MPPlan{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\useKV[ClesReperage]{Unitey}}{\useKV[ClesReperage]{Pasy}}{\the\toklistepointrepere}{1}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurUnitey}}\]% - }{% - \[\MPPlan{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\useKV[ClesReperage]{Unitey}}{\useKV[ClesReperage]{Pasy}}{\the\toklistepointrepere}{0}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurUnitey}}\]% - } - }% + \xdef\AfficheNom{0}\ifboolKV[ClesReperage]{AffichageNom}{\ifboolKV[ClesReperage]{LectureCoord}{\xdef\AfficheNom{3}}{\xdef\AfficheNom{2}}}{\ifboolKV[ClesReperage]{LectureCoord}{\xdef\AfficheNom{1}}{}}% + \xdef\AfficheGrad{0}\ifboolKV[ClesReperage]{AffichageGrad}{\xdef\AfficheGrad{1}}{}% + \xdef\AfficheCoord{\useKV[ClesReperage]{AffichageAbs}}% + \MPPlannew{(\useKV[ClesReperage]{Unitex},\useKV[ClesReperage]{Pasx})}{(\useKV[ClesReperage]{Unitey},\useKV[ClesReperage]{Pasy})}{\the\toklistepointrepere}{\AfficheNom}{\AfficheCoord}{\AfficheGrad}{(\useKV[ClesReperage]{ValeurUnitex},\useKV[ClesReperage]{ValeurUnitey})}% }% } -\def\MPPlan#1#2#3#4#5#6#7#8{% +\def\MPPlannew#1#2#3#4#5#6#7{% + %#1 : Unitex, pasx + %#2 : unitey, pasy + %#3 : liste de points + %#4 : Affichage nom + lecture graphique + %#5 : Affichage des (abscisses/ordonnées) + %#6 : Graduation complète ? + %#7 : (unitex,unitey) \ifluatex \begin{mplibcode} maxx:=-4000; - minx=4000; - unitex:=#1*cm; - pasx=#2; - unitpx:=unitex/pasx; - maxy:=-4000; - miny:=4000; - unitey:=#3*cm; - pasy:=#4; - unitpy:=unitey/pasy; - n:=1; - vardef toto(text t)= + minx=4000; + unitex:=(xpart(#1))*cm; + pasx=ypart(#1); + unitpx:=unitex/pasx; + maxy:=-4000; + miny:=4000; + unitey:=(xpart(#2))*cm; + pasy:=ypart(#2); + unitpy:=unitey/pasy; + n:=1; + vardef toto(text t)= for p_=t: if (n mod 3)=1: - if p_>maxx: + if p_>maxx: maxx:=p_; fi; if p_(-#2-1): - minx:=-#2-1; + if minx>(-ypart(#1)-1): + minx:=-ypart(#1)-1; fi; maxy:=maxy+1; miny:=miny-1; - if maxy<(#4+1): - maxy:=#2+1; + if maxy<(ypart(#2)+1): + maxy:=ypart(#2)+1; fi; - if miny>(-#4-1): - miny:=-#4-1; + if miny>(-ypart(#2)-1): + miny:=-ypart(#2)-1; fi; enddef; - toto(#5); + toto(#3); Figure((minx-1)*unitpx,(miny-1)*unitpy,(maxx+1)*unitpx,(maxy+1)*unitpy); pair A,B,C,D,E; A=(0,0); @@ -9654,14 +10536,32 @@ vardef Positions(expr Step)= endfor; drawarrow (B+(-0.75*unitpx,0))--(C+(0.75*unitpx,0)); drawarrow (D+(0,-0.75*unitpy))--(E+(0,0.75*unitpy)); - dotlabel.bot(TEX("\footnotesize\num{"&decimal(#7)&"}"),(unitex,0)); - dotlabel.lft(TEX("\footnotesize\num{"&decimal(#8)&"}"),(0,unitey)); - label.llft(btex 0 etex,A); + % graduation complète ou pas ? + label.llft(btex \footnotesize 0 etex,A); + if #6>0: + for k=minx upto maxx: + if (xpart((k*unitex,0))>xpart(B+(-0.75*unitpx,0))) and (xpart((k*unitex,0))0: + dotlabel.lrt(TEX("\footnotesize\num{"&decimal(k)&"}"),(k*unitex,0)); + fi; + fi; + endfor; + for k=miny upto maxy: + if (ypart((0,k*unitey))>ypart(D+(0,-0.75*unitpy))) and (ypart((0,k*unitey))0: + dotlabel.ulft(TEX("\footnotesize\num{"&decimal(k)&"}"),(0,k*unitey)); + fi; + fi; + endfor; + else: + dotlabel.lrt(TEX("\footnotesize\num{"&decimal(xpart(#7))&"}"),(unitex,0)); + dotlabel.ulft(TEX("\footnotesize\num{"&decimal(ypart(#7))&"}"),(0,unitey)); + fi; % apparition du nom des points ou pas m_c:=m_c*3; marque_p:="croix"; vardef tata(text t)=%on place les points - if #6>0: + if #4>0: n:=1; k:=0;%pour retenir la coordonnée en x l:=0;%pour retenir la coordonnée en y @@ -9677,15 +10577,14 @@ vardef Positions(expr Step)= fi; fi; if (n mod 3)=0: - if #6>1: - message("p = "&p_); - % if p_<>"": + if #4>1: + if p_<>"": if (k>0) and (l>0): label.urt(TEX(p_),(k*unitpx,l*unitpy)); fi; - if (k=0) and (l>0): - label.urt(TEX(p_),(k*unitpx,l*unitpy)); - fi; + if (k=0) and (l>0): + label.urt(TEX(p_),(k*unitpx,l*unitpy)); + fi; if (k>0) and (l=0): label.urt(TEX(p_),(k*unitpx,l*unitpy)); fi; @@ -9705,35 +10604,92 @@ vardef Positions(expr Step)= label.lrt(TEX(p_),(k*unitpx,l*unitpy)); fi; pointe((k*unitpx,l*unitpy)); - % fi; fi; - if (#6=1) or (#6=3): + fi; + if (#4=1) or (#4=3): draw (0,l*unitpy)--(k*unitpx,l*unitpy)--(k*unitpx,0) dashed evenly; fi; fi; n:=n+1; endfor; fi; + if #5=2: + n:=1; + k:=0;%pour retenir la coordonnée en x + l:=0;%pour retenir la coordonnée en y + for p_=t: + if (n mod 3)=1: + if numeric p_: + k:=p_; + fi; + fi; + if (n mod 3)=2: + if numeric p_: + l:=p_; + fi; + fi; + if (n mod 3)=0: + if p_<>"": + if (k mod pasx)<>0: + label.lrt(TEX("\footnotesize$\frac{\num{"&decimal(k)&"}}{\num{"&decimal(pasx)&"}}$"),(k*unitpx,0)); + else: + label.lrt(TEX("\footnotesize\num{\fpeval{"&decimal(k)&"/"&decimal(pasx)&"}}"),(k*unitpx,0)); + fi; + if (l mod pasy)<>0: + label.ulft(TEX("\footnotesize$\frac{\num{"&decimal(l)&"}}{\num{"&decimal(pasy)&"}}$"),(0,l*unitpy)); + else: + label.ulft(TEX("\footnotesize\num{\fpeval{"&decimal(l)&"/"&decimal(pasy)&"}}"),(0,l*unitpy)); + fi; + pointe((k*unitpx,0),(0,l*unitpy)); + fi; + fi; + n:=n+1; + endfor; + elseif #5=1: + n:=1; + k:=0;%pour retenir la coordonnée en x + l:=0;%pour retenir la coordonnée en y + for p_=t: + if (n mod 3)=1: + if numeric p_: + k:=p_; + fi; + fi; + if (n mod 3)=2: + if numeric p_: + l:=p_; + fi; + fi; + if (n mod 3)=0: + if p_<>"": + label.lrt(TEX("\footnotesize\num{\fpeval{"&decimal(k)&"/"&decimal(pasx)&"}}"),(k*unitpx,0)); + label.ulft(TEX("\footnotesize\num{\fpeval{"&decimal(l)&"/"&decimal(pasy)&"}}"),(0,l*unitpy)); + pointe((k*unitpx,0),(0,l*unitpy)); + fi; + fi; + n:=n+1; + endfor; + fi; enddef; - tata(#5); + tata(#3); \end{mplibcode} \else - \begin{mpost}[mpsettings={input PfC-Geometrie;}] - maxx:=-4000; - minx=4000; - unitex:=#1*cm; - pasx=#2; - unitpx:=unitex/pasx; - maxy:=-4000; - miny:=4000; - unitey:=#3*cm; - pasy:=#4; - unitpy:=unitey/pasy; - n:=1; - vardef toto(text t)= + \begin{mpost} + maxx:=-4000; + minx=4000; + unitex:=(xpart(#1))*cm; + pasx=ypart(#1); + unitpx:=unitex/pasx; + maxy:=-4000; + miny:=4000; + unitey:=(xpart(#2))*cm; + pasy:=ypart(#2); + unitpy:=unitey/pasy; + n:=1; + vardef toto(text t)= for p_=t: if (n mod 3)=1: - if p_>maxx: + if p_>maxx: maxx:=p_; fi; if p_(-#2-1): - minx:=-#2-1; + if minx>(-ypart(#1)-1): + minx:=-ypart(#1)-1; fi; maxy:=maxy+1; miny:=miny-1; - if maxy<(#4+1): - maxy:=#2+1; + if maxy<(ypart(#2)+1): + maxy:=ypart(#2)+1; fi; - if miny>(-#4-1): - miny:=-#4-1; + if miny>(-ypart(#2)-1): + miny:=-ypart(#2)-1; fi; enddef; - toto(#5); + toto(#3); Figure((minx-1)*unitpx,(miny-1)*unitpy,(maxx+1)*unitpx,(maxy+1)*unitpy); pair A,B,C,D,E; A=(0,0); @@ -9783,14 +10739,32 @@ vardef Positions(expr Step)= endfor; drawarrow (B+(-0.75*unitpx,0))--(C+(0.75*unitpx,0)); drawarrow (D+(0,-0.75*unitpy))--(E+(0,0.75*unitpy)); - dotlabel.bot(LATEX("\noexpand\footnotesize\num{"&decimal(#7)&"}"),(unitex,0)); - dotlabel.lft(LATEX("\noexpand\footnotesize\num{"&decimal(#8)&"}"),(0,unitey)); - label.llft(btex 0 etex,A); + % graduation complète ou pas ? + label.llft(btex \noexpand\footnotesize 0 etex,A); + if #6>0: + for k=minx upto maxx: + if (xpart((k*unitex,0))>xpart(B+(-0.75*unitpx,0))) and (xpart((k*unitex,0))0: + dotlabel.lrt(LATEX("\noexpand\footnotesize\noexpand\num{"&decimal(k)&"}"),(k*unitex,0)); + fi; + fi; + endfor; + for k=miny upto maxy: + if (ypart((0,k*unitey))>ypart(D+(0,-0.75*unitpy))) and (ypart((0,k*unitey))0: + dotlabel.ulft(LATEX("\noexpand\footnotesize\noexpand\num{"&decimal(k)&"}"),(0,k*unitey)); + fi; + fi; + endfor; + else: + dotlabel.lrt(LATEX("\noexpand\footnotesize\noexpand\num{"&decimal(xpart(#7))&"}"),(unitex,0)); + dotlabel.ulft(LATEX("\noexpand\footnotesize\noexpand\num{"&decimal(ypart(#7))&"}"),(0,unitey)); + fi; % apparition du nom des points ou pas m_c:=m_c*3; marque_p:="croix"; vardef tata(text t)=%on place les points - if #6>0: + if #4>0: n:=1; k:=0;%pour retenir la coordonnée en x l:=0;%pour retenir la coordonnée en y @@ -9806,7 +10780,8 @@ vardef Positions(expr Step)= fi; fi; if (n mod 3)=0: - if #6>1: + if #4>1: + if p_<>"": if (k>0) and (l>0): label.urt(LATEX(p_),(k*unitpx,l*unitpy)); fi; @@ -9833,15 +10808,73 @@ vardef Positions(expr Step)= fi; pointe((k*unitpx,l*unitpy)); fi; - if (#6=1) or (#6=3): + fi; + if (#4=1) or (#4=3): draw (0,l*unitpy)--(k*unitpx,l*unitpy)--(k*unitpx,0) dashed evenly; fi; fi; n:=n+1; endfor; fi; - enddef; - tata(#5); + if #5=2: + n:=1; + k:=0;%pour retenir la coordonnée en x + l:=0;%pour retenir la coordonnée en y + for p_=t: + if (n mod 3)=1: + if numeric p_: + k:=p_; + fi; + fi; + if (n mod 3)=2: + if numeric p_: + l:=p_; + fi; + fi; + if (n mod 3)=0: + if p_<>"": + if (k mod pasx)<>0: + label.lrt(LATEX("\noexpand\footnotesize$\noexpand\frac{\noexpand\num{"&decimal(k)&"}}{\noexpand\num{"&decimal(pasx)&"}}$"),(k*unitpx,0)); + else: + label.lrt(LATEX("\noexpand\footnotesize\noexpand\num{\noexpand\fpeval{"&decimal(k)&"/"&decimal(pasx)&"}}"),(k*unitpx,0)); + fi; + if (l mod pasy)<>0: + label.ulft(LATEX("\noexpand\footnotesize$\noexpand\frac{\noexpand\num{"&decimal(l)&"}}{\noexpand\num{"&decimal(pasy)&"}}$"),(0,l*unitpy)); + else: + label.ulft(LATEX("\noexpand\footnotesize\noexpand\num{\noexpand\fpeval{"&decimal(l)&"/"&decimal(pasy)&"}}"),(0,l*unitpy)); + fi; + pointe((k*unitpx,0),(0,l*unitpy)); + fi; + fi; + n:=n+1; + endfor; + elseif #5=1: + n:=1; + k:=0;%pour retenir la coordonnée en x + l:=0;%pour retenir la coordonnée en y + for p_=t: + if (n mod 3)=1: + if numeric p_: + k:=p_; + fi; + fi; + if (n mod 3)=2: + if numeric p_: + l:=p_; + fi; + fi; + if (n mod 3)=0: + if p_<>"": + label.lrt(LATEX("\noexpand\footnotesize\noexpand\num{\noexpand\fpeval{"&decimal(k)&"/"&decimal(pasx)&"}}"),(k*unitpx,0)); + label.ulft(LATEX("\noexpand\footnotesize\noexpand\num{\noexpand\fpeval{"&decimal(l)&"/"&decimal(pasy)&"}}"),(0,l*unitpy)); + pointe((k*unitpx,0),(0,l*unitpy)); + fi; + fi; + n:=n+1; + endfor; + fi; + enddef; + tata(#3); \end{mpost} \fi } @@ -10146,231 +11179,68 @@ vardef Positions(expr Step)= \fi } -% Pour construire la demi-droite graduée -\def\builddemidroite{% - \toklistepointdroite{}% - \foreachitem\compteur\in\ListePointDroite{\expandafter\Updatetoksdroite\compteur\nil}% - \ifboolKV[ClesReperage]{DemiDroite}{% - \ifboolKV[ClesReperage]{AffichageNom}{% - \[\MPDemiGraduee{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\the\toklistepointdroite}{1}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurOrigine}}\]% - }{% - \[\MPDemiGraduee{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\the\toklistepointdroite}{0}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurOrigine}}\]% - } - }{% - \ifboolKV[ClesReperage]{AffichageNom}{% - \[\MPDroiteGraduee{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\the\toklistepointdroite}{1}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurOrigine}}\]% - }{% - \[\MPDroiteGraduee{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\the\toklistepointdroite}{0}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurOrigine}}\]% - }% - }% -}% - -\def\MPDemiGraduee#1#2#3#4#5#6{% - % #1 : unite +\def\MPDEMIGraduee#1#2#3#4#5#6#7#8{% + % #1 : unite % #2 : pas % #3 : liste des points à placer en pas. pour gérer le cas des repérages fractionnaires % #4 : on affiche le nom des points ou pas % #5 : quelle est la valeur de la longueur unité ? % #6 : la valeur de l'unité (ne sert à rien ici, mais en prévision % de Droite) + % #7 : on affiche les abscisses ou pas : 0 non, 1 oui, 2 fraction + % #8 : on affiche tous les multiples de la graduation "principale" \ifluatex + \mplibforcehmode \begin{mplibcode} maxx:=0; - unitex:=#1*cm; - pasx:=#2; - unitp:=unitex/pasx;%unité de déplacement - vardef toto(text t)=%On détermine le nombre "d'unités" à placer - for p_=t: - if numeric p_: - if p_>maxx: - maxx:=p_; - fi; - fi; - endfor; - maxx:=maxx+1; - if maxx<(#2+1): - maxx:=#2+1; - fi; - enddef; - toto(#3); - Figure(-u,-u,(maxx+0.75)*unitp,u); - pair A,B; - A=(0,0); - B=unitp*(maxx,0); - drawarrow A--(B+(0.75*unitp,0)); - %marquage secondaire - marque_s:=marque_s/3; - for k=0 step 2 until (maxx): - draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); - endfor; - drawoptions(); - % marquage primaire - marque_s:=marque_s*3; - for k=0 step pasx until (maxx-1): - draw marquesegment((k/maxx)[A,B],((k+pasx)/maxx)[A,B]); - endfor; - % marquage des points - m_c:=m_c*3; - marque_p:="croix"; - labeloffset:=labeloffset*2; - dotlabel.bot(TEX("\footnotesize\num{"&decimal(#5)&"}"),unitex*(1,0)); - label.bot(TEX("\footnotesize\num{"&decimal(#6)&"}"),A); - vardef tata(text t)=%on place les points - if #4>0: - for p_=t: - if numeric p_: - label("",unitp*(p_,0)); - k:=p_; - fi; - if string p_: - if p_<>"": - label.top(TEX(p_),unitp*(k,0)); - pointe(unitp*(k,0)); - fi; - fi; - endfor; - fi; - enddef; - tata(#3); - \end{mplibcode} - \else - \begin{mpost}[mpsettings={input PfC-Geometrie;}] - maxx:=0; - unitex:=#1*cm; - pasx:=#2; - unitp:=unitex/pasx;%unité de déplacement - vardef toto(text t)=%On détermine le nombre "d'unités" à placer - for p_=t: - if numeric p_: - if p_>maxx: - maxx:=p_; - fi; - fi; - endfor; - maxx:=maxx+1; - if maxx<(#2+1): - maxx:=#2+1; - fi; - enddef; - toto(#3); - Figure(-u,-u,(maxx+0.75)*unitp,u); - pair A,B; - A=(0,0); - B=unitp*(maxx,0); - drawarrow A--(B+(0.75*unitp,0)); - %marquage secondaire - marque_s:=marque_s/3; - for k=0 step 2 until (maxx): - draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); - endfor; - drawoptions(); - % marquage primaire - marque_s:=marque_s*3; - for k=0 step pasx until (maxx-1): - draw marquesegment((k/maxx)[A,B],((k+pasx)/maxx)[A,B]); - endfor; - % marquage des points - m_c:=m_c*3; - marque_p:="croix"; - labeloffset:=labeloffset*2; - dotlabel.bot(LATEX("\noexpand\footnotesize\num{"&decimal(#5)&"}"),unitex*(1,0)); - label.bot(LATEX("\noexpand\footnotesize\num{"&decimal(#6)&"}"),A); - vardef tata(text t)=%on place les points - if #4>0: - for p_=t: - if numeric p_: - label("",unitp*(p_,0)); - k:=p_; - fi; - if string p_: - label.top(LATEX(p_),unitp*(k,0)); - if p_<>"": - pointe(unitp*(k,0)); - fi; - fi; - endfor; - fi; - enddef; - tata(#3); -\end{mpost} -\fi -} - -\def\MPDroiteGraduee#1#2#3#4#5#6{% - % #1 : unite - % #2 : pas - % #3 : liste des points à placer en pas. pour gérer le cas des repérages fractionnaires - % #4 : on affiche le nom des points ou pas - % #5 : quelle est la valeur de la longueur unité ? - \ifluatex - \begin{mplibcode} - maxx:=0; - minx:=4000; unitex:=#1*cm; pasx:=#2; unitp:=unitex/pasx;%unité de déplacement vardef toto(text t)=%On détermine le nombre "d'unités" à placer - for p_=t: - if numeric p_: - if p_>maxx: - maxx:=p_; - fi; - if p_(-#2-1): - minx:=-#2-1; - fi; + for p_=t: + if numeric p_: + if p_>maxx: + maxx:=p_; + fi; + fi; + endfor; + maxx:=maxx+1; + if maxx<(#2+1): + maxx:=#2+1; + fi; enddef; toto(#3); - Figure((minx-1)*u,-u,(maxx+1)*unitp,u); - pair A,B,C; + Figure(-u,-u,(maxx+0.75)*unitp,u); + pair A,B; A=(0,0); B=unitp*(maxx,0); - C=unitp*(minx,0); - drawarrow (C+unitp*(-0.75,0))--(B+unitp*(0.75,0)); + drawarrow A--(B+(0.75*unitp,0)); + % marquage secondaire marque_s:=marque_s/3; - labeloffset:=labeloffset*2; - if ((maxx-minx) mod 2)=0: -% show maxx; show minx; - for k=(minx+1) step 2 until (maxx-1): - draw marquedemidroite(C,B); - draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); - endfor; - else: - % show maxx; show minx; - for k=(minx) step 2 until (maxx-1): - draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); - endfor; - fi; - % marquage primaire%%%%%%%%%%%%%%%%%%%%%%%% - marque_s:=marque_s*3; - for k=0 step pasx until (maxx-pasx): - draw marquesegment((k/maxx)[A,B],((k+pasx)/maxx)[A,B]); - endfor; - for k=0 step -pasx until (minx+pasx): - draw marquesegment((k/maxx)[A,B],((k-pasx)/maxx)[A,B]); - endfor; + for k=0 step 2 until (maxx): + draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); + endfor; + drawoptions(); + % marquage primaire + marque_s:=marque_s*3; + for k=0 step pasx until (maxx-1): + draw marquesegment((k/maxx)[A,B],((k+pasx)/maxx)[A,B]); + endfor; + % marquage des points m_c:=m_c*3; marque_p:="croix"; + labeloffset:=labeloffset*2; dotlabel.bot(TEX("\footnotesize\num{"&decimal(#5)&"}"),unitex*(1,0)); label.bot(TEX("\footnotesize\num{"&decimal(#6)&"}"),A); - if #5=1: - label.top(TEX("I"),unitex*(1,0)); + if #8>0: + for k=2 upto maxx: + dotlabel.bot(TEX("\footnotesize\num{\fpeval{"&decimal(#5)&"*"&decimal(k)&"}}"),unitex*(k,0)); + endfor; fi; - label.top(TEX("O"),A); vardef tata(text t)=%on place les points if #4>0: for p_=t: if numeric p_: - label("",unitp*(p_,0)); k:=p_; fi; if string p_: @@ -10381,83 +11251,123 @@ vardef Positions(expr Step)= fi; endfor; fi; + if #7=2: + for p_=t: + if numeric p_: + k:=p_; + fi; + if string p_: + if p_<>"": + if ((#5*k) mod pasx)<>0: + label.bot(TEX("\footnotesize$\frac{\num{\fpeval{"&decimal(#5)&"*"&decimal(k)&"}}}{\num{"&decimal(pasx)&"}}$"),unitp*(k,0)); + else: + label.bot(TEX("\footnotesize\num{\fpeval{"&decimal(#5)&"*"&decimal(k)&"/"&decimal(pasx)&"}}"),unitp*(k,0)); + fi; + pointe(unitp*(k,0)); + fi; + fi; + endfor; + elseif #7=1: + for p_=t: + if numeric p_: + k:=p_; + fi; + if string p_: + if p_<>"": + label.bot(TEX("\footnotesize\num{\fpeval{"&decimal(#5)&"*"&decimal(k)&"/"&decimal(pasx)&"}}"),unitp*(k,0)); + pointe(unitp*(k,0)); + fi; + fi; + endfor; + fi; enddef; tata(#3); \end{mplibcode} \else - \begin{mpost}[mpsettings={input PfC-Geometrie;}] + \begin{mpost} maxx:=0; - minx:=4000; unitex:=#1*cm; pasx:=#2; unitp:=unitex/pasx;%unité de déplacement vardef toto(text t)=%On détermine le nombre "d'unités" à placer - for p_=t: - if numeric p_: - if p_>maxx: - maxx:=p_; - fi; - if p_(-#2-1): - minx:=-#2-1; - fi; + for p_=t: + if numeric p_: + if p_>maxx: + maxx:=p_; + fi; + fi; + endfor; + maxx:=maxx+1; + if maxx<(#2+1): + maxx:=#2+1; + fi; enddef; toto(#3); - Figure((minx-1)*u,-u,(maxx+1)*unitp,u); - pair A,B,C; + Figure(-u,-u,(maxx+0.75)*unitp,u); + pair A,B; A=(0,0); B=unitp*(maxx,0); - C=unitp*(minx,0); - drawarrow (C+unitp*(-0.75,0))--(B+unitp*(0.75,0)); + drawarrow A--(B+(0.75*unitp,0)); + % marquage secondaire marque_s:=marque_s/3; - labeloffset:=labeloffset*2; - if ((maxx-minx) mod 2)=0: -% show maxx; show minx; - for k=(minx+1) step 2 until (maxx-1): - draw marquedemidroite(C,B); - draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); - endfor; - else: - % show maxx; show minx; - for k=(minx) step 2 until (maxx-1): - draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); - endfor; - fi; - % marquage primaire%%%%%%%%%%%%%%%%%%%%%%%% - marque_s:=marque_s*3; - for k=0 step pasx until (maxx-pasx): - draw marquesegment((k/maxx)[A,B],((k+pasx)/maxx)[A,B]); - endfor; - for k=0 step -pasx until (minx+pasx): - draw marquesegment((k/maxx)[A,B],((k-pasx)/maxx)[A,B]); - endfor; + for k=0 step 2 until (maxx): + draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); + endfor; + drawoptions(); + % marquage primaire + marque_s:=marque_s*3; + for k=0 step pasx until (maxx-1): + draw marquesegment((k/maxx)[A,B],((k+pasx)/maxx)[A,B]); + endfor; + % marquage des points m_c:=m_c*3; marque_p:="croix"; + labeloffset:=labeloffset*2; dotlabel.bot(LATEX("\noexpand\footnotesize\num{"&decimal(#5)&"}"),unitex*(1,0)); label.bot(LATEX("\noexpand\footnotesize\num{"&decimal(#6)&"}"),A); - if #5=1: - label.top(LATEX("I"),unitex*(1,0)); + if #8>0: + for k=2 upto maxx: + dotlabel.bot(LATEX("\noexpand\footnotesize\noexpand\num{\noexpand\fpeval{"&decimal(#5)&"*"&decimal(k)&"}}"),unitex*(k,0)); + endfor; fi; - label.top(LATEX("O"),A); vardef tata(text t)=%on place les points if #4>0: for p_=t: if numeric p_: - label("",unitp*(p_,0)); k:=p_; fi; if string p_: + if p_<>"": label.top(LATEX(p_),unitp*(k,0)); + pointe(unitp*(k,0)); + fi; + fi; + endfor; + fi; + if #7=2: + for p_=t: + if numeric p_: + k:=p_; + fi; + if string p_: + if p_<>"": + if ((#5*k) mod pasx)<>0: + label.bot(LATEX("\noexpand\footnotesize$\noexpand\frac{\noexpand\num{\noexpand\fpeval{"&decimal(#5)&"*"&decimal(k)&"}}}{\noexpand\num{"&decimal(pasx)&"}}$"),unitp*(k,0)); + else: + label.bot(LATEX("\noexpand\footnotesize\noexpand\num{\noexpand\fpeval{"&decimal(#5)&"*"&decimal(k)&"/"&decimal(pasx)&"}}"),unitp*(k,0)); + fi; + pointe(unitp*(k,0)); + fi; + fi; + endfor; + elseif #7=1: + for p_=t: + if numeric p_: + k:=p_; + fi; + if string p_: if p_<>"": + label.bot(LATEX("\noexpand\footnotesize\noexpand\num{\noexpand\fpeval{"&decimal(#5)&"*"&decimal(k)&"/"&decimal(pasx)&"}}"),unitp*(k,0)); pointe(unitp*(k,0)); fi; fi; @@ -10468,64 +11378,417 @@ vardef Positions(expr Step)= \end{mpost} \fi } - -\newcommand\Reperage[2][]{% - \useKVdefault[ClesReperage]% - \setKV[ClesReperage]{#1}% - \ifboolKV[ClesReperage]{Espace}{% - \setKV[ClesReperage]{Unitex=2,Unitey=2.5,Unitez=1.5}% - \setKV[ClesReperage]{#1}% - \setsepchar[*]{,*/}\ignoreemptyitems% - \readlist*\ListePointEspace{#2}% - \buildespace% - }{\ifboolKV[ClesReperage]{Plan}{% - \setsepchar[*]{,*/}\ignoreemptyitems% - \readlist*\ListePointRepere{#2}% - \buildrepere% - }{\ifboolKV[ClesReperage]{Droite}{% - \setsepchar[*]{,*/}\ignoreemptyitems% - \readlist*\ListePointDroite{#2}% - \builddemidroite% - }{% - \setsepchar[*]{,*/}\ignoreemptyitems% - \readlist*\ListePointDroite{#2}% - \builddemidroite% - }% - }% + +% Pour construire les droite/demi-droite graduée +\def\builddemidroitenew{% + \toklistepointdroite{}% + \foreachitem\compteur\in\ListePointDroite{\expandafter\Updatetoksdroite\compteur\nil}% + \xdef\AffichageNom{0}\ifboolKV[ClesReperage]{AffichageNom}{\xdef\AffichageNom{1}}{} + \xdef\AffichageCoord{\useKV[ClesReperage]{AffichageAbs}} + \xdef\AffichageGrad{0}\ifboolKV[ClesReperage]{AffichageGrad}{\xdef\AffichageGrad{1}}{} + \ifboolKV[ClesReperage]{DemiDroite}{% + \[\MPDEMIGraduee{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\the\toklistepointdroite}{\AffichageNom}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurOrigine}}{\AffichageCoord}{\AffichageGrad}\]% + }{% + \[\MPDROITEGraduee{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\the\toklistepointdroite}{\AffichageNom}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurOrigine}}{\AffichageCoord}{\AffichageGrad}\]% }% }% -%%%%%%%% -%% Puissances -%%%%%% -\newcommand\Puissances[2]{% - \ensuremath{ - \xintifboolexpr{#2=0}{1}{\xintifboolexpr{#2>0}{\xdef\total{\fpeval{#2-1}}#1\multido{\i=1+1}{\total}{\times#1}}{\xdef\total{\fpeval{-#2-1}}\frac{1}{#1\multido{\i=1+1}{\total}{\times#1}}}}% - } -} - -%%%%%%%%% -% Ecritures d'unités -%%%%%%%%%% -\setKVdefault[Unites]{m=false,km=false,hm=false,dam=false,dm=false,cm=true,mm=false,g=true,kg=false,hg=false,dag=false,dg=false,cg=false,mg=false,kmh=true,ms=false,kgm=false,gcm=true,L=true,kL=false,hL=false,daL=false,dL=false,cL=false,mL=false,l=true,kl=false,hl=false,dal=false,dl=false,cl=false,ml=false} - -\newcommand\Lg[2][]{% - \useKVdefault[Unites]% - \setKV[Unites]{#1}% - \ifboolKV[Unites]{km}{% - \SI{#2}{\km}% - }{\ifboolKV[Unites]{hm}{% - \SI{#2}{\hecto\metre}% - }{\ifboolKV[Unites]{dam}{% - \SI{#2}{\deca\metre}% - }{\ifboolKV[Unites]{dm}{% - \SI{#2}{\dm}% - }{\ifboolKV[Unites]{m}{% - \SI{#2}{\m}% - }{\ifboolKV[Unites]{mm}{% - \SI{#2}{\mm}% - }{\SI{#2}{\cm}% +\def\MPDROITEGraduee#1#2#3#4#5#6#7#8{% + % #1 : unite + % #2 : pas + % #3 : liste des points à placer en pas. pour gérer le cas des repérages fractionnaires + % #4 : on affiche le nom des points ou pas + % #5 : quelle est la valeur de la longueur unité ? + % #6 : la valeur de l'unité + % #7 : on affiche les abscisses ou pas : 0 non, 1 oui, 2 fraction + % #8 : on affiche tous les multiples de la graduation "principale" + \ifluatex + \mplibforcehmode + \begin{mplibcode} + maxx:=0; + minx:=4000; + unitex:=#1*cm; + pasx:=#2; + unitp:=unitex/pasx;%unité de déplacement + vardef toto(text t)=%On détermine le nombre "d'unités" à placer + for p_=t: + if numeric p_: + if p_>maxx: + maxx:=p_; + fi; + if p_(-#2-1): + minx:=-#2-(pasx-1); + fi; + enddef; + toto(#3); + Figure((minx-1)*unitp,-u,(maxx+1)*unitp,u); + pair A,B,C; + A=(0,0); + B=unitp*(maxx,0); + C=unitp*(minx,0); + drawarrow (C+unitp*(-0.75,0))--(B+unitp*(0.75,0)); + % marquage secondaire + marque_s:=marque_s/3; + labeloffset:=labeloffset*2; + if ((maxx-minx) mod 2)=0: + for k=(minx+1) step 2 until (maxx-1): + draw marquedemidroite(C,B); + draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); + endfor; + else: + for k=(minx) step 2 until (maxx-1): + draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); + endfor; + fi; + % marquage primaire + marque_s:=marque_s*3; + for k=0 step pasx until (maxx-pasx): + draw marquesegment((k/maxx)[A,B],((k+pasx)/maxx)[A,B]); + endfor; + for k=0 step -pasx until (minx+pasx): + draw marquesegment((k/maxx)[A,B],((k-pasx)/maxx)[A,B]); + endfor; + % marquage des points + m_c:=m_c*3; + marque_p:="croix"; + labeloffset:=labeloffset*2; + label.bot(TEX("\footnotesize\num{"&decimal(#5)&"}"),unitex*(1,0)); + label.bot(TEX("\footnotesize\num{"&decimal(#6)&"}"),A); + if #8>0: + for k=2 upto maxx: + label.bot(TEX("\footnotesize\num{\fpeval{"&decimal(#6)&"+"&decimal(#5-(#6))&"*"&decimal(k)&"}}"),unitex*(k,0));%%% + endfor; + for k=minx upto -1: + label.bot(TEX("\footnotesize\num{\fpeval{"&decimal(#6)&"+"&decimal(#5-(#6))&"*"&decimal(k)&"}}"),unitex*(k,0));%%% + endfor; + fi; + vardef tata(text t)=%on place les points + if #4>0: + for p_=t: + if numeric p_: + k:=p_; + fi; + if string p_: + if p_<>"": + label.top(TEX(p_),unitp*(k,0)); + pointe(unitp*(k,0)); + fi; + fi; + endfor; + fi; + if #7=2: + for p_=t: + if numeric p_: + k:=p_; + fi; + if string p_: + if p_<>"": + if ((#5*k) mod pasx)<>0: + label.bot(TEX("\footnotesize$\frac{\num{\fpeval{"&decimal(#5)&"*"&decimal(k)&"}}}{\num{"&decimal(pasx)&"}}$"),unitp*(k,0)); + else: + label.bot(TEX("\footnotesize\num{\fpeval{"&decimal(#5)&"*"&decimal(k)&"/"&decimal(pasx)&"}}"),unitp*(k,0)); + fi; + pointe(unitp*(k-#6,0)); + fi; + fi; + endfor; + elseif #7=1: + for p_=t: + if numeric p_: + k:=p_; + fi; + if string p_: + if p_<>"": + label.bot(TEX("\footnotesize\num{\fpeval{"&decimal(#6)&"+"&decimal(#5-(#6))&"*"&decimal(k)&"/"&decimal(pasx)&"}}"),unitp*(k,0)); + pointe(unitp*(k,0)); + fi; + fi; + endfor; + fi; + enddef; + tata(#3); + \end{mplibcode} + \else + \begin{mpost} + maxx:=0; + minx:=4000; + unitex:=#1*cm; + pasx:=#2; + unitp:=unitex/pasx;%unité de déplacement + vardef toto(text t)=%On détermine le nombre "d'unités" à placer + for p_=t: + if numeric p_: + if p_>maxx: + maxx:=p_; + fi; + if p_(-#2-1): + minx:=-#2-(pasx-1); + fi; + enddef; + toto(#3); + Figure((minx-1)*unitp,-u,(maxx+1)*unitp,u); + pair A,B,C; + A=(0,0); + B=unitp*(maxx,0); + C=unitp*(minx,0); + drawarrow (C+unitp*(-0.75,0))--(B+unitp*(0.75,0)); + % marquage secondaire + marque_s:=marque_s/3; + labeloffset:=labeloffset*2; + if ((maxx-minx) mod 2)=0: + for k=(minx+1) step 2 until (maxx-1): + draw marquedemidroite(C,B); + draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); + endfor; + else: + for k=(minx) step 2 until (maxx-1): + draw marquesegment((k/maxx)[A,B],((k+1)/maxx)[A,B]); + endfor; + fi; + % marquage primaire + marque_s:=marque_s*3; + for k=0 step pasx until (maxx-pasx): + draw marquesegment((k/maxx)[A,B],((k+pasx)/maxx)[A,B]); + endfor; + for k=0 step -pasx until (minx+pasx): + draw marquesegment((k/maxx)[A,B],((k-pasx)/maxx)[A,B]); + endfor; + % marquage des points + m_c:=m_c*3; + marque_p:="croix"; + labeloffset:=labeloffset*2; + label.bot(LATEX("\noexpand\footnotesize\noexpand\num{"&decimal(#5)&"}"),unitex*(1,0)); + label.bot(LATEX("\noexpand\footnotesize\noexpand\num{"&decimal(#6)&"}"),A); + if #8>0: + for k=2 upto maxx: + label.bot(LATEX("\noexpand\footnotesize\noexpand\num{\noexpand\fpeval{"&decimal(#6)&"+"&decimal(#5-(#6))&"*"&decimal(k)&"}}"),unitex*(k,0));%%% + endfor; + for k=minx upto -1: + label.bot(LATEX("\noexpand\footnotesize\noexpand\num{\noexpand\fpeval{"&decimal(#6)&"+"&decimal(#5-(#6))&"*"&decimal(k)&"}}"),unitex*(k,0));%%% + endfor; + fi; + vardef tata(text t)=%on place les points + if #4>0: + for p_=t: + if numeric p_: + k:=p_; + fi; + if string p_: + if p_<>"": + label.top(LATEX(p_),unitp*(k,0)); + pointe(unitp*(k,0)); + fi; + fi; + endfor; + fi; + if #7=2: + for p_=t: + if numeric p_: + k:=p_; + fi; + if string p_: + if p_<>"": + if ((#5*k) mod pasx)<>0: + label.bot(LATEX("\noexpand\footnotesize$\noexpand\frac{\noexpand\num{\noexpand\fpeval{"&decimal(#5)&"*"&decimal(k)&"}}}{\noexpand\num{"&decimal(pasx)&"}}$"),unitp*(k,0)); + else: + label.bot(LATEX("\noexpand\footnotesize\noexpand\num{\noexpand\fpeval{"&decimal(#5)&"*"&decimal(k)&"/"&decimal(pasx)&"}}"),unitp*(k,0)); + fi; + pointe(unitp*(k-#6,0)); + fi; + fi; + endfor; + elseif #7=1: + for p_=t: + if numeric p_: + k:=p_; + fi; + if string p_: + if p_<>"": + label.bot(LATEX("\noexpand\footnotesize\noexpand\num{\noexpand\fpeval{"&decimal(#6)&"+"&decimal(#5-(#6))&"*"&decimal(k)&"/"&decimal(pasx)&"}}"),unitp*(k,0)); + pointe(unitp*(k,0)); + fi; + fi; + endfor; + fi; + enddef; + tata(#3); + \end{mpost} + \fi +} + +\newcommand\Reperage[2][]{% + \useKVdefault[ClesReperage]% + \setKV[ClesReperage]{#1}% + \ifboolKV[ClesReperage]{Espace}{% + \setKV[ClesReperage]{Unitex=2,Unitey=2.5,Unitez=1.5}% + \setKV[ClesReperage]{#1}% + \setsepchar[*]{,*/}\ignoreemptyitems% + \readlist*\ListePointEspace{#2}% + \buildespace% + }{\ifboolKV[ClesReperage]{Plan}{% + \setsepchar[*]{,*/}\ignoreemptyitems% + \readlist*\ListePointRepere{#2}% + \buildreperenew% + }{% + \setsepchar[*]{,*/}\ignoreemptyitems% + \readlist*\ListePointDroite{#2}% + \builddemidroitenew% + }% + }% +}% + +%%% +% Puissances +%%% +\newcommand\Puissances[2]{% + \ensuremath{% + \xintifboolexpr{#2=0}{1}{\xintifboolexpr{#2>0}{\xdef\total{\fpeval{#2-1}}#1\multido{\i=1+1}{\total}{\times#1}}{\xdef\total{\fpeval{-#2-1}}\frac{1}{#1\multido{\i=1+1}{\total}{\times#1}}}}% + }% +} + +%%% +% Ecritures d'unités +%%% +\setKVdefault[Unites]{m=false,km=false,hm=false,ha=false,dam=false,a=false,dm=false,cm=true,mm=false,um=false,nm=false,g=true,t=false,q=false,kg=false,hg=false,dag=false,dg=false,cg=false,mg=false,ug=false,ng=false,kmh=true,kms=false,ms=false,kgm=false,gcm=true,L=true,kL=false,hL=false,daL=false,dL=false,cL=false,mL=false,l=true,kl=false,hl=false,dal=false,dl=false,cl=false,ml=false,Go=true,Mo=false,ko=false,To=false,o=false,kWh=true,C=true,K=false,F=false} + +%D'apres https://tex.stackexchange.com/questions/38905/time-of-the-day-or-time-period-using-the-package-siunitx +\ExplSyntaxOn +\NewDocumentCommand \Temps { o > { \SplitArgument { 5 } { ; } } m } +{ + \group_begin: + \IfNoValueF {#1} + { \keys_set:nn { siunitx } {#1} } + \siunitx_hms_output:nnn #2 + \group_end: +} +\cs_new_protected:Npn \siunitx_hms_output:nnn #1#2#3#4#5#6 +{ + \IfNoValueF {#1} + { + \tl_if_blank:nF {#1} + { + \SI {#1} { \annee\xintifboolexpr{#1>1}{s}{} } + \IfNoValueF {#2} { ~ } + } + } + \IfNoValueF {#2} + { + \tl_if_blank:nF {#2} + { + \SI {#2} { \mois } + \IfNoValueF {#3} { ~ } + } + } + \IfNoValueF {#3} + { + \tl_if_blank:nF {#3} + { + \SI {#3} { \jour } + \IfNoValueF {#4} { ~ } + } + } + \IfNoValueF {#4} + { + \tl_if_blank:nF {#4} + { + \SI {#4} { \hour } + \IfNoValueF {#5} { ~ } + } + } + \IfNoValueF {#5} + { + \tl_if_blank:nF {#5} + { + \SI {#5} { \minute } + \IfNoValueF {#6} { ~ } + } + } + \IfNoValueF {#6} + { \tl_if_blank:nF {#6} { \SI {#6} { \second } } } +} +\ExplSyntaxOff + +\newcommand\Temp[2][]{% + \useKVdefault[Unites]% + \setKV[Unites]{#1}% + \ifboolKV[Unites]{F}{% + \SI{#2}{\fahrenheit}% + }{% + \ifboolKV[Unites]{K}{% + \SI{#2}{\kelvin}% + }{% + \SI{#2}{\celsius}% + }% + }% +}% + +\newcommand\Conso[2][]{% + \SI{#2}{\kWh}% +} + +\newcommand\Octet[2][]{% + \useKVdefault[Unites]% + \setKV[Unites]{#1}% + \ifboolKV[Unites]{o}{% + \SI{#2}{\octet}% + }{% + \ifboolKV[Unites]{ko}{% + \SI{#2}{\kilo\octet}% + }{\ifboolKV[Unites]{Mo}{% + \SI{#2}{\mega\octet}% + }{\ifboolKV[Unites]{To}{% + \SI{#2}{\tera\octet}% + }{% + \SI{#2}{\giga\octet}% + }% + }% + }% + }% +}% + +\newcommand\Lg[2][]{% + \useKVdefault[Unites]% + \setKV[Unites]{#1}% + \ifboolKV[Unites]{nm}{% + \SI{#2}{\nm}% + }{\ifboolKV[Unites]{um}{% + \SI{#2}{\um}% + }{\ifboolKV[Unites]{km}{% + \SI{#2}{\km}% + }{\ifboolKV[Unites]{hm}{% + \SI{#2}{\hecto\metre}% + }{\ifboolKV[Unites]{dam}{% + \SI{#2}{\deca\metre}% + }{\ifboolKV[Unites]{dm}{% + \SI{#2}{\dm}% + }{\ifboolKV[Unites]{m}{% + \SI{#2}{\m}% + }{\ifboolKV[Unites]{mm}{% + \SI{#2}{\mm}% + }{\SI{#2}{\cm}% + }% + }% }% }% }% @@ -10537,19 +11800,32 @@ vardef Positions(expr Step)= \newcommand\Masse[2][]{% \useKVdefault[Unites]% \setKV[Unites]{#1}% - \ifboolKV[Unites]{kg}{% - \SI{#2}{\kg}% - }{\ifboolKV[Unites]{hg}{% - \SI{#2}{\hecto\gram}% - }{\ifboolKV[Unites]{dag}{% - \SI{#2}{\deca\gram}% - }{\ifboolKV[Unites]{dg}{% - \SI{#2}{\deci\gram}% - }{\ifboolKV[Unites]{cg}{% - \SI{#2}{\centi\gram}% - }{\ifboolKV[Unites]{mg}{% - \SI{#2}{\milli\gram}% - }{\SI{#2}{\gram}% + \ifboolKV[Unites]{ng}{% + \SI{#2}{\ng}% + }{\ifboolKV[Unites]{ug}{% + \SI{#2}{\ug}% + }{\ifboolKV[Unites]{t}{% + \SI{#2}{\tonne}% + }{\ifboolKV[Unites]{q}{% + \SI{#2}{\quintal}% + }{% + \ifboolKV[Unites]{kg}{% + \SI{#2}{\kg}% + }{\ifboolKV[Unites]{hg}{% + \SI{#2}{\hecto\gram}% + }{\ifboolKV[Unites]{dag}{% + \SI{#2}{\deca\gram}% + }{\ifboolKV[Unites]{dg}{% + \SI{#2}{\deci\gram}% + }{\ifboolKV[Unites]{cg}{% + \SI{#2}{\centi\gram}% + }{\ifboolKV[Unites]{mg}{% + \SI{#2}{\milli\gram}% + }{\SI{#2}{\gram}% + }% + }% + }% + }% }% }% }% @@ -10589,15 +11865,21 @@ vardef Positions(expr Step)= \SI{#2}{\square\km}% }{\ifboolKV[Unites]{hm}{% \SI{#2}{\square\hecto\metre}% - }{\ifboolKV[Unites]{dam}{% - \SI{#2}{\square\deca\metre}% - }{\ifboolKV[Unites]{dm}{% - \SI{#2}{\square\dm}% - }{\ifboolKV[Unites]{m}{% - \SI{#2}{\square\metre}% - }{\ifboolKV[Unites]{mm}{% - \SI{#2}{\square\mm}% - }{\SI{#2}{\square\cm}% + }{\ifboolKV[Unites]{ha}{% + \SI{#2}{\hectare}% + }{\ifboolKV[Unites]{dam}{% + \SI{#2}{\square\deca\metre}% + }{\ifboolKV[Unites]{a}{% + \SI{#2}{\are}% + }{\ifboolKV[Unites]{dm}{% + \SI{#2}{\square\dm}% + }{\ifboolKV[Unites]{m}{% + \SI{#2}{\square\metre}% + }{\ifboolKV[Unites]{mm}{% + \SI{#2}{\square\mm}% + }{\SI{#2}{\square\cm}% + }% + }% }% }% }% @@ -10636,7 +11918,11 @@ vardef Positions(expr Step)= \ifboolKV[Unites]{ms}{% \SI[per-mode=symbol]{#2}{\meter\per\second}% }{% - \SI[per-mode=symbol]{#2}{\kilo\meter\per\hour}% + \ifboolKV[Unites]{kms}{% + \SI[per-mode=symbol]{#2}{\kilo\meter\per\second}% + }{% + \SI[per-mode=symbol]{#2}{\kilo\meter\per\hour}% + }% }% }% @@ -10650,177 +11936,378 @@ vardef Positions(expr Step)= }% }% -%%%%%%%%% -%% Tableaux d'unités -%%%%%%%%% -\setKVdefault[ClesTableaux]{Entiers=false,Decimaux=false,Milliards=false,Millions=false,Milliers=true,Partie=false,CouleurG=gray!15,CouleurM=gray!15,Couleurm=gray!15,Couleuru=gray!15,Classes=false,Nombres=false,Metre=false,Carre=false,Cube=false,Litre=false,Gramme=false,Fleches=false,Colonnes=false,Prefixes=false} +%%% +% Tableaux d'unités +%%% +\setKVdefault[ClesTableaux]{Virgule=true,Entiers=false,Decimaux=false,Milliards=false,Millions=false,Micro=false,Nano=false,Partie=false,CouleurG=gray!15,CouleurM=gray!15,Couleurm=gray!15,Couleuru=gray!15,Classes=false,Nombres=false,Puissances=false,NbLignes=2,Metre=false,Are=false,Capacite=false,Carre=false,Cube=false,Litre=false,Gramme=false,Fleches=false,FlechesB=false,FlechesH=false,Colonnes=false,Prefixes=false} \newcommand\Tableau[1][]{% \useKVdefault[ClesTableaux]% \setKV[ClesTableaux]{#1}% + % + %%% Clé Prefixes + % \ifboolKV[ClesTableaux]{Prefixes}{% - \setlength{\tabcolsep}{0.01\tabcolsep} - \begin{center} - \begin{tabular}{|*{12}{>{\centering\arraybackslash}m{3.25em}|}>{\columncolor{gray!15},}{c}|*{12}{>{\centering\arraybackslash}m{3.25em}|}} + \setlength{\tabcolsep}{0.01\tabcolsep}% + \begin{center}% + % + %%% Definition du tableau + % + \begin{tabular}{|*{\ifboolKV[ClesTableaux]{Milliards}{12}{% + \ifboolKV[ClesTableaux]{Millions}{9}{6}% + }}{>{\centering\arraybackslash}m{3.25em}|}>{\columncolor{gray!15}}{c}|*{% + \ifboolKV[ClesTableaux]{Micro}{6}{% + \ifboolKV[ClesTableaux]{Nano}{9}{3}% + }}% + {>{\centering\arraybackslash}m{3.25em}|}}% + % + %%% Prise en compte de la clé Partie + % \ifboolKV[ClesTableaux]{Partie}{% - \multicolumn{12}{c}{\bfseries Partie entière} - &\multicolumn{1}{c}{\cellcolor{gray!15},}% - &\multicolumn{12}{c}{\bfseries Partie décimale}\\}{} + \multicolumn{% + \ifboolKV[ClesTableaux]{Milliards}{12}{% + \ifboolKV[ClesTableaux]{Millions}{9}{6}% + }}{c}{\bfseries Partie entière} + &\multicolumn{1}{c}{\cellcolor{gray!15}\ifboolKV[ClesTableaux]{Virgule}{,}{}}% + &\multicolumn{% + \ifboolKV[ClesTableaux]{Micro}{6}{% + \ifboolKV[ClesTableaux]{Nano}{9}{3}% + }}% + {c}{\bfseries Partie décimale}\\}{}% + % + %%% Prise en compte de la clé Classes + % \ifboolKV[ClesTableaux]{Classes}{% - \hline% - \multicolumn{3}{|c|}{\cellcolor{\useKV[ClesTableaux]{CouleurG}}Classe - des milliards}% - &\multicolumn{3}{c|}{\cellcolor{\useKV[ClesTableaux]{CouleurM}}Classe + \hline + \ifboolKV[ClesTableaux]{Milliards}{% + \cline{1-12}\multicolumn{3}{|c|}{\cellcolor{\useKV[ClesTableaux]{CouleurG}}Classe des milliards}% + &\multicolumn{3}{c|}{\cellcolor{\useKV[ClesTableaux]{CouleurM}}Classe des millions}% + &}{% + \ifboolKV[ClesTableaux]{Millions}{% + \cline{1-9}\multicolumn{3}{|c|}{\cellcolor{\useKV[ClesTableaux]{CouleurM}}Classe des millions}% - &\multicolumn{3}{c|}{\cellcolor{\useKV[ClesTableaux]{Couleurm}}Classe + &}{% + \cline{1-6}}}% + \ifboolKV[ClesTableaux]{Milliards}{% + \multicolumn{3}{c|}}{% + \ifboolKV[ClesTableaux]{Millions}{% + \multicolumn{3}{c|}}{\multicolumn{3}{|c|}}}% + {\cellcolor{\useKV[ClesTableaux]{Couleurm}}Classe des milliers}% &\multicolumn{3}{c|}{\cellcolor{\useKV[ClesTableaux]{Couleuru}}Classe des unités}% - &&&&&&&&&&&&&\\}{} - \hline - % + &\ifboolKV[ClesTableaux]{Virgule}{,}{}% + &\multicolumn{% + \ifboolKV[ClesTableaux]{Micro}{6}{% + \ifboolKV[ClesTableaux]{Nano}{9}{3}% + }}% + {c|}{}\\}{}% + % + %%% Valeurs par défaut + % + \hline% + \ifboolKV[ClesTableaux]{Milliards}{% &% &\fontsize{8.5}{8.5}\selectfont giga% &% &% &\fontsize{8.5}{8.5}\selectfont méga% &% + }{% + \ifboolKV[ClesTableaux]{Millions}{% + &% + &\fontsize{8.5}{8.5}\selectfont méga% + &% + }{% + }}% &% &\fontsize{8.5}{8.5}\selectfont kilo% &\fontsize{8.5}{8.5}\selectfont hecto% &\fontsize{8.5}{8.5}\selectfont déca% &\fontsize{8.5}{8.5}\selectfont unités% - &% + &\ifboolKV[ClesTableaux]{Virgule}{,}{}% &\fontsize{8.5}{8.5}\selectfont deci% &\fontsize{8.5}{8.5}\selectfont centi% - &\fontsize{8.5}{8.5}\selectfont milli% + &\fontsize{8.5}{8.5}\selectfont milli% + \ifboolKV[ClesTableaux]{Micro}{&% &% + &\fontsize{8.5}{8.5}\selectfont micro\\}{% + \ifboolKV[ClesTableaux]{Nano}{&% &% &\fontsize{8.5}{8.5}\selectfont micro% &% &% - &\fontsize{8.5}{8.5}\selectfont nano% + &\fontsize{8.5}{8.5}\selectfont nano\\}{\\}% + }% + % + %%% Prise en compte de la clé Nombres + % + \ifboolKV[ClesTableaux]{Nombres}{% + \ifboolKV[ClesTableaux]{Milliards}{% + \fontsize{4.5}{4.5}\selectfont\num{100000000000}% + &\fontsize{4.5}{4.5}\selectfont\num{10000000000}% + &\fontsize{4.5}{4.5}\selectfont\num{1000000000}% + &\fontsize{4.5}{4.5}\selectfont \num{100000000}% + &\fontsize{4.5}{4.5}\selectfont \num{10000000}% + &\fontsize{4.5}{4.5}\selectfont \num{1000000}% &% + }{} + \ifboolKV[ClesTableaux]{Millions}{% + \fontsize{4.5}{4.5}\selectfont \num{100000000}% + &\fontsize{4.5}{4.5}\selectfont \num{10000000}% + &\fontsize{4.5}{4.5}\selectfont \num{1000000}% &% - &\\ - \ifboolKV[ClesTableaux]{Nombres}{% + }{} + \fontsize{4.5}{4.5}\selectfont \num{100000}% + &\fontsize{4.5}{4.5}\selectfont \num{10000}% + &\fontsize{4.5}{4.5}\selectfont \num{1000}% + &\fontsize{4.5}{4.5}\selectfont \num{100}% + &\fontsize{4.5}{4.5}\selectfont \num{10}% + &\fontsize{4.5}{4.5}\selectfont \num{1}% + &\ifboolKV[ClesTableaux]{Virgule}{,}{}% + &\fontsize{4.5}{4.5}\selectfont \num{0,1} ou $\dfrac{\strut1}{\strut10}$% + &\fontsize{4.5}{4.5}\selectfont \num{0,01} ou $\dfrac{\strut1}{\strut100}$% + &\fontsize{4.5}{4.5}\selectfont \num{0,001} ou $\dfrac{\strut1}{\strut\num{1000}}$% + \ifboolKV[ClesTableaux]{Micro}{% + &\fontsize{4.5}{4.5}\selectfont \num{0,0001} ou $\dfrac{\strut1}{\strut\num{10000}}$% + &\fontsize{4.5}{4.5}\selectfont \num{0,00001} ou $\dfrac{\strut1}{\strut\num{100000}}$% + &\fontsize{4.5}{4.5}\selectfont \num{0,000001} ou $\dfrac{\strut1}{\strut\num{1000000}}$% + }{% + \ifboolKV[ClesTableaux]{Nano}{% + &\fontsize{4.5}{4.5}\selectfont \num{0,0001} ou $\dfrac{\strut1}{\strut\num{10000}}$% + &\fontsize{4.5}{4.5}\selectfont \num{0,00001} ou $\dfrac{\strut1}{\strut\num{100000}}$% + &\fontsize{4.5}{4.5}\selectfont \num{0,000001} ou $\dfrac{\strut1}{\strut\num{1000000}}$% + &\fontsize{4.5}{4.5}\selectfont \num{0,0000001} ou $\dfrac{\strut1}{\strut\num{10000000}}$% + &\fontsize{4.5}{4.5}\selectfont \num{0,00000001} ou $\dfrac{\strut1}{\strut\num{100000000}}$% + &\fontsize{4.5}{4.5}\selectfont \num{0,000000001} ou $\dfrac{\strut1}{\strut\num{1000000000}}$% + }{}% + }{}\\}{}% + % + %%% Prise en compte de la clé Puissances + % + \ifboolKV[ClesTableaux]{Puissances}{% + \ifboolKV[ClesTableaux]{Milliards}{% &% &\fontsize{4.5}{4.5}\selectfont $\times10^{9}$% &% &% &\fontsize{4.5}{4.5}\selectfont $\times10^{6}$% + & + }{% + \ifboolKV[ClesTableaux]{Millions}{% &% + &\fontsize{4.5}{4.5}\selectfont $\times10^{6}$% + & + }{% + }}% &% &\fontsize{4.5}{4.5}\selectfont $\times10^3$% &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^2$% &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^1$% &\fontsize{4.5}{4.5}\selectfont $\times\num{1}$% + &\ifboolKV[ClesTableaux]{Virgule}{,}{}% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^{-1}$% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^{-2}$% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^{-3}$% + \ifboolKV[ClesTableaux]{Micro}{&% &% - &\fontsize{4.5}{4.5}\selectfont$\times\num{10}^{-1}$% - &\fontsize{4.5}{4.5}\selectfont$\times\num{10}^{-2}$% - &\fontsize{4.5}{4.5}\selectfont$\times\num{10}^{-3}$% - &% - &% - &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^{-6}$% - &% - &% - &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^{-9}$% - & - & - &\\ - }{} - \hline - &&&&&&&&&&&&&&&&&&&&&&&&\\ - &&&&&&&&&&&&&&&&&&&&&&&&\\ - \end{tabular} - \end{center} - \setlength{\tabcolsep}{100\tabcolsep} + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^{-6}$}{% + \ifboolKV[ClesTableaux]{Nano}{&% + &% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^{-6}$% + &% + &% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^{-9}$}{}% + }% + \\% + }{}% + % + %%% Lignes vierges + % + \hline% + \xintFor* ##1 in {\xintSeq{1}{\useKV[ClesTableaux]{NbLignes}}}\do{% + \ifboolKV[ClesTableaux]{Milliards}{% + &&&&&&% + }{% + \ifboolKV[ClesTableaux]{Millions}{% + &&&% + }{% + }}% + &&&&&&,&&&% + \ifboolKV[ClesTableaux]{Micro}{&&&}{% + \ifboolKV[ClesTableaux]{Nano}{&&&&&&}{}% + } + \\}% + \end{tabular}% + \end{center}% + \setlength{\tabcolsep}{100\tabcolsep}% }{}% + % + %%% Clé Entiers + % \ifboolKV[ClesTableaux]{Entiers}{% - \setlength{\tabcolsep}{0.01\tabcolsep} - \begin{center} - \begin{tabular}{|*{12}{>{\centering\arraybackslash}m{4.75em}|}} - \ifboolKV[ClesTableaux]{Classes}{\hline\multicolumn{3}{|c|}{\cellcolor{\useKV[ClesTableaux]{CouleurG}}Classe - des milliards}% - &\multicolumn{3}{c|}{\cellcolor{\useKV[ClesTableaux]{CouleurM}}Classe - des millions}% - &\multicolumn{3}{c|}{\cellcolor{\useKV[ClesTableaux]{Couleurm}}Classe + \setlength{\tabcolsep}{0.01\tabcolsep}% + \begin{center}% + % + %%% Definition du tableau + % + \begin{tabular}{|*{% + \ifboolKV[ClesTableaux]{Milliards}{12}{% + \ifboolKV[ClesTableaux]{Millions}{9}{6}% + }% + }{>{\centering\arraybackslash}m{4.75em}|}}% + \ifboolKV[ClesTableaux]{Classes}{% + \hline + \ifboolKV[ClesTableaux]{Milliards}{\multicolumn{3}{|c}{\cellcolor{\useKV[ClesTableaux]{CouleurG}}Classe des milliards}&\multicolumn{3}{|c}{\cellcolor{\useKV[ClesTableaux]{CouleurM}}Classe des millions}&}{} + \ifboolKV[ClesTableaux]{Millions}{\multicolumn{3}{|c}{\cellcolor{\useKV[ClesTableaux]{CouleurM}}Classe des millions}&}{} + \multicolumn{3}{|c|}{\cellcolor{\useKV[ClesTableaux]{Couleurm}}Classe des milliers}% &\multicolumn{3}{c|}{\cellcolor{\useKV[ClesTableaux]{Couleuru}}Classe des unités}\\}{} \hline + \ifboolKV[ClesTableaux]{Milliards}{% \fontsize{4.5}{4.5}\selectfont centaines de milliards% &\fontsize{4.5}{4.5}\selectfont dizaines de milliards% &\fontsize{4.5}{4.5}\selectfont unités de milliards% &\fontsize{4.5}{4.5}\selectfont centaines de millions% &\fontsize{4.5}{4.5}\selectfont dizaines de millions% &\fontsize{4.5}{4.5}\selectfont unités de millions% - &\fontsize{4.5}{4.5}\selectfont centaines de milliers% + & + }{} + \ifboolKV[ClesTableaux]{Millions}{% + \fontsize{4.5}{4.5}\selectfont centaines de millions% + &\fontsize{4.5}{4.5}\selectfont dizaines de millions% + &\fontsize{4.5}{4.5}\selectfont unités de millions% + & + }{} + \fontsize{4.5}{4.5}\selectfont centaines de milliers% &\fontsize{4.5}{4.5}\selectfont dizaines de milliers% &\fontsize{4.5}{4.5}\selectfont unités de milliers% &\fontsize{4.5}{4.5}\selectfont centaines% &\fontsize{4.5}{4.5}\selectfont dizaines% &\fontsize{4.5}{4.5}\selectfont unités\\% \ifboolKV[ClesTableaux]{Nombres}{% - \fontsize{4.5}{4.5}\selectfont \num{100000000000}% - &\fontsize{4.5}{4.5}\selectfont \num{10000000000}% - &\fontsize{4.5}{4.5}\selectfont \num{1000000000}% + \ifboolKV[ClesTableaux]{Milliards}{% + \fontsize{4.5}{4.5}\selectfont\num{100000000000}% + &\fontsize{4.5}{4.5}\selectfont\num{10000000000}% + &\fontsize{4.5}{4.5}\selectfont\num{1000000000}% &\fontsize{4.5}{4.5}\selectfont \num{100000000}% &\fontsize{4.5}{4.5}\selectfont \num{10000000}% &\fontsize{4.5}{4.5}\selectfont \num{1000000}% - &\fontsize{4.5}{4.5}\selectfont \num{100000}% + &% + }{} + \ifboolKV[ClesTableaux]{Millions}{% + \fontsize{4.5}{4.5}\selectfont \num{100000000}% + &\fontsize{4.5}{4.5}\selectfont \num{10000000}% + &\fontsize{4.5}{4.5}\selectfont \num{1000000}% + &% + }{} + \fontsize{4.5}{4.5}\selectfont \num{100000}% &\fontsize{4.5}{4.5}\selectfont \num{10000}% &\fontsize{4.5}{4.5}\selectfont \num{1000}% &\fontsize{4.5}{4.5}\selectfont \num{100}% &\fontsize{4.5}{4.5}\selectfont \num{10}% &\fontsize{4.5}{4.5}\selectfont \num{1}% \\ - }{} - \hline - &&&&&&&&&&&\\ - &&&&&&&&&&&\\ - \end{tabular} - \end{center} - \setlength{\tabcolsep}{100\tabcolsep} + }{} + % + %%% Prise en compte de la clé Puissances + % + \ifboolKV[ClesTableaux]{Puissances}{% + \ifboolKV[ClesTableaux]{Milliards}{% + &% + &\fontsize{4.5}{4.5}\selectfont $\times10^{9}$% + &% + &% + &\fontsize{4.5}{4.5}\selectfont $\times10^{6}$% + & + }{% + \ifboolKV[ClesTableaux]{Millions}{% + &% + &\fontsize{4.5}{4.5}\selectfont $\times10^{6}$% + & + }{% + }}% + &% + &\fontsize{4.5}{4.5}\selectfont $\times10^3$% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^2$% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^1$% + &\fontsize{4.5}{4.5}\selectfont $\times\num{1}$% + \\% + }{}% + % + %%% Lignes vierges + % + \hline% + \xintFor* ##1 in {\xintSeq{1}{\useKV[ClesTableaux]{NbLignes}}}\do{% + \ifboolKV[ClesTableaux]{Milliards}{% + &&&&&&}{}% + \ifboolKV[ClesTableaux]{Millions}{% + &&&}{} + &&&&&\\}% + \end{tabular}% + \end{center}% + \setlength{\tabcolsep}{100\tabcolsep}% }{}% + % + %%% Clé Decimaux + % \ifboolKV[ClesTableaux]{Decimaux}{% - \setlength{\tabcolsep}{0.01\tabcolsep} - \ifboolKV[ClesTableaux]{Milliards}{% - \newcolumntype{X}{|*{12}{>{\centering\arraybackslash}m{4.75em}|}>{\columncolor{gray!15},}{c}|*{3}{>{\centering\arraybackslash}m{4.75em}|}}% - }{\ifboolKV[ClesTableaux]{Millions}{% - \newcolumntype{X}{|*{9}{>{\centering\arraybackslash}m{4.75em}|}>{\columncolor{gray!15},}{c}|*{3}{>{\centering\arraybackslash}m{4.75em}|}}% - }{\newcolumntype{X}{|*{6}{>{\centering\arraybackslash}m{4.75em}|}>{\columncolor{gray!15},}{c}|*{3}{>{\centering\arraybackslash}m{4.75em}|}}% - } - } - \begin{center} - \begin{tabular}{X} + \setlength{\tabcolsep}{0.01\tabcolsep}% + \begin{center}% + % + %%% Definition du tableau + % + \begin{tabular}{|*{\ifboolKV[ClesTableaux]{Milliards}{12}{% + \ifboolKV[ClesTableaux]{Millions}{9}{6}% + }}{>{\centering\arraybackslash}m{4.75em}|}>{\columncolor{gray!15}}{c}|*{3}% + {>{\centering\arraybackslash}m{4.75em}|}}% + % + %%% Prise en compte de la clé Partie + % \ifboolKV[ClesTableaux]{Partie}{% - \ifboolKV[ClesTableaux]{Milliards}{\multicolumn{12}{c}{\bfseries Partie entière}}{\ifboolKV[ClesTableaux]{Millions}{\multicolumn{9}{c}{\bfseries Partie entière}}{\multicolumn{6}{c}{\bfseries Partie entière}}} - &\multicolumn{1}{c}{\cellcolor{gray!15},}% + \ifboolKV[ClesTableaux]{Milliards}{% + \multicolumn{12}{c}{\bfseries Partie entière}}{% + \ifboolKV[ClesTableaux]{Millions}{% + \multicolumn{9}{c}{\bfseries Partie entière}}{% + \multicolumn{6}{c}{\bfseries Partie entière}}}% + &\multicolumn{1}{c}{\cellcolor{gray!15}\ifboolKV[ClesTableaux]{Virgule}{,}{}}% &\multicolumn{3}{c}{\bfseries Partie décimale}\\}{} + % + %%% Prise en compte de la clé Classes + % \ifboolKV[ClesTableaux]{Classes}{% \hline% - \ifboolKV[ClesTableaux]{Milliards}{\multicolumn{3}{|c}{\cellcolor{\useKV[ClesTableaux]{CouleurG}}Classe des milliards}\uppercase{&}\multicolumn{3}{|c}{\cellcolor{\useKV[ClesTableaux]{CouleurM}}Classe des millions}\uppercase{&}}{} - \ifboolKV[ClesTableaux]{Millions}{\multicolumn{3}{|c}{\cellcolor{\useKV[ClesTableaux]{CouleurM}}Classe des millions}\uppercase{&}}{} - \multicolumn{3}{|c|}{\cellcolor{\useKV[ClesTableaux]{Couleurm}}Classe + \ifboolKV[ClesTableaux]{Milliards}{% + \multicolumn{3}{|c|}{\cellcolor{\useKV[ClesTableaux]{CouleurG}}Classe des milliards}&\multicolumn{3}{c|}{\cellcolor{\useKV[ClesTableaux]{CouleurM}}Classe des millions}&}{}% + \ifboolKV[ClesTableaux]{Millions}{% + \multicolumn{3}{|c|}{\cellcolor{\useKV[ClesTableaux]{CouleurM}}Classe des millions}&}{}% + \ifboolKV[ClesTableaux]{Milliards}{% + \multicolumn{3}{c|}}{% + \ifboolKV[ClesTableaux]{Millions}{% + \multicolumn{3}{c|}}{\multicolumn{3}{|c|}}}% + {\cellcolor{\useKV[ClesTableaux]{Couleurm}}Classe des milliers}% &\multicolumn{3}{c|}{\cellcolor{\useKV[ClesTableaux]{Couleuru}}Classe des unités}% - &&&&\\}{} + &\ifboolKV[ClesTableaux]{Virgule}{,}{}&\multicolumn{3}{c|}{}\\}{} + % + %%% Valeurs ci-dessous par défaut + % \hline \ifboolKV[ClesTableaux]{Milliards}{% \fontsize{4.5}{4.5}\selectfont centaines de milliards% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont dizaines de milliards% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont unités de milliards% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont centaines de millions% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont dizaines de millions% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont unités de millions% - \uppercase{&} + &\fontsize{4.5}{4.5}\selectfont dizaines de milliards% + &\fontsize{4.5}{4.5}\selectfont unités de milliards% + &\fontsize{4.5}{4.5}\selectfont centaines de millions% + &\fontsize{4.5}{4.5}\selectfont dizaines de millions% + &\fontsize{4.5}{4.5}\selectfont unités de millions% + & }{} \ifboolKV[ClesTableaux]{Millions}{% \fontsize{4.5}{4.5}\selectfont centaines de millions% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont dizaines de millions% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont unités de millions% - \uppercase{&} + &\fontsize{4.5}{4.5}\selectfont dizaines de millions% + &\fontsize{4.5}{4.5}\selectfont unités de millions% + & }{} \fontsize{4.5}{4.5}\selectfont centaines de milliers% &\fontsize{4.5}{4.5}\selectfont dizaines de milliers% @@ -10828,53 +12315,84 @@ vardef Positions(expr Step)= &\fontsize{4.5}{4.5}\selectfont centaines% &\fontsize{4.5}{4.5}\selectfont dizaines% &\fontsize{4.5}{4.5}\selectfont unités% - &% + &\ifboolKV[ClesTableaux]{Virgule}{,}{}% &\fontsize{4.5}{4.5}\selectfont dixièmes% &\fontsize{4.5}{4.5}\selectfont centièmes% &\fontsize{4.5}{4.5}\selectfont millièmes\\ \ifboolKV[ClesTableaux]{Nombres}{% \ifboolKV[ClesTableaux]{Milliards}{% \fontsize{4.5}{4.5}\selectfont\num{100000000000}% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont\num{10000000000}% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont\num{1000000000}% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont \num{100000000}% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont \num{10000000}% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont \num{1000000}% - \uppercase{&}% + &\fontsize{4.5}{4.5}\selectfont\num{10000000000}% + &\fontsize{4.5}{4.5}\selectfont\num{1000000000}% + &\fontsize{4.5}{4.5}\selectfont \num{100000000}% + &\fontsize{4.5}{4.5}\selectfont \num{10000000}% + &\fontsize{4.5}{4.5}\selectfont \num{1000000}% + &% }{} \ifboolKV[ClesTableaux]{Millions}{% \fontsize{4.5}{4.5}\selectfont \num{100000000}% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont \num{10000000}% - \uppercase{&}\fontsize{4.5}{4.5}\selectfont \num{1000000}% - \uppercase{&}% - }{} + &\fontsize{4.5}{4.5}\selectfont \num{10000000}% + &\fontsize{4.5}{4.5}\selectfont \num{1000000}% + &% + }{} \fontsize{4.5}{4.5}\selectfont \num{100000}% &\fontsize{4.5}{4.5}\selectfont \num{10000}% &\fontsize{4.5}{4.5}\selectfont \num{1000}% &\fontsize{4.5}{4.5}\selectfont \num{100}% &\fontsize{4.5}{4.5}\selectfont \num{10}% &\fontsize{4.5}{4.5}\selectfont \num{1}% - &% + &\ifboolKV[ClesTableaux]{Virgule}{,}{}% &\fontsize{4.5}{4.5}\selectfont \num{0,1} ou $\dfrac{\strut1}{\strut10}$% &\fontsize{4.5}{4.5}\selectfont \num{0,01} ou $\dfrac{\strut1}{\strut100}$% &\fontsize{4.5}{4.5}\selectfont \num{0,001} ou $\dfrac{\strut1}{\strut\num{1000}}$% \\ + }{}% + % + %%% Prise en compte de la clé Puissances + % + \ifboolKV[ClesTableaux]{Puissances}{% + \ifboolKV[ClesTableaux]{Milliards}{% + &% + &\fontsize{4.5}{4.5}\selectfont $\times10^{9}$% + &% + &% + &\fontsize{4.5}{4.5}\selectfont $\times10^{6}$% + & + }{% + \ifboolKV[ClesTableaux]{Millions}{% + &% + &\fontsize{4.5}{4.5}\selectfont $\times10^{6}$% + & + }{% + }}% + &% + &\fontsize{4.5}{4.5}\selectfont $\times10^3$% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^2$% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^1$% + &\fontsize{4.5}{4.5}\selectfont $\times\num{1}$% + &\ifboolKV[ClesTableaux]{Virgule}{,}{}% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^{-1}$% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^{-2}$% + &\fontsize{4.5}{4.5}\selectfont $\times\num{10}^{-3}$% + \\% }{} - \hline - \ifboolKV[ClesTableaux]{Milliards}{% - \uppercase{&}\uppercase{&}\uppercase{&}\uppercase{&}\uppercase{&}\uppercase{&}}{} % - \ifboolKV[ClesTableaux]{Millions}{% - \uppercase{&}\uppercase{&}\uppercase{&}}{} - &&&&&&&&&\\ - \ifboolKV[ClesTableaux]{Milliards}{% - \uppercase{&}\uppercase{&}\uppercase{&}\uppercase{&}\uppercase{&}\uppercase{&}}{} % + \hline% + % + %%% Lignes vierges + % + \xintFor* ##1 in {\xintSeq{1}{\useKV[ClesTableaux]{NbLignes}}}\do{% + \ifboolKV[ClesTableaux]{Milliards}{% + &&&&&&}{}% \ifboolKV[ClesTableaux]{Millions}{% - \uppercase{&}\uppercase{&}\uppercase{&}}{} - &&&&&&&&&\\ + &&&}{} + &&&&&&,&&&\\} \end{tabular} - \end{center} - \setlength{\tabcolsep}{100\tabcolsep} - }{} + \end{center}% + \setlength{\tabcolsep}{100\tabcolsep}% + }{}% + % + %%% Prise en compte de la clé Metre + % \ifboolKV[ClesTableaux]{Metre}{% \[\renewcommand{\arraystretch}{1.15}% \begin{tabular}{|*{7}{p{7.5mm}|}}% @@ -10888,7 +12406,8 @@ vardef Positions(expr Step)= \hline \multicolumn{1}{|c|}{km}&\multicolumn{1}{c|}{hm}&\multicolumn{1}{c|}{dam}&\multicolumn{1}{c|}{m}&\multicolumn{1}{c|}{dm}&\multicolumn{1}{c|}{cm}&\multicolumn{1}{c|}{mm}\\ \hline - &&&&&&\\ + \xintFor* ##1 in {\xintSeq{1}{\useKV[ClesTableaux]{NbLignes}}}\do{% + &&&&&&\\} \multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (G1);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (F1);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (E1);}}% @@ -10896,33 +12415,25 @@ vardef Positions(expr Step)= &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (C1);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (B1);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (A1);}}\\% - \end{tabular} - \] - \ifboolKV[ClesTableaux]{Fleches}{% - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (A) to node[above, midway]{\small$\times\mbox{10}$}(B);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (B) to node[above, midway]{\small$\times\mbox{10}$}(C);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (C) to node[above, midway]{\small$\times\mbox{10}$}(D);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (D) to node[above, midway]{\small$\times\mbox{10}$}(E);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (E) to node[above, midway]{\small$\times\mbox{10}$}(F);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (F) to node[above, midway]{\small$\times\mbox{10}$}(G);} - % bas - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (A1) to node[below, midway]{\small$\div\mbox{10}$}(B1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (B1) to node[below, midway]{\small$\div\mbox{10}$}(C1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (C1) to node[below, midway]{\small$\div\mbox{10}$}(D1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (D1) to node[below, midway]{\small$\div\mbox{10}$}(E1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (E1) to node[below, midway]{\small$\div\mbox{10}$}(F1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (F1) to node[below, midway]{\small$\div\mbox{10}$}(G1);} - }{} - } - {} + \end{tabular}% + \]% + \Conversion{10}% + }% + {}% + % + %%% Prise en compte de la clé Carre + % \ifboolKV[ClesTableaux]{Carre}{% \[\renewcommand{\arraystretch}{1.15}% \ifboolKV[ClesTableaux]{Colonnes}{% - \newcolumntype{X}{|*{7}{p{2.5mm}!{\color{gray!50}\vrule}p{2.5mm}|}}% + \newcolumntype{X}{|*{7}{>{\centering\arraybackslash}p{3.5mm}!{\color{gray!50}\vrule}>{\centering\arraybackslash}p{3.5mm}|}}% }{% - \newcolumntype{X}{|*{7}{p{2.5mm}p{2.5mm}|}} - } - \begin{tabular}{X} + \ifboolKV[ClesTableaux]{Are}{% + \newcolumntype{X}{|*{7}{>{\centering\arraybackslash}p{3.5mm}!{\color{gray!50}\vrule}>{\centering\arraybackslash}p{3.5mm}|}}% + }{ + \newcolumntype{X}{|*{7}{p{3.5mm}p{3.5mm}|}}% + }}% + \begin{tabular}{X}% \multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate (A);}}% &\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate (B);}}% &\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate (C);}}% @@ -10931,9 +12442,14 @@ vardef Positions(expr Step)= &\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate (F);}}% &\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate (G);}}\\% \hline - \multicolumn{2}{|c|}{km$^2$}&\multicolumn{2}{c|}{hm$^2$}&\multicolumn{2}{c|}{dam$^2$}&\multicolumn{2}{c|}{m$^2$}&\multicolumn{2}{c|}{dm$^2$}&\multicolumn{2}{c|}{cm$^2$}&\multicolumn{2}{c|}{mm$^2$}\\ - \hline - &&&&&&&&&&&&&\\ + \multicolumn{2}{|c|}{km$^2$}&\multicolumn{2}{c|}{hm$^2$}&\multicolumn{2}{c|}{dam$^2$}&\multicolumn{2}{c|}{m$^2$}&\multicolumn{2}{c|}{dm$^2$}&\multicolumn{2}{c|}{cm$^2$}&\multicolumn{2}{c|}{mm$^2$}\\% + \ifboolKV[ClesTableaux]{Are}{% + \cline{3-6} + \multicolumn{2}{|c|}{}&&{\scriptsize ha}&&{\scriptsize a}&\multicolumn{2}{c|}{}&\multicolumn{2}{c|}{}&\multicolumn{2}{c|}{}&\multicolumn{2}{c|}{}\\ + }{} + \hline + \xintFor* ##1 in {\xintSeq{1}{\useKV[ClesTableaux]{NbLignes}}}\do{% + &&&&&&&&&&&&&\\} \multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em] (G1);}}% &\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em] (F1);}}% &\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em] (E1);}}% @@ -10942,32 +12458,23 @@ vardef Positions(expr Step)= &\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em] (B1);}}% &\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em] (A1);}}\\% \end{tabular} - \] - \ifboolKV[ClesTableaux]{Fleches}{% - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (A) to node[above, midway]{\small$\times\mbox{100}$}(B);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (B) to node[above, midway]{\small$\times\mbox{100}$}(C);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (C) to node[above, midway]{\small$\times\mbox{100}$}(D);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (D) to node[above, midway]{\small$\times\mbox{100}$}(E);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (E) to node[above, midway]{\small$\times\mbox{100}$}(F);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (F) to node[above, midway]{\small$\times\mbox{100}$}(G);} - % bas - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (A1) to node[below, midway]{\small$\div\mbox{100}$}(B1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (B1) to node[below, midway]{\small$\div\mbox{100}$}(C1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (C1) to node[below, midway]{\small$\div\mbox{100}$}(D1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (D1) to node[below, midway]{\small$\div\mbox{100}$}(E1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (E1) to node[below, midway]{\small$\div\mbox{100}$}(F1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (F1) to node[below, midway]{\small$\div\mbox{100}$}(G1);} - }{}% - }% - {}% + \]% + \Conversion{100}% + }{}% + % + %%% Prise en compte de la clé Cube + % \ifboolKV[ClesTableaux]{Cube}{% \setlength{\tabcolsep}{0.625\tabcolsep}% - \ifboolKV[ClesTableaux]{Colonnes}{% - \newcolumntype{X}{|*{7}{p{2.5mm}!{\color{gray!50}\vrule}p{2.5mm}!{\color{gray!50}\vrule}p{2.5mm}|}}% + \ifboolKV[ClesTableaux]{Colonnes}{% + \newcolumntype{X}{|*{7}{>{\centering\arraybackslash}p{3.5mm}!{\color{gray!50}\vrule}>{\centering\arraybackslash}p{3.5mm}!{\color{gray!50}\vrule}>{\centering\arraybackslash}p{3.5mm}|}}% }{% - \newcolumntype{X}{|*{7}{p{2.5mm}p{2.5mm}p{2.5mm}|}}% - } - \[\renewcommand{\arraystretch}{1.15} + \ifboolKV[ClesTableaux]{Capacite}{% + \newcolumntype{X}{|*{7}{>{\centering\arraybackslash}p{3.5mm}!{\color{gray!50}\vrule}>{\centering\arraybackslash}p{3.5mm}!{\color{gray!50}\vrule}>{\centering\arraybackslash}p{3.5mm}|}}% + }{% + \newcolumntype{X}{|*{7}{p{3.5mm}p{3.5mm}p{3.5mm}|}}% + }}% + \[\renewcommand{\arraystretch}{1.15}% \begin{tabular}{X} \multicolumn{3}{c}{\tikz[remember picture,overlay]{\coordinate (A);}}% &\multicolumn{3}{c}{\tikz[remember picture,overlay]{\coordinate (B);}}% @@ -10978,8 +12485,14 @@ vardef Positions(expr Step)= &\multicolumn{3}{c}{\tikz[remember picture,overlay]{\coordinate (G);}}\\% \hline \multicolumn{3}{|c|}{km$^3$}&\multicolumn{3}{c|}{hm$^3$}&\multicolumn{3}{c|}{dam$^3$}&\multicolumn{3}{c|}{m$^3$}&\multicolumn{3}{c|}{dm$^3$}&\multicolumn{3}{c|}{cm$^3$}&\multicolumn{3}{c|}{mm$^3$}\\ + \ifboolKV[ClesTableaux]{Capacite}{% + \cline{10-15} + \multicolumn{3}{|c|}{}&\multicolumn{3}{c|}{}&\multicolumn{3}{c|}{}&{\scriptsize hL}&{\scriptsize daL}&{\scriptsize L}&{\scriptsize dL}&{\scriptsize cL}&{\scriptsize mL}&\multicolumn{3}{c|}{}&\multicolumn{3}{c|}{}\\ + }{}% \hline + \xintFor* ##1 in {\xintSeq{1}{\useKV[ClesTableaux]{NbLignes}}}\do{% &&&&&&&&&&&&&&&&&&&&\\ + }% \multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate (G1);}}% &\multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate (F1);}}% &\multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate (E1);}}% @@ -10988,75 +12501,41 @@ vardef Positions(expr Step)= &\multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate (B1);}}% &\multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate (A1);}}\\% \end{tabular} - \] - \setlength{\tabcolsep}{1.6\tabcolsep} - \ifboolKV[ClesTableaux]{Fleches}{% - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] - (A) to node[above, midway]{$\times\mbox{\num{1000}}$}(B);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (B) to - node[above, midway]{$\times\mbox{\num{1000}}$}(C);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (C) to - node[above, midway]{$\times\mbox{\num{1000}}$}(D);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (D) to - node[above, midway]{$\times\mbox{\num{1000}}$}(E);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (E) to - node[above, midway]{$\times\mbox{\num{1000}}$}(F);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (F) to - node[above, midway]{$\times\mbox{\num{1000}}$}(G);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (A1) to - node[below, midway]{$\div\mbox{\num{1000}}$}(B1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (B1) to - node[below, midway]{$\div\mbox{\num{1000}}$}(C1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (C1) to - node[below, midway]{$\div\mbox{\num{1000}}$}(D1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (D1) to - node[below, midway]{$\div\mbox{\num{1000}}$}(E1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (E1) to - node[below, midway]{$\div\mbox{\num{1000}}$}(F1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (F1) to - node[below, midway]{$\div\mbox{\num{1000}}$}(G1);} - }{} - } - {} + \]% + \setlength{\tabcolsep}{1.6\tabcolsep}% + \Conversion{1000}% + }{}% + % + %%% Prise en compte de la clé Litre + % \ifboolKV[ClesTableaux]{Litre}{% \[\renewcommand{\arraystretch}{1.15}% - \begin{tabular}{|*{7}{p{7.5mm}|}} + \begin{tabular}{|*{6}{p{7.5mm}|}} \multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (A);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (B);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (C);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (D);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (E);}}% - &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (F);}}% - &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (G);}}\\% + &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (F);}}\\% \hline - \multicolumn{1}{|c|}{kL}&\multicolumn{1}{c|}{hL}&\multicolumn{1}{c|}{daL}&\multicolumn{1}{c|}{L}&\multicolumn{1}{c|}{dL}&\multicolumn{1}{c|}{cL}&\multicolumn{1}{c|}{mL}\\ - \hline - &&&&&&\\ - \multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (G1);}}% - &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (F1);}} + \multicolumn{1}{|c|}{hL}&\multicolumn{1}{c|}{daL}&\multicolumn{1}{c|}{L}&\multicolumn{1}{c|}{dL}&\multicolumn{1}{c|}{cL}&\multicolumn{1}{c|}{mL}\\ + \hline + \xintFor* ##1 in {\xintSeq{1}{\useKV[ClesTableaux]{NbLignes}-1}}\do{% + &&&&&\\}% + &&&&&\\% + \multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (F1);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (E1);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (D1);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (C1);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (B1);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (A1);}}\\% \end{tabular} - \] - \ifboolKV[ClesTableaux]{Fleches}{% - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (A) to node[above, midway]{\small$\times\mbox{10}$}(B);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (B) to node[above, midway]{\small$\times\mbox{10}$}(C);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (C) to node[above, midway]{\small$\times\mbox{10}$}(D);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (D) to node[above, midway]{\small$\times\mbox{10}$}(E);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (E) to node[above, midway]{\small$\times\mbox{10}$}(F);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (F) to node[above, midway]{\small$\times\mbox{10}$}(G);} - % bas - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (A1) to node[below, midway]{\small$\div\mbox{10}$}(B1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (B1) to node[below, midway]{\small$\div\mbox{10}$}(C1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (C1) to node[below, midway]{\small$\div\mbox{10}$}(D1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (D1) to node[below, midway]{\small$\div\mbox{10}$}(E1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (E1) to node[below, midway]{\small$\div\mbox{10}$}(F1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (F1) to node[below, midway]{\small$\div\mbox{10}$}(G1);} - }{}% + \]% + \Conversion{10}% }{}% + % + %%% Prise en compte de la clé Gramme + % \ifboolKV[ClesTableaux]{Gramme}{% \[\renewcommand{\arraystretch}{1.15}% \begin{tabular}{|*{7}{p{7.5mm}|}} @@ -11066,11 +12545,12 @@ vardef Positions(expr Step)= &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (D);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (E);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (F);}}% - &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (G);}} - \\% + &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (G);}}\\% \hline \multicolumn{1}{|c|}{kg}&\multicolumn{1}{c|}{hg}&\multicolumn{1}{c|}{dag}&\multicolumn{1}{c|}{g}&\multicolumn{1}{c|}{dg}&\multicolumn{1}{c|}{cg}&\multicolumn{1}{c|}{mg}\\ \hline + \xintFor* ##1 in {\xintSeq{1}{\useKV[ClesTableaux]{NbLignes}-1}}\do{% + &&&&&&\\}% &&&&&&\\ \multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (G1);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (F1);}}% @@ -11080,21 +12560,483 @@ vardef Positions(expr Step)= &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (B1);}}% &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (A1);}}\\% \end{tabular} - \] - \ifboolKV[ClesTableaux]{Fleches}{% - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (A) to node[above, midway]{\small$\times\mbox{10}$}(B);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (B) to node[above, midway]{\small$\times\mbox{10}$}(C);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (C) to node[above, midway]{\small$\times\mbox{10}$}(D);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (D) to node[above, midway]{\small$\times\mbox{10}$}(E);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (E) to node[above, midway]{\small$\times\mbox{10}$}(F);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (F) to node[above, midway]{\small$\times\mbox{10}$}(G);} -% % bas - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (A1) to node[below, midway]{\small$\div\mbox{10}$}(B1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (B1) to node[below, midway]{\small$\div\mbox{10}$}(C1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (C1) to node[below, midway]{\small$\div\mbox{10}$}(D1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (D1) to node[below, midway]{\small$\div\mbox{10}$}(E1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (E1) to node[below, midway]{\small$\div\mbox{10}$}(F1);} - \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (F1) to node[below, midway]{\small$\div\mbox{10}$}(G1);} - }{}% + \]% + \Conversion{10}% + }{}% +}% + +\newcommand\Conversion[1]{% + \ifboolKV[ClesTableaux]{Fleches}{\setKV[ClesTableaux]{FlechesH,FlechesB}}{}% + \ifboolKV[ClesTableaux]{FlechesH}{% + \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (A) to node[above, midway]{\small$\times\num{#1}$}(B);}% + \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (B) to node[above, midway]{\small$\times\num{#1}$}(C);}% + \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (C) to node[above, midway]{\small$\times\num{#1}$}(D);}% + \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (D) to node[above, midway]{\small$\times\num{#1}$}(E);}% + \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (E) to node[above, midway]{\small$\times\num{#1}$}(F);}% + \ifboolKV[ClesTableaux]{Litre}{}{\tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=30,in=150] (F) to node[above, midway]{\small$\times\num{#1}$}(G);}% + }% + }{}% + \ifboolKV[ClesTableaux]{FlechesB}{% + \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (A1) to node[below, midway]{\small$\div\num{#1}$}(B1);}% + \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (B1) to node[below, midway]{\small$\div\num{#1}$}(C1);}% + \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (C1) to node[below, midway]{\small$\div\num{#1}$}(D1);}% + \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (D1) to node[below, midway]{\small$\div\num{#1}$}(E1);}% + \tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (E1) to node[below, midway]{\small$\div\num{#1}$}(F1);}% + \ifboolKV[ClesTableaux]{Litre}{}{\tikz[remember picture, overlay]{\draw[gray,->,>=latex,out=-150,in=-30] (F1) to node[below, midway]{\small$\div\num{#1}$}(G1);}}% }{}% +}% + +%%% +% Cards +%%% +\newtcolorbox{Mybox}[3]{% + enhanced, + nobeforeafter, + left=0pt,right=0pt,top=0pt, + text fill, + width=\largeurcarte, + height=\hauteurcarte, + arc=5pt, + overlay unbroken and first={% + \coordinate[yshift=-0.5\hauteurtitre] (A1) at (frame.north west); + \coordinate[yshift=-0.5\hauteurtitre] (B1) at (frame.north east); + \coordinate[yshift=-\hauteurtitre] (A) at (frame.north west); + \coordinate[yshift=-\hauteurtitre] (B) at (frame.north east); + \coordinate[xshift=1.5pt,yshift=8mm] (S1) at (frame.south west); + \coordinate[xshift=-1.5pt,yshift=8mm] (S2) at (frame.south east); + \coordinate[xshift=3mm+(\largeurtitre/2)] (A2) at (A1); + \coordinate[xshift=-3mm-(\largeurtitre/2)] (B2) at (B1); + \node[rounded corners, draw=black, rectangle,minimum height=1cm,text width=\largeurtitre,fill=TrameCouleur] (T1) at (A2){}; + \node[TexteCouleur] (T1a) at (T1){\Large #1}; + \node[yshift=-0.65cm] (T1b) at (T1){\tiny réponse précédente}; + \node[inner sep=0pt,rounded corners, rectangle, draw=black,minimum height=1cm,text width=\largeurtitre,fill=TrameCouleur] (T2) at (B2){}; + \node[inner sep=0pt,TexteCouleur] (T2a) at (T2){ + \begin{minipage}{\largeurtitre} + \begin{center} + #2 + \end{center} + \end{minipage} + }; + \node[yshift=-0.65cm] (T2b) at (T2){}; + \ifboolKV[Cards]{Titre}{\node[] at (T2b) {\tiny\useKV[Cards]{NomTitre}};}{}, + \node[rectangle,xshift=5mm,yshift=4.25mm,minimum width=2em,rounded corners,fill=TrameCouleur,draw=black] (R) at (frame.south west) {\color{black}\Large\bfseries #3}; + \draw[dashed] (S1) -- (S2); + }, + colback=white, + colbacktitle=TrameCouleur, +} + +\usetikzlibrary{backgrounds} + +\makeatletter +%https://tex.stackexchange.com/questions/347434/clip-background-image-inside-tcolorbox +\newtcolorbox{MyboxSimpleAv}[1]{% + enhanced, + nobeforeafter, + left=0pt,right=0pt,top=\hauteurtitre,bottom=0pt, + text fill, + width=\largeurcarte, + height=\hauteurcarte, + arc=5pt, + colback=white, + underlay={% + \ifboolKV[Cards]{BackgroundAv}{% + \begin{tcbclipinterior} + \node[anchor=center,opacity=1] + at (interior.center) {% + \includegraphics[% + height=\tcb@height, + width=\tcb@width, + ]{\useKV[Cards]{ImageAv}}}; + \end{tcbclipinterior}, + }{} + }, + overlay unbroken and first={% + \coordinate[yshift=-0.5\hauteurtitre] (A) at (frame.north); + \node[rounded corners, draw=black, rectangle,minimum height=1cm,text width=\largeurcarte-6mm,fill=TrameCouleur] (T1) at + (A){\begin{minipage}{\largeurcarte-6mm} + \begin{center} + #1 + \end{center} + \end{minipage}}; + \node[yshift=-0.5em-0.5\hauteurtitre] (B) at (A){}; + \ifboolKV[Cards]{Titre}{\node[fill=white] at (B) {\useKV[Cards]{NomTitre}};}{}, + } +} + +\newtcolorbox{MyboxSimpleAr}[1]{% + enhanced, + nobeforeafter, + left=0pt,right=0pt,top=\hauteurtitre,bottom=0pt, + text fill, + width=\largeurcarte, + height=\hauteurcarte, + arc=5pt, + colback=white, + underlay={% + \ifboolKV[Cards]{BackgroundAr}{% + \begin{tcbclipinterior} + \node[anchor=center,opacity=1] + at (interior.center) {% + \includegraphics[% + height=\tcb@height, + width=\tcb@width, + ]{\useKV[Cards]{ImageAr}}}; + \end{tcbclipinterior}, + }{} + }, + overlay unbroken and first={% + \coordinate[yshift=-0.5\hauteurtitre] (A) at (frame.north); + \node[rounded corners, draw=black, rectangle,minimum height=1cm,text width=\largeurcarte-6mm,fill=TrameCouleur] (T1) at + (A){\begin{minipage}{\largeurcarte-6mm} + \begin{center} + #1 + \end{center} + \end{minipage}}; + %\node[yshift=-1em] (B) at (A){}; + %\ifboolKV[Cards]{Titre}{\node[fill=white] at (B) {\useKV[Cards]{NomTitre}};}{}, + } +} +\makeatother + +\newlength{\largeurcards} +\newlength{\hauteurcards} +\newlength{\largeurcarte} +\newlength{\hauteurcarte} +\newlength{\hauteurtitre} +\newlength{\largeurtitre} + +\newlength{\margeh} +\newlength{\margev} + +\NewEnviron{Trame}{% + \begin{tikzpicture}[remember picture,overlay] + % quadrillages horizontal et vertical + \coordinate[yshift=-\margev] (A) at (current page.north west); + \coordinate[yshift=-\margev] (B) at (current page.north east); + \coordinate[yshift=-\hauteurcards] (A1) at (A); + \coordinate[yshift=-\hauteurcards] (B1) at (B); + \coordinate[yshift=-\hauteurcards] (A2) at (A1); + \coordinate[yshift=-\hauteurcards] (B2) at (B1); + \coordinate[yshift=-\hauteurcards] (A3) at (A2); + \coordinate[yshift=-\hauteurcards] (B3) at (B2); + \coordinate[yshift=-\hauteurcards] (A4) at (A3); + \coordinate[yshift=-\hauteurcards] (B4) at (B3); + \coordinate[xshift=\margeh] (C) at (current page.north west); + \coordinate[xshift=\margeh] (D) at (current page.south west); + \coordinate[xshift=\largeurcards] (C1) at (C); + \coordinate[xshift=\largeurcards] (D1) at (D); + \coordinate[xshift=\largeurcards] (C2) at (C1); + \coordinate[xshift=\largeurcards] (D2) at (D1); + \coordinate[xshift=\largeurcards] (C3) at (C2); + \coordinate[xshift=\largeurcards] (D3) at (D2); + \draw (A) -- (B); + \draw (A1) -- (B1); + \draw (A2) -- (B2); + \draw (A3) -- (B3); + \draw (A4) -- (B4); + \draw (C)--(D); + \draw (C1)--(D1); + \draw (C2)--(D2); + \draw (C3)--(D3); + % point pour placer les cartes + \coordinate[xshift=\margeh+0.5\largeurcards,yshift=-0.5\hauteurcards] (Carte1) at (A); + \coordinate[xshift=\largeurcards,yshift=0mm] (Carte2) at (Carte1); + \coordinate[xshift=2\largeurcards,yshift=0mm] (Carte3) at (Carte1); + \coordinate[xshift=0mm,yshift=-\hauteurcards] (Carte4) at (Carte1); + \coordinate[xshift=0mm,yshift=-\hauteurcards] (Carte5) at (Carte2); + \coordinate[xshift=0mm,yshift=-\hauteurcards] (Carte6) at (Carte3); + \coordinate[xshift=0mm,yshift=-\hauteurcards] (Carte7) at (Carte4); + \coordinate[xshift=0mm,yshift=-\hauteurcards] (Carte8) at (Carte5); + \coordinate[xshift=0mm,yshift=-\hauteurcards] (Carte9) at (Carte6); + \BODY + \end{tikzpicture} +} + +\setKVdefault[Cards]{Largeur=59,Hauteur=89,HauteurTheme=15,Marge=4,Landscape=false,Couleur=Cornsilk,Theme=Théorème\\de + Pythagore,ThemeSol=Solution,Trame=false,Titre=false,NomTitre=Jeu 1,Loop,BackgroundAv=false,BackgroundAr=false,ImageAv=4813762.jpg,ImageAr=4813762.jpg} + +\newcommand\Cartes[2][]{% + \useKVdefault[Cards]% + \setKV[Cards]{#1}% + \setsepchar[*]{§*/}% + \readlist*\ListeCards{#2}% + \ifboolKV[Cards]{Landscape}{% + \setlength{\hauteurcarte}{\fpeval{\useKV[Cards]{Largeur}-\useKV[Cards]{Marge}}mm}% + \setlength{\largeurcarte}{\fpeval{\useKV[Cards]{Hauteur}-\useKV[Cards]{Marge}}mm}% + \setlength{\largeurcards}{95mm}% + \setlength{\hauteurcards}{65mm}% + \setlength{\margeh}{(297mm-3\largeurcards)/2}% + \setlength{\margev}{(210mm-3\hauteurcards)/2}% + }{ + \setlength{\hauteurcarte}{\fpeval{\useKV[Cards]{Hauteur}-\useKV[Cards]{Marge}}mm}% + \setlength{\largeurcarte}{\fpeval{\useKV[Cards]{Largeur}-\useKV[Cards]{Marge}}mm}% + \setlength{\largeurcards}{65mm} + \setlength{\hauteurcards}{95mm} + \setlength{\margeh}{(210mm-3\largeurcards)/2} + \setlength{\margev}{(297mm-3\hauteurcards)/2} + } + \setlength{\hauteurtitre}{\fpeval{\useKV[Cards]{HauteurTheme}}mm}% + \setlength{\largeurtitre}{\fpeval{(\useKV[Cards]{Largeur}-\useKV[Cards]{Marge}-9)/2}mm}% + \colorlet{TexteCouleur}{black} + \colorlet{TrameCouleur}{\useKV[Cards]{Couleur}} + \ifboolKV[Cards]{Loop}{% + \ifboolKV[Cards]{Trame}{% + \clearpage% + \thispagestyle{empty}% + \begin{Trame} + \multido{\i=1+1}{9}{% + \node at (Carte\i) {% + \begin{Mybox}{\ListeCards[\i,1]}{\useKV[Cards]{Theme}}{\ListeCards[\i,2]}% + \ListeCards[\i,3]% + \end{Mybox}% + };% + }% + \end{Trame}% + \clearpage% + }{% + \begin{Mybox}{\ListeCards[1,1]}{\useKV[Cards]{Theme}}{\ListeCards[1,2]}% + \ListeCards[1,3]% + \end{Mybox}% + }% + }{% + \ifboolKV[Cards]{Trame}{% + \clearpage% + \thispagestyle{empty}% + \begin{Trame} + \multido{\i=1+1}{9}{% + \node[] at (Carte\i) {% + \begin{MyboxSimpleAv}{\useKV[Cards]{Theme}}% + \ListeCards[\i,1]% + \end{MyboxSimpleAv}% + };% + }% + \end{Trame}% + \clearpage% + \thispagestyle{empty}% + \begin{Trame} + \multido{\i=1+1}{3}{% + \node at (Carte\i) {% + \begin{MyboxSimpleAr}{\useKV[Cards]{ThemeSol}}% + \ListeCards[\fpeval{4-\i},2]% + \end{MyboxSimpleAr}% + };% + }% + \multido{\i=4+1}{3}{% + \node at (Carte\i) {% + \begin{MyboxSimpleAr}{\useKV[Cards]{ThemeSol}}% + \ListeCards[\fpeval{10-\i},2]% + \end{MyboxSimpleAr}% + };% + }% + \multido{\i=7+1}{3}{% + \node at (Carte\i) {% + \begin{MyboxSimpleAr}{\useKV[Cards]{ThemeSol}}% + \ListeCards[\fpeval{16-\i},2]% + \end{MyboxSimpleAr}% + };% + }% + \end{Trame}% + \clearpage% + }{% + \begin{MyboxSimpleAv}{\useKV[Cards]{Theme}}% + \ListeCards[1,1]% + \end{MyboxSimpleAv} + \begin{MyboxSimpleAr}{\useKV[Cards]{ThemeSol}}% + \ListeCards[1,2]% + \end{MyboxSimpleAr} + }% + }% +} + +\newcommand\SolutionCarte[2]{% + \begin{center} + \bfseries#1 + \end{center} + + #2 +} + +%%% +% Tableur +%%% +\setKVdefault[Tableur]{Colonnes=4,Largeur=3,Formule={},Cellule=A1,Ligne=0,Colonne=0,PasL=1,PasC=1} + +%Basé sur un code de Christian Télléchéa. +\makeatletter +\newcount\cntlin +\newcount\cntcol + +\newtoks\t@b +\long\def\ifremain@lines#1\\#2\@nil{% + \csname @\ifx\@empty#2\@empty second\else first\fi oftwo\endcsname} +\long\def\subst@eol#1\\#2\@nil{\addtot@b{#1\\\hline}% + \ifremain@lines#2\\\@nil{\addtot@b&\subst@eol#2\@nil}{\addtot@b{#2\CodeAfter\xintifboolexpr{\useKV[Tableur]{Ligne}=0 || \useKV[Tableur]{Colonne}=0}{}{\tikz\draw[line width=2pt](row-\fpeval{\useKV[Tableur]{Ligne}+1}-|col-\fpeval{\useKV[Tableur]{Colonne}+1}) rectangle (row-\fpeval{\useKV[Tableur]{Ligne}+1+\useKV[Tableur]{PasL}}-|col-\fpeval{\useKV[Tableur]{Colonne}+1+\useKV[Tableur]{PasC}});}\end{NiceTabular}}}} +\long\def\collectcp@body#1\end{\subst@eol#1\@nil\end} + +\newcommand\addtot@b[1]{\t@b\expandafter{\the\t@b#1}} +\newcommand\edftot@b[1]{\edef\temp@{#1}\expandafter\addtot@b\expandafter{\temp@}} + +\newlength\LongInter +\newlength\TotalInter + +\newenvironment{Tableur}[1][]{% + \useKVdefault[Tableur]% + \setKV[Tableur]{#1}% + \ttfamily% + \setlength{\LongInter}{\fpeval{(\useKV[Tableur]{Colonnes}-1)*\useKV[Tableur]{Largeur}-4}em+\fpeval{\useKV[Tableur]{Colonnes}*2-6}\tabcolsep+\fpeval{\useKV[Tableur]{Colonnes}-3}\arrayrulewidth} + \newcolumntype X{>{\centering\arraybackslash}p{\useKV[Tableur]{Largeur}em}}% + \begin{tabular}{|p{\useKV[Tableur]{Largeur}em}|p{1em}|p{5em}|p{\LongInter}|} + \cline{1-2}\cline{4-4}% + \useKV[Tableur]{Cellule}&\centering\arraybackslash\scriptsize$\blacktriangledown$&$f_x$\hfill$\sum$~\scriptsize$\blacktriangledown$\hfill$=$&\useKV[Tableur]{Formule}\hfill\scriptsize$\blacktriangledown$\\ + \cline{1-2}\cline{4-4}% + \end{tabular} + + \cntlin\z@ + \t@b{% + \begin{NiceTabular}{% + |>{% + \columncolor{gray!15} + \global\cntcol\z@\global\advance\cntlin\@ne + \centering\arraybackslash + \ifnum\cntlin>\@ne\number\numexpr\cntlin-1\relax\fi} + p{2em}|*{\useKV[Tableur]{Colonnes}}{X|}}% + \hline + \rowcolor{gray!15}}% + \loop + \ifnum\cntcol<\useKV[Tableur]{Colonnes} + \advance\cntcol\@ne + \addtot@b{&}% + \edftot@b{{\noexpand\@Alph\the\cntcol}}% + \repeat + \addtot@b{\\\hline&}% + \collectcp@body}{\the\t@b} +\makeatother + +%%% +% Domino +%%% +\newtcolorbox{MyDominoMini}[1][]{% + enhanced, + nobeforeafter, + left skip=0pt, + right skip=0pt, + left=0pt,right=0pt,top=0pt,bottom=0pt, + width=\textwidth/\ColonneDomino, + height=\textheight/\LigneDomino, + segmentation style={solid, line width=1.5pt}, + colback=\CouleurDomino, + center upper, + valign upper=center, + center lower, + valign lower=center, + arc=2pt, + #1 +} + +\newtcolorbox{MyDominoLogo}[1][]{% + enhanced, + nobeforeafter, + left skip=0pt, + right skip=0pt, + left=0pt,right=0pt,top=0pt,bottom=0pt, + width=\textwidth/\ColonneDomino, + height=\textheight/\LigneDomino, + valign=center, + halign=center, + arc=2pt, + colback=white, + #1 +} + +\NewEnviron{TrameDomino}{% + \setlength{\margev}{1cm} + \setlength{\margeh}{1cm} + \begin{tikzpicture}[remember picture,overlay] + % quadrillages horizontal et vertical + \coordinate[yshift=-\margev] (A0) at (current page.north west); + \coordinate[yshift=-\margev] (B0) at (current page.north east); + \foreach \i in {1,...,\useKV[Domino]{Lignes}}{% + \coordinate[yshift=-\i*\textheight/\LigneDomino] (A\i) at (A0); + \coordinate[yshift=-\i*\textheight/\LigneDomino] (B\i) at (B0); + } + \coordinate[xshift=\margeh] (C0) at (current page.north west); + \coordinate[xshift=\margeh] (D0) at (current page.south west); + \foreach \i in {1,...,\useKV[Domino]{Colonnes}}{ + \coordinate[xshift=\i*\textwidth/\ColonneDomino] (C\i) at (C0); + \coordinate[xshift=\i*\textwidth/\ColonneDomino] (D\i) at (D0); + } + \foreach \i in {0,...,\LigneDomino}{% + \draw (A\i) -- (B\i); + } + \foreach \i in {0,...,\ColonneDomino}{% + \draw (C\i) -- (D\i); + } + \draw[blue, line width=3pt] (A0)--(B0); + \draw[blue, line width=3pt] (A\LigneDomino)--(B\LigneDomino); + \draw[blue, line width=3pt] (C0)--(D0); + \draw[blue, line width=3pt] (C\ColonneDomino)--(D\ColonneDomino); + % point pour placer les cartes + \foreach \i in {0,...,\fpeval{\ColonneDomino-1}}{% + \foreach \j in {0,...,\fpeval{\LigneDomino-1}}{% + \coordinate[xshift=\margeh+(0.5\textwidth/\ColonneDomino)+\i*\textwidth/\ColonneDomino,yshift=-0.5\textheight/\LigneDomino-\j*\textheight/\LigneDomino] + (Domino\fpeval{\i+\ColonneDomino*\j+1}) at (A0); + } + } + \BODY + \end{tikzpicture} +} + +\setKVdefault[Domino]{Couleur=white,Trame,Ratio=0.5,Lignes=7,Colonnes=5,Superieur=false,Logo=false,Image=tiger.pdf} + +\newcommand\Dominos[2][]{% + \useKVdefault[Domino]% + \setKV[Domino]{#1}% + \setsepchar[*]{§*/}% + \readlist*\ListeDominos{#2}% + \xdef\CouleurDomino{\useKV[Domino]{Couleur}}% + \xdef\ratiodomino{\useKV[Domino]{Ratio}}% + \xdef\LigneDomino{\useKV[Domino]{Lignes}}% + \xdef\ColonneDomino{\useKV[Domino]{Colonnes}}% + \ifboolKV[Domino]{Trame}{% + \clearpage + \begin{TrameDomino} + \foreach\i in {1,...,\fpeval{\LigneDomino*\ColonneDomino}}{% + \node[] at (Domino\i){% + \ifboolKV[Domino]{Superieur}{% + \begin{MyDominoMini}[space=\ratiodomino]% + \ListeDominos[\i,1]\tcblower\ListeDominos[\i,2]% + \end{MyDominoMini}% + }{% + \begin{MyDominoMini}[sidebyside,sidebyside gap=4mm,righthand ratio=\ratiodomino]% + \ListeDominos[\i,1]\tcblower\ListeDominos[\i,2]% + \end{MyDominoMini}% + }% + }; + }% + \end{TrameDomino}% + \ifboolKV[Domino]{Logo}{% + \clearpage + \begin{TrameDomino} + \foreach\i in {1,...,\fpeval{\LigneDomino*\ColonneDomino}}{% + \node at (Domino\i){% + \begin{MyDominoLogo}% + \includegraphics[height=\tcbtextheight]{\useKV[Domino]{Image}} + \end{MyDominoLogo}% + }; + }% + \end{TrameDomino}% + }{}% + }{% + \ifboolKV[Domino]{Superieur}{% + \begin{MyDominoMini}[space=\ratiodomino]% + \ListeDominos[1,1]\tcblower\ListeDominos[1,2]% + \end{MyDominoMini}% + }{% + \begin{MyDominoMini}[sidebyside,sidebyside gap=4mm,righthand ratio=\ratiodomino]% + \ListeDominos[1,1]\tcblower% + \ListeDominos[1,2]% + \end{MyDominoMini}% + }% + }% }% \ No newline at end of file -- cgit v1.2.3