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diff --git a/macros/latex/contrib/proflycee/tex/proflycee-tools-analyse.tex b/macros/latex/contrib/proflycee/tex/proflycee-tools-analyse.tex new file mode 100644 index 0000000000..921a053556 --- /dev/null +++ b/macros/latex/contrib/proflycee/tex/proflycee-tools-analyse.tex @@ -0,0 +1,386 @@ +% proflycee-tools-analyse.tex +% Copyright 2023 Cédric Pierquet +% This work may be distributed and/or modified under the +% conditions of the LaTeX Project Public License, either version 1.3 +% of this license or (at your option) any later version. +% The latest version of this license is in +% http://www.latex-project.org/lppl.txt +% and version 1.3 or later is part of all distributions of LaTeX +% version 2005/12/01 or later. + +%%------SimplFrac nouvelle version +\NewDocumentCommand\ConversionFraction{ s O{} m }{% + %*=moins sur le numérateur + %2=argument.optionnel[d/t/dec=...] + %3=argument mandataire {calcul ou fraction} + \def\calculargument{\xintPRaw{\xintIrr{\xinteval{#3}}}}%on calcule et on transforme en A/B + \IfSubStr{\calculargument}{/}%on teste si le symbole / apparaît + {%si oui := fraction + \StrBefore{\calculargument}{/}[\numerateur]%on extrait le numérateur + \StrBehind{\calculargument}{/}[\denominateur]%on extrait le dénominateur + \ifblank{#2}% + {% + \IfBooleanTF{#1}% + {\ensuremath{\frac{\num{\numerateur}}{\num{\denominateur}}}}% + {% + \ifthenelse{\numerateur < 0}% + {\ensuremath{-\frac{\num{\fpeval{abs(\numerateur)}}}{\num{\denominateur}}}}% + {\ensuremath{\frac{\num{\numerateur}}{\num{\denominateur}}}}% + }% + }% + {}%si l'argument optionnel est vide + \IfStrEq{#2}{d}% + {% + \IfBooleanTF{#1}% + {\ensuremath{\dfrac{\num{\numerateur}}{\num{\denominateur}}}}% + {% + \ifthenelse{\numerateur < 0}% + {\ensuremath{-\dfrac{\num{\fpeval{abs(\numerateur)}}}{\num{\denominateur}}}}% + {\ensuremath{\dfrac{\num{\numerateur}}{\num{\denominateur}}}}% + }% + }% + {}%si l'argument optionnel est vide + \IfStrEq{#2}{t}% + {% + \IfBooleanTF{#1}% + {\ensuremath{\tfrac{\num{\numerateur}}{\num{\denominateur}}}}% + {% + \ifthenelse{\numerateur < 0}% + {\ensuremath{-\tfrac{\num{\fpeval{abs(\numerateur)}}}{\num{\denominateur}}}}% + {\ensuremath{\tfrac{\num{\numerateur}}{\num{\denominateur}}}}% + }% + }% + {}%si l'argument optionnel est vide + \IfStrEq{#2}{n}% + {% + %\IfBooleanTF{#1}% + {\ensuremath{\nicefrac{\num{\numerateur}}{\num{\denominateur}}}}% + %{% + % \ifthenelse{\numerateur < 0}% + % {\ensuremath{-\nicefrac{\num{\fpeval{abs(\numerateur)}}}{\num{\denominateur}}}}% + % {\ensuremath{\nicefrac{\num{\numerateur}}{\num{\denominateur}}}}% + %}% + }% + {}%si l'argument optionnel est vide + \IfSubStr{#2}{dec}%on veut la forme décimale + {% + \IfSubStr{#2}{=}%si on rajoute une précision + {% + \StrBehind{#2}{=}[\precdecimal]% + \ensuremath{\num{\xintfloateval{round(#3,\precdecimal)}}}% + }% + {% + \ensuremath{\num{\xintfloateval{#3}}}% + }% + }% + {}%si l'argument optionnel est vide + }{%si non := entier + \num{\calculargument}%on affiche l'entier, avec le package siunitx + }% +} + +%%------AideTds +\defKV[aidetds]{% + Code=\def\tdsparam{#1},% + Couleur=\def\tdscouleur{#1},% + Racines=\def\tdsracine{#1},% + Largeur=\def\tdslarg{#1},% + Hauteur=\def\tdshaut{#1} +} + +\setKVdefault[aidetds]{% + Code=da+, + Couleur=red,% + Largeur=2,% + Hauteur=1,% + Cadre=true,% + Racines=2 +} + +\NewDocumentCommand\schematdsaff{ s m m m m }{%pour les droites (interne) + % * = étoilée -> a négatif + % #2 = couleur + % #3 = largeur + % #4 = hauteur + % #5 = racine + \IfBooleanTF{#1}%si étoile := droite qui descend + {% + \def\possgnavant{above right}\def\possgnapres{below left}\def\sgnavant{\strut+}\def\sgnapres{\strut-}% + \draw[thick,#2] ({-0.5*#3},{0.5*#4})--({0.5*#3},{-0.5*#4}); + } + {% + \def\possgnavant{below right}\def\possgnapres{above left}\def\sgnavant{\strut-}\def\sgnapres{\strut+}% + \draw[thick,#2] ({-0.5*#3},{-0.5*#4})--({0.5*#3},{0.5*#4}); + } + \draw[#2] ({-0.5*#3},0) node[inner sep=0pt,\possgnavant=1pt,font=\scriptsize] {\textcircled{$\sgnavant$}}; + \draw[#2] ({0.5*#3},0) node[inner sep=0pt,\possgnapres=1pt,font=\scriptsize] {\textcircled{$\sgnapres$}}; + \draw[#2] (0,0) node[inner sep=0pt,above=3pt,font=\scriptsize] {$\strut#5$} ; + \filldraw[#2] (0,0) circle[radius=2pt] ; +} + +\NewDocumentCommand\schematdsparab{ m m m m m o }{%pour les paraboles (interne) + % #1 = signe de a (1 ou -1) ? + % #2 = couleur + % #3 = largeur + % #4 = hauteur + % #5 = nb racine + % #6 = liste racines (option) + \xintifboolexpr{ #1 > 0 'and' #5 == 2 } %a>0 et delta>0 + {% + \saveexpandmode\expandarg + \StrCut{#6}{/}{\xun}{\xdeux} + \restoreexpandmode + \draw[thick,#2] ({-0.375*#3},{0.5*#4}) parabola bend (0,{-0.5*#4}) ({0.375*#3},{0.5*#4}) ; + \draw[#2] ({-0.5*#3},0) node[above right=1pt,inner sep=0pt,font=\scriptsize] {\textcircled{$\strut+$}}; + \draw[#2] ({0.5*#3},0) node[above left=1pt,inner sep=0pt,font=\scriptsize] {\textcircled{$\strut+$}}; + \draw[#2] (0,0) node[below=1pt,inner sep=0pt,font=\scriptsize] {\textcircled{$\strut-$}}; + \filldraw[#2] ({0.2625*#3},0) circle[radius=2pt] node[below right=1pt,inner sep=0pt,font=\scriptsize] {$\strut\xdeux$}; + \filldraw[#2] ({-0.2625*#3},0) circle[radius=2pt] node[below left=1pt,inner sep=0pt,font=\scriptsize] {$\strut\xun$};% + } + {} + \xintifboolexpr{ #1 < 0 'and' #5 == 2 } %a<0 et delta>0 + {% + \saveexpandmode\expandarg + \StrCut{#6}{/}{\xun}{\xdeux} + \restoreexpandmode + \draw[thick,#2] ({-0.375*#3},{-0.5*#4}) parabola bend (0,{0.5*#4}) ({0.375*#3},{-0.5*#4}) ; + \draw[#2] ({-0.5*#3},0) node[below right=1pt,inner sep=0pt,font=\scriptsize] {\textcircled{$\strut-$}}; + \draw[#2] ({0.5*#3},0) node[below left=1pt,inner sep=0pt,font=\scriptsize] {\textcircled{$\strut-$}}; + \draw[#2] (0,0) node[above=1pt,inner sep=0pt,font=\scriptsize] {\textcircled{$\strut+$}}; + \filldraw[#2] ({0.2625*#3},0) circle[radius=2pt] node[above right=1pt,inner sep=0pt,font=\scriptsize] {$\strut\xdeux$}; + \filldraw[#2] ({-0.2625*#3},0) circle[radius=2pt] node[above left=1pt,inner sep=0pt,font=\scriptsize] {$\strut\xun$};% + } + {} + \xintifboolexpr{ #1 > 0 'and' #5 == 1 } %a>0 et delta=0 + {% + \draw[thick,#2] ({-0.375*#3},{0.5*#4}) parabola bend (0,0) ({0.375*#3},{0.5*#4}) ; + \filldraw[#2] (0,0) circle[radius=2pt] node[below=3pt,inner sep=1pt,font=\scriptsize] {$#6$}; + \draw[#2] (0,0) node[above=3pt,inner sep=0pt,font=\scriptsize] {\textcircled{$\strut+$}}; + } + {} + \xintifboolexpr{ #1 < 0 'and' #5 == 1 } %a>0 et delta=0 + {% + \draw[thick,#2] ({-0.375*#3},{-0.5*#4}) parabola bend (0,0) ({0.375*#3},{-0.5*#4}) ; + \filldraw[#2] (0,0) circle[radius=2pt] node[above=3pt,inner sep=0pt,font=\scriptsize] {$#6$}; + \draw[#2] (0,0) node[below=3pt,inner sep=0pt,font=\scriptsize] {\textcircled{$\strut-$}}; + } + {} + \xintifboolexpr{ #1 > 0 'and' #5 == 0 } %a>0 et delta<0 + {% + \draw[thick,#2] ({-0.375*#3},{0.5*#4}) parabola bend (0,{0.075*#4}) ({0.375*#3},{0.5*#4}) ; + \draw[#2] (0,{0.075*#4}) node[above=2pt,inner sep=0pt,font=\scriptsize] {\textcircled{$\strut+$}}; + } + {} + \xintifboolexpr{ #1 < 0 'and' #5 == 0 } %a>0 et delta<0 + {% + \draw[thick,#2] ({-0.375*#3},{-0.5*#4}) parabola bend (0,{-0.075*#4}) ({0.375*#3},{-0.5*#4}) ; + \draw[#2] (0,{-0.075*#4}) node[below=2pt,inner sep=0pt,font=\scriptsize] {\textcircled{$\strut-$}}; + } + {} +} + +\NewDocumentCommand\MiniSchemaSignes{ s O{} D<>{} }{% + \useKVdefault[aidetds] + \setKV[aidetds]{#2} + %simplification des codes + \IfEq{\tdsparam}{da+}{\def\xcode{1}}{} + \IfEq{\tdsparam}{da-}{\def\xcode{-1}}{} + \IfEq{\tdsparam}{pa+d+}{\def\xcode{12}}{} + \IfEq{\tdsparam}{pa-d+}{\def\xcode{-12}}{} + \IfEq{\tdsparam}{pa+d0}{\def\xcode{11}}{} + \IfEq{\tdsparam}{pa-d0}{\def\xcode{-11}}{} + \IfEq{\tdsparam}{pa+d-}{\def\xcode{10}}{} + \IfEq{\tdsparam}{pa-d-}{\def\xcode{-10}}{} + %si commande étoilée := commande autonome + \IfBooleanTF{#1}% + {\begin{tikzpicture}[#3]}{}% + %cadre si booléen true + \ifboolKV[aidetds]{Cadre} + {\draw[lightgray] ({-0.5*\tdslarg},{-0.5*\tdshaut}) rectangle ({0.55*\tdslarg},{0.5*\tdshaut}) ;} + {} + %restriction de la petite fenêtre + \clip ({-0.5*\tdslarg},{-0.5*\tdshaut}) rectangle ({0.55*\tdslarg},{0.5*\tdshaut}) ; + %axe (Ox) + \draw[thick,->] ({-0.5*\tdslarg},0)--({0.55*\tdslarg},0); + %1er degré a+ code = 1 + \ifnum\xcode=1 + \schematdsaff{\tdscouleur}{\tdslarg}{\tdshaut}{\tdsracine} + \fi + %1er degré a- code = -1 + \ifnum\xcode=-1 + \schematdsaff*{\tdscouleur}{\tdslarg}{\tdshaut}{\tdsracine} + \fi + %2d degré a+delta+ code = 12 + \ifnum\xcode=12 + \schematdsparab{1}{\tdscouleur}{\tdslarg}{\tdshaut}{2}[\tdsracine] + \fi + %2d degré a-delta+ code = -12 + \ifnum\xcode=-12 + \schematdsparab{-1}{\tdscouleur}{\tdslarg}{\tdshaut}{2}[\tdsracine] + \fi + %2d degré a+delta0 code = 11 + \ifnum\xcode=11 + \schematdsparab{1}{\tdscouleur}{\tdslarg}{\tdshaut}{1}[\tdsracine] + \fi + %2d degré a-delta0 code = -11 + \ifnum\xcode=-11 + \schematdsparab{-1}{\tdscouleur}{\tdslarg}{\tdshaut}{1}[\tdsracine] + \fi + %2d degré a+delta- code = 10 + \ifnum\xcode=10 + \schematdsparab{1}{\tdscouleur}{\tdslarg}{\tdshaut}{0} + \fi + %2d degré a-delta- code = -10 + \ifnum\xcode=-10 + \schematdsparab{-1}{\tdscouleur}{\tdslarg}{\tdshaut}{0} + \fi + \IfBooleanTF{#1}% + {\end{tikzpicture}}{}% +} + +%pour l'interaction avec tkz-tab +\defKV[aidetdstkz]{% + Echelle=\def\tdstkzscale{#1},% + Decal=\def\tdstkzoffset{#1} +} + +\setKVdefault[aidetdstkz]{% + Echelle=1,% + Decal=1.25 +} + +\NewDocumentCommand\MiniSchemaSignesTkzTab{ o m O{0.85} O{1.5} }{% + %#1 = codeaidetikz + %#2 = numligne + %#3 = échelle + %#4 = décalage + %\shorthandoff{:}\shorthandoff{!} %bizzzzzzzzare + %\NoAutoSpacing + \coordinate (ZZZ) at ($(T2#2)!.5!(T2\the\numexpr#2+1\relax)$) ; + %\shorthandon{:}\shorthandon{!} + \path (ZZZ.east) + (#4,0) pic[right,scale=#3,every node/.style={scale=#3}] {code={\MiniSchemaSignes[#1]}} ; +} + +%%------TVISOLUTION +\defKV[dichoto]{% + NomFct=\def\DHTnomfct{#1},% + va=\def\DHTva{#1},% + vb=\def\DHTvb{#1},% + Precision=\def\DHTprec{#1},% + NomSol=\def\DHTnomsol{#1},% + Stretch=\def\DHTstretch{#1} +} + +\setKVdefault[dichoto]{% + NomFct=f,% + Precision=2,% + NomSol=\alpha,% + Stretch=1.15,% + Balayage=false,% + Calculatrice=false,% + Majuscule=true +} + +\newcommand\SolutionTVI[3][]{% + \useKVdefault[dichoto]% + \setKV[dichoto]{#1}% + \xintdeffloatfunc varfct(x) := #2 ;% + \ifboolKV[dichoto]{Balayage}{\ifboolKV[dichoto]{Majuscule}{P}{p}ar balayage, on obtient }{}% + \ifboolKV[dichoto]{Calculatrice}{\ifboolKV[dichoto]{Majuscule}{P}{p}ar calculatrice, on obtient }{}% + \ensuremath{% + \left\lbrace \begin{tblr}{stretch=\DHTstretch,colsep=1pt,rll}% + {\DHTnomfct}{\left( \num{\DHTva} \right)} &\approx \num[minimum-decimal-digits=\DHTprec]{\xintFloatToDecimal{\xintfloateval{round(varfct(\DHTva),\DHTprec)}}} & \xintifGt{\xintfloateval{varfct(\DHTva)-#3}}{0}{> \num{#3}}{< \num{#3}} \: \\ % + {\DHTnomfct}{\left( \num{\DHTvb} \right)} &\approx \num[minimum-decimal-digits=\DHTprec]{\xintFloatToDecimal{\xintfloateval{round(varfct(\DHTvb),\DHTprec)}}} & \xintifGt{\xintfloateval{varfct(\DHTvb)-#3}}{0}{> \num{#3}}{< \num{#3}} \:% + \end{tblr}% + \right|% + \Rightarrow% + \num{\DHTva} < \DHTnomsol < \num{\DHTvb}% + }% +} + +%%------SIMPLIFRACINES +\DeclareDocumentCommand\SimplificationRacine{ m }{% argument mandataire {calcul ou fraction} + \xdef\calculargument{\xintIrr{\xinteval{#1}}}% + \IfEndWith{\calculargument}{/1}% + {%si c'est un entier ! + \xdef\calculargument{\xintiieval{#1}}% + \xdef\ExtractRacStop{\xintiFloor{\xintfloateval{sqrt(\calculargument)}}}% + \xintFor* ##1 in {\xintSeq{1}{\ExtractRacStop}}\do{% + \xintifboolexpr{ \xintiiRem{\calculargument}{\xintiieval{##1*##1}} == 0}%si le carré divise + {\xdef\ExtractRacID{##1}}% + {}% + }% + \xdef\ExtracReste{\xintiieval{\calculargument/(\ExtractRacID*\ExtractRacID)}}% + \ensuremath{\xintifboolexpr{\ExtractRacID == 1 && \ExtracReste == 1}% + {1}% + { \xintifboolexpr{\ExtractRacID == 1}{}{\num{\xintiieval{\ExtractRacID}}}% + \xintifboolexpr{\ExtracReste == 1}{}{\sqrt{\num{\ExtracReste}}} }}% +% }% + }% + {%on va mettre sous forme a\sqrt(d)/b := buggue avec des millièmes... + \StrBefore{\calculargument}{/}[\numerateur]%on extrait le numérateur + \StrBehind{\calculargument}{/}[\denominateur]%on extrait le dénominateur + \xdef\ExtractRacNNum{\xintiieval{\numerateur*\denominateur}}% + \xdef\ExtractRacStop{\xintiFloor{\xintfloateval{sqrt(\ExtractRacNNum)}}}% + \xintFor* ##1 in {\xintSeq{1}{\ExtractRacStop}}\do{% + \xintifboolexpr{ \xintiiRem{\ExtractRacNNum}{\xintiieval{##1*##1}} == 0}%si le carré divise + {\xdef\ExtractRacID{##1}}% + {} + }% + \xdef\ExtractRacGCD{\xintiiGCD{\ExtractRacID}{\denominateur}}% + \xdef\RacNumSimpl{\xintiieval{\ExtractRacID/\ExtractRacGCD}}%simpl num + \xdef\RacDenomSimpl{\xintiieval{\denominateur/\ExtractRacGCD}}% + \xdef\RacRacSimpl{\xintiieval{\ExtractRacNNum/(\ExtractRacID*\ExtractRacID)}}% + \ensuremath{\frac{% + \xintifboolexpr{\RacNumSimpl == 1 && \RacRacSimpl == 1}% + {1}% + { \xintifboolexpr{\RacNumSimpl == 1}{}{\RacNumSimpl} \xintifboolexpr{\RacRacSimpl == 1}{}{\sqrt{\RacRacSimpl}} }% + }% + { \RacDenomSimpl }}% + }% +} + +%%------DICHOTOMIE +\defKV[SolDichoto]{% + Precision=\xdef\DICHOTOstep{#1},% + Intervalle=\xdef\DICHOTOinterv{#1},% + Variable=\xdef\DICHOTOvar{#1} +} + +\setKVdefault[SolDichoto]{% + Precision=2,% + Variable=x,% + Intervalle={0:10} +} + +\NewDocumentCommand\ResolutionApprochee{ O{} m O{masolution} }{%1=options,2=equation,3=macro + \useKVdefault[SolDichoto]% + %extraction fonction + valeur + \setKV[SolDichoto]{#1}% + \IfSubStr{#2}{=}%on coupe mmb gauche / mmb droit + {\StrCut{#2}{=}{\SolDiFCT}{\SolDiVal}}% + {\xdef\SolDiFCT{#2}\xdef\SolDiVal{0}}% + %création des variables temporaires + \xintdeffloatfunc dichotovarfct(\DICHOTOvar) := \SolDiFCT ;% + \StrCut{\DICHOTOinterv}{:}{\varvala}{\varvalb}% + \xdef\varstep{\fpeval{10**(-\DICHOTOstep-1)}}%un chiffre en plus :-) + %boucles + \whiledo{\xintGt{\xintfloateval{\varvalb-\varvala-\varstep}}{0} = 1}% + {% + \xdef\varvalm{\xintfloateval{(\varvala+\varvalb)*0.5}}% + \xintifboolexpr{\xintGt{\xintfloateval{(dichotovarfct(\varvala)-\SolDiVal)*(dichotovarfct(\varvalm)-\SolDiVal)}}{0}==1}% + {\xdef\varvala{\fpeval{\varvalm}}}% + {\xdef\varvalb{\fpeval{\varvalm}}}% + }% + \xdef\varvalm{\xintfloateval{(\varvala+\varvalb)*0.5}}% + \xdef\vartmpmd{\fpeval{floor(\varvalm,\DICHOTOstep)}}% + \xdef\vartmpme{\fpeval{\vartmpmd+10**(-\DICHOTOstep)}}% + %les variables créées + \expandafter\def\csname#3d\endcsname{\fpeval{\vartmpmd}}% + \expandafter\def\csname#3e\endcsname{\fpeval{\vartmpme}}% + %valeur approchée + \expandafter\def\csname#3a\endcsname{\fpeval{round(\varvalm,\DICHOTOstep)}}% +} + + +\endinput
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