profcollege (17jan21)

git-svn-id: svn://tug.org/texlive/trunk@57456 c570f23f-e606-0410-a88d-b1316a301751

19 files changed, 13744 insertions, 1 deletions

diff --git a/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.pdf b/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.pdf
new file mode 100644
index 00000000000..7bdee3edec6
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.pdf
diff --git a/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.zip b/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.zip
new file mode 100644
index 00000000000..ffd4e8dd82a
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/profcollege/ProfCollege-doc.zip
diff --git a/Master/texmf-dist/doc/latex/profcollege/README b/Master/texmf-dist/doc/latex/profcollege/README
new file mode 100644
index 00000000000..1c43726c9dc
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/profcollege/README
@@ -0,0 +1,13 @@
+Vous êtes un enseignant de mathématiques en collège ?
+profcollege est un package qui vous aidera à utiliser LaTeX au quotidien.
+
+----------------
+
+You are a french mathematics teacher ?
+profcollege is a useful package to daily use of LaTeX.
+
+---------------
+
+Author : Christophe Poulain
+email : chrpoulain@gmail.com
+Licence : Released under the LaTeX Project Public License v1.3c or later, see http://www.latex-project.org/lppl.txtf
diff --git a/Master/texmf-dist/metapost/profcollege/PfC-Calculatrice.mp b/Master/texmf-dist/metapost/profcollege/PfC-Calculatrice.mp
new file mode 100644
index 00000000000..a6326e19258
--- /dev/null
+++ b/Master/texmf-dist/metapost/profcollege/PfC-Calculatrice.mp
@@ -0,0 +1,198 @@
+%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[];
+
+u:=0.5mm;
+
+vardef BlocAffichage=
+  for k=0 upto 34:
+    carre[k]:=(unitsquare scaled u) shifted(u*(k mod 5,5-(k div 5)));
+  endfor;
+enddef;
+
+vardef Affichage(expr decomp)=
+  save $;
+  picture $;
+  drawoptions(withpen pensquare scaled0.1);
+  $=image(%
+      for k=0 upto 34:
+      if (substring(k,k+1) of decomp)="1":
+	fill carre[k];
+      fi;
+    endfor;
+    );
+  drawoptions();
+  $
+enddef;
+
+nblignes:=0;
+
+boolean print;
+print:=false;
+
+color CouleurEcran;
+CouleurEcran=(107/255,148/255,107/255);
+
+boolean Math;
+Math=true;
+
+decahoriz:=0;
+
+vardef Test(expr cptk,cptnt)=
+  pair decalage;
+  if nblignes mod 2=0:
+    decalage:=u*((20-length(cptnt)+cptk)*6,-8*(nblignes-1));
+  else:
+    decalage:=u*(decahoriz,-8*(nblignes-1));
+    decahoriz:=decahoriz+6;
+  fi;
+  if substring(cptk,cptk+1) of cptnt="A":draw Affichage("01110100011000110001111111000110001") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="B":draw Affichage("11110100011000111110100011000111110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="C":draw Affichage("01110100011000010000100001000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="D":draw Affichage("11100100101000110001100011001011100") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="E":draw Affichage("11111100001000011111100001000011111") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="F":draw Affichage("11111100001000011111100001000010000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="G":draw Affichage("01110100011000010111100011000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="H":draw Affichage("10001100011000111111100011000110001") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="I":draw Affichage("01110001000010000100001000010001110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="J":draw Affichage("00111000100001000010000101001001100") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="K":draw Affichage("10001100101010011000101001001010001") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="L":draw Affichage("10000100001000010000100001000011111") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="M":draw Affichage("10001110111010110101100011000110001") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="N":draw Affichage("10001100011100110101100111000110001") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="O":draw Affichage("01110100011000110001100011000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="P":draw Affichage("11110100011000111110100001000010000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="Q":draw Affichage("01110100011000110001101011001001101") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="R":draw Affichage("11110100011000111110101001001010001") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="S":draw Affichage("01111100001000001110000010000111110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="T":draw Affichage("11111001000010000100001000010000100") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="U":draw Affichage("10001100011000110001100011000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="V":draw Affichage("10001100011000110001100010101000100") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="W":draw Affichage("10101101011010110101101011010101010") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="X":draw Affichage("10001100010101000100010101000110001") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="Y":draw Affichage("10001100011000101010001000010000100") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="Z":draw Affichage("11111000010001000100010001000011111") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="a":draw Affichage("00000000000111100001011111000101111") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="b":draw Affichage("10000100001011011001100011000111110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="c":draw Affichage("00000000000111010000100001000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="d":draw Affichage("00001000010110110011100011000101111") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="e":if Math:
+	draw Affichage("00000000000000000001101000100010100") shifted(decalage);
+	decalage:=u*(decahoriz-1,-8*(nblignes-1));
+	draw Affichage("00000000001001010101101011010110010")  shifted(decalage);
+	decahoriz:=decahoriz+6;
+      else:
+	draw Affichage("00000000000111010001111111000001110") shifted(decalage);
+      fi;
+    elseif substring(cptk,cptk+1) of cptnt="@":draw Affichage("00010001000111010001111111000001110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="f":draw Affichage("00110010010100011100010000100001000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="g":draw Affichage("00000011111000110001011110000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="h":draw Affichage("10000100001011011001100011000110001") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="i":draw Affichage("00100000000110000100001000010001110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="j":if Math=true:
+	draw Affichage("00011000011110100001000000000000000") shifted(decalage);
+      else:
+	draw Affichage("00010000000011000010000101001001100") shifted(decalage);
+      fi;
+    elseif substring(cptk,cptk+1) of cptnt="k":if Math=true:
+	draw Affichage("11100001000100011100000000000000000") shifted(decalage);
+      else:
+	draw Affichage("10000100001001010100110001010010010") shifted(decalage);
+      fi;
+    elseif substring(cptk,cptk+1) of cptnt="l":if Math=true:
+	draw Affichage("11100010000010011100000000000000000") shifted(decalage);
+      else:
+	draw Affichage("01100001000010000100001000010001110") shifted(decalage);
+      fi;
+    elseif substring(cptk,cptk+1) of cptnt="m":draw Affichage("00000000001101010101101011000110001") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="n":draw Affichage("00000000001011011001100011000110001") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="o":draw Affichage("00000000000111010001100011000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="p":draw Affichage("00000000001111010001111101000010000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="q":if Math=true:
+	draw Affichage("00000000001111101010010100101010001") shifted(decalage);
+      else:
+	draw Affichage("00000000000110110011011110000100001") shifted(decalage);
+      fi;
+    elseif substring(cptk,cptk+1) of cptnt="r":draw Affichage("00000000001011011001100001000010000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="s":draw Affichage("00000000000111010000011100000111110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="t":draw Affichage("01000010001110001000010000100100110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="u":draw Affichage("00000000001000110001100011001101101") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="v":if Math=true:
+	draw Affichage("00111001000010000100101000110000100") shifted(decalage);	
+      else:
+	draw Affichage("00000000001000110001100010111000100") shifted(decalage);
+      fi;
+    elseif substring(cptk,cptk+1) of cptnt="w":draw Affichage("00000000001010110101101011010101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="x":draw Affichage("00000000001000101010001000101010001") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="y":draw Affichage("00000000001000110001011110000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="z":draw Affichage("00000000001111100010001000100011111") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="0":draw Affichage("01110100011001110101110011000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="1":draw Affichage("00100011000010000100001000010001110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="2":draw Affichage("01110100010000100010001000100011111") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="3":draw Affichage("11111000100010000010000011000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="4":draw Affichage("00010001100101010010111110001000010") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="5":draw Affichage("11111100001111000001000011000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="6":draw Affichage("00110010001000011110100011000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="7":draw Affichage("11111000010001000100010000100001000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="8":draw Affichage("01110100011000101110100011000101110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="9":draw Affichage("01110100011000101111000010001001100") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="!":draw Affichage("00100001000010000100000000000000100") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="'":draw Affichage("01100001000100000000000000000000000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="(":draw Affichage("00010001000100001000010000010000010") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt=")":draw Affichage("01000001000001000010000100010001000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="*":draw Affichage("00000001001010101110101010010000000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="+":draw Affichage("00000001000010011111001000010000000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt=",":draw Affichage("00000000000000000000011000010001000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="-":draw Affichage("00000000000000011111000000000000000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt=".":draw Affichage("00000000000000000000000000110001100") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="/":draw Affichage("00000000010001000100010001000000000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt=":":if Math=true:
+	draw Affichage("00000000000000000000000000000000000") shifted(decalage);
+      else:
+	draw Affichage("00000011000110000000011000110000000") shifted(decalage);
+      fi;
+    elseif substring(cptk,cptk+1) of cptnt=";":if Math=true:
+	  draw Affichage("00000001000000011111000000010000000") shifted(decalage);
+      else:
+	draw Affichage("00000011000110000000011000010001000") shifted(decalage);
+      fi;
+    elseif substring(cptk,cptk+1) of cptnt="<":draw Affichage("00010001000100010000010000010000010") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="=":draw Affichage("00000000001111100000111110000000000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt=">":draw Affichage("10000010000010000010001000100010000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="?":draw Affichage("01110100010000100010001000000000100") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="[":draw Affichage("01110010000100001000010000100001110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="]":draw Affichage("01110000100001000010000100001001110") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="`":draw Affichage("01000001000001000000000000000000000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="|":draw Affichage("00100001000010000100001000010000100") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt=" ":draw Affichage("00000100010101000100010101000100000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="&":draw Affichage("00000100001100011100110001000000000") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="$":draw Affichage("00000000000000100001000010000111111") shifted(decalage);
+    elseif substring(cptk,cptk+1) of cptnt="^":draw Affichage("00100010101000100000000000000000000") shifted(decalage);
+    fi;
+enddef;
+
+vardef LCD(text nt)(text rep)=
+  decahoriz:=0;
+  nblignes:=nblignes+1;
+  path Ecran;
+  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;
+  for k=0 upto length(nt)-1:
+    BlocAffichage;
+    Test(k,nt);
+  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;
+  draw Ecran withcolor if print=true:0.8white else:CouleurEcran fi;
+  for k=0 upto length(rep)-1:
+    BlocAffichage;
+    Test(k,rep);
+  endfor;
+enddef;
+
+endinput;
diff --git a/Master/texmf-dist/metapost/profcollege/PfC-Constantes.mp b/Master/texmf-dist/metapost/profcollege/PfC-Constantes.mp
new file mode 100644
index 00000000000..b97bd8a4c0a
--- /dev/null
+++ b/Master/texmf-dist/metapost/profcollege/PfC-Constantes.mp
@@ -0,0 +1,23 @@
+%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;
+pi:=3.141592654;
+e:=2.718281828;
+c:=57.29578; % conversion d'un radian en degres
+color rouge,vert,bleu,jaune,noir,blanc,orange,rose,violet,ciel,cielfonce,orangevif,gris;
+rouge=(1,0,0);
+bleu=(0,0,1);
+noir=(0,0,0);
+blanc=(1,1,1);
+orange=(1,0.5,0);
+violet=blanc-vert;
+rose=(1,0.7,0.7);
+cielfonce=0.9*(0.25,1,1);
+ciel=bleu+vert;
+orangevif=(1,0.25,0.1);
+vert=(0,1,0);
+jaune=rouge+vert;
+gris=0.8*white;
diff --git a/Master/texmf-dist/metapost/profcollege/PfC-Geometrie.mp b/Master/texmf-dist/metapost/profcollege/PfC-Geometrie.mp
new file mode 100644
index 00000000000..222df574193
--- /dev/null
+++ b/Master/texmf-dist/metapost/profcollege/PfC-Geometrie.mp
@@ -0,0 +1,1206 @@
+%===============================================
+%% PfC-Geometrie
+%% christophe.poulain@melusine.eu.org
+%%===============================================
+%------------------------------------------------
+% Appel fichier
+%------------------------------------------------
+%input PfC-Constantes;
+%------------------------------------------------
+% La figure (debut et fin) JMS/CP
+%------------------------------------------------
+path feuillet;
+numeric _tfig,_nfig;
+_tfig:=5cm;
+_nfig:=0;
+pair coinbg,coinbd,coinhd,coinhg;
+
+string typetrace;
+typetrace="normal";
+
+def feuille(expr xa,ya,xb,yb) =
+  feuillet := (xa,ya)--(xa,yb)--(xb,yb)--(xb,ya)--cycle;
+  coinbg := (xa,ya);
+  coinbd := (xb,ya);
+  coinhd := (xb,yb);
+  coinhg := (xa,yb);
+  %modifie le 29.09.04
+  z.so=(xpart(coinbg/1cm),ypart(coinbg/1cm));
+  z.ne=(xpart(coinhd/1cm),ypart(coinhd/1cm));
+  %fin modification
+  extra_endfig := "clip currentpicture to feuillet;" & extra_endfig;
+enddef;
+
+def Figure(expr xa,ya,xb,yb) =
+  feuille(xa,ya,xb,yb);
+  _tfig:= if (xb-xa)>(yb-ya): xb-xa else: yb-ya fi;
+  _tfig:=2*_tfig;
+enddef;
+
+%%-----------------------------------------------
+%% Les marques (JMS)
+%%-----------------------------------------------
+string marque_p;
+marque_p := "non";
+marque_r := 20;
+marque_a := 20;
+marque_s := 5;
+marque_ang := 10;
+m_c := 10 ;%Pour la croix du marquage des points
+
+%------------------------------------------------
+% Les tables
+%------------------------------------------------
+numeric _tn;
+_tn:=0;
+pair _t[];
+color _T[];
+
+%%-----------------------------------------------
+%% Procedures d'affichage
+%%-----------------------------------------------
+def MarquePoint(expr p)=
+  if typetrace="3D":
+    %JMS
+    if marque_p = "plein":
+      fill fullcircle scaled (marque_r/5) shifted Projette(p);
+    elseif marque_p = "creux":
+      fill fullcircle scaled (marque_r/5) shifted (Projette(p)) withcolor white;
+      draw fullcircle scaled (marque_r/5) shifted (Projette(p));
+        %fin JMS
+    elseif marque_p = "croix":
+      draw (Projette(p) shifted (-u/10,u/10))--(Projette(p) shifted (u/10,-u/10));
+      draw (Projette(p) shifted (-u/10,-u/10))--(Projette(p) shifted (u/10,u/10));
+    elseif marque_p = "tiretv":
+      draw (Projette(p) shifted (0,u/10))--(Projette(p) shifted(0,-u/10));
+    elseif marque_p = "tireth":
+      draw (Projette(p) shifted (u/10,0))--(Projette(p) shifted(-u/10,0));
+    fi;
+  else:
+    if marque_p = "plein":
+      fill fullcircle scaled (marque_r/5) shifted p;
+    elseif marque_p = "creux":
+      fill fullcircle scaled (marque_r/5) shifted p withcolor white;
+      draw fullcircle scaled (marque_r/5) shifted p;
+    elseif marque_p = "croix":
+      draw (p shifted (-u/m_c,u/m_c))--(p shifted (u/m_c,-u/m_c));
+      draw (p shifted (-u/m_c,-u/m_c))--(p shifted (u/m_c,u/m_c));
+    elseif marque_p = "tiretv":
+      draw (p shifted (0,u/10))--(p shifted(0,-u/10));
+    elseif marque_p = "tireth":
+      draw (p shifted (u/10,0))--(p shifted(-u/10,0));
+    fi;
+  fi;
+enddef;
+
+vardef pointe(text t) =
+  for p_ = t: if (pair p_) or (color p_): MarquePoint(p_); fi endfor;
+enddef;
+
+%------------------------------------------------
+% Points
+%------------------------------------------------
+%JMS
+vardef iso(text t) =
+  save s,n; numeric n;
+  if typetrace="3D":
+    color s; s := (0,0,0) ; n := 0;
+    for p_ = t: s := s + p_; n := n + 1 ; endfor;
+  else:
+    pair s; s := (0,0) ; n := 0;
+    for p_ = t: s := s + p_; n := n + 1 ; endfor;
+  fi;
+  if n>0: (1/n)*s fi
+enddef;
+
+vardef milieu(expr AA,BB)=
+  save $;
+  pair $;
+  if typetrace="mainlevee":
+    $=point((length segment(AA,BB))*(1/2+(-1+uniformdeviate(2))/10)) of segment(AA,BB)
+  else:
+    $=iso(AA,BB)
+  fi;
+  $
+enddef;
+
+vardef CentreCercleI(expr aa,bb,cc)=
+  save $,a,c;
+  pair $;
+  numeric a,c;
+  a=(angle(aa-cc)-angle(bb-cc))/2;
+  c=(angle(cc-bb)-angle(aa-bb))/2;
+  ($-cc) rotated a shifted cc=whatever[aa,cc];
+  ($-bb) rotated c shifted bb=whatever[bb,cc];
+  $
+enddef;
+
+%------------------------------------------------
+% Cercles
+%------------------------------------------------
+%Cercle connaissant le centre A et le rayon q
+vardef cercle(expr aa, q)=fullcircle scaled (2*q) shifted aa
+enddef;
+%Cercle de centre A et passant par B
+vardef cerclepoint(expr aa,bb)=fullcircle scaled (2*abs(aa-bb)) shifted aa
+enddef;
+%Cercle connaissant le diametre [AB]
+vardef cercledia(expr aa,bb)=cercles(iso(aa,bb),bb)
+  %fullcircle scaled (2*abs(1/2[aa,bb]-bb)) shifted (1/2[aa,bb])
+enddef;
+%Cercles complets
+vardef cercles(text t)=
+  save Cer;
+  save n;
+  n:=0;
+  for p_=t:
+    if pair p_:
+      n:=n+1;
+      _t[n]:=p_;
+    fi
+    if numeric p_:
+      rayon:=p_;
+    fi;
+    if color p_:
+      n:=n+1;
+      _T[n]:=p_;
+    fi;
+  endfor;
+  if typetrace="3D":%centre aa passant par bb dans le plan (ccddee) généralement aa=cc
+    path Cer;
+    color ptcer[];
+    for k=0 step 5 until 360 :
+      ptcer[k div 5]-_T[1]=Distance(_T[1],_T[2])*((_T[4]-_T[3])*cosd(k)/Distance(_T[3],_T[4])+(_T[5]-_T[3])*sind(k)/Distance(_T[3],_T[5]));
+    endfor;
+    Cer=Projette(ptcer0)
+      for k=0 step 5 until 360 :
+      ..Projette(ptcer[k div 5])
+    endfor
+    ..cycle;
+  else:
+    path Cer;
+    if n=1 : Cer=fullcircle scaled (2*rayon) shifted _t[1];
+    elseif n=2 : Cer=fullcircle scaled (2*abs(_t[1]-_t[2])) shifted _t[1];
+    elseif n=3 : Cer=cercles(CentreCercleC(_t[1],_t[2],_t[3]),_t[1]);
+    fi
+  fi
+  Cer
+enddef;
+
+%Point particulier sur le cercle
+vardef pointarc(expr cercla,angle)=
+  point(arctime((angle/360)*arclength cercla) of cercla) of cercla
+enddef;
+
+%Arc de cercle AB de centre 0(dans le sens direct) : les points A et B doivent etre sur le cercle.
+vardef arccercle(expr aa,bb,oo)=
+  path tempo;
+  path arc;
+  tempo=fullcircle scaled (2*abs(aa-oo)) shifted oo;
+  if (angle(aa-oo)=0) or (angle(aa-oo)>0) :
+    if (angle(bb-oo)=0) or (angle(bb-oo)>0):
+      if (angle(aa-oo)<angle(bb-oo)):
+	arc=subpath(angle(aa-oo)*(length tempo)/360,angle(bb-oo)*(length tempo)/360) of tempo;
+      else:
+	arc=subpath(angle(aa-oo)*(length tempo)/360,(length tempo)+angle(bb-oo)*(length tempo)/360) of tempo;
+      fi;
+    elseif (angle(bb-oo)<0):
+      arc=subpath(angle(aa-oo)*(length tempo)/360,(length tempo)+angle(bb-oo)*(length tempo)/360) of tempo;
+    fi;
+  elseif (angle(aa-oo)<0):
+    if (angle(bb-oo)=0) or (angle(bb-oo)>0):
+      arc=subpath(length tempo+angle(aa-oo)*(length tempo)/360,length tempo+angle(bb-oo)*(length tempo)/360) of tempo;
+    elseif (angle(bb-oo)<0):
+      if (angle(aa-oo)=angle(bb-oo)) or (angle(aa-oo)<angle(bb-oo)):
+	arc=subpath((length tempo)+angle(aa-oo)*(length tempo)/360,(length tempo)+angle(bb-oo)*(length tempo)/360) of tempo;
+      else:
+	arc=subpath((length tempo)+angle(aa-oo)*(length tempo)/360,2*(length tempo)+angle(bb-oo)*(length tempo)/360) of tempo;
+      fi;
+    fi;
+  fi;
+  arc
+enddef;
+
+vardef coupdecompas(expr ab,ac,ad)=arccercle(pointarc(cercles(ab,ac),angle(ac-ab)-ad),pointarc(cercles(ab,ac),angle(ac-ab)+ad),ab)
+enddef;
+
+%------------------------------------------------
+% Procedures de codage
+%------------------------------------------------
+%Codage de l'angle droit de sommet B
+vardef codeperp(expr aa,bb,cc,m)=%normalement m=5
+  save codep;
+  path codep;
+  if typetrace="3D":
+    codep=(Projette(bb)+m*unitvector(Projette(aa)-Projette(bb)))--(Projette(bb)+m*unitvector(Projette(aa)-Projette(bb))+m*unitvector(Projette(cc)-Projette(bb)))--(Projette(bb)+m*unitvector(Projette(cc)-Projette(bb)));
+  else:
+    codep=(bb+m*unitvector(aa-bb))--(bb+m*unitvector(aa-bb)+m*unitvector(cc-bb))--(bb+m*unitvector(cc-bb));
+  fi;
+  codep
+enddef;
+
+%Codage d'un milieu
+vardef codemil(expr AA,BB, n) =%extremites-angle de codage
+  save $,a,b,c,d;
+  path $;
+  pair a,b,c,d;
+  a=1/2[AA,BB];
+  b=(a+marque_s*unitvector(BB-AA))-(a-marque_s*unitvector(BB-AA));
+  c=b rotated n shifted a;
+  d=2[c,a];
+  $=c--d;
+  $
+enddef;
+%Codage de deux segments egaux
+vardef codesegments(expr aa,bb,cc,dd,n)=%extremites des segments(4)-type de codage
+  save $,v,w;
+  picture $;
+  pair AA,BB,CC,DD;
+  $=image(
+    if typetrace="3D":
+      AA=Projette(aa);      BB=Projette(bb);      CC=Projette(cc);      DD=Projette(dd);
+    else:
+      AA=aa;BB=bb;CC=cc;DD=dd;
+    fi;
+    if n=5 :
+      draw fullcircle scaled 0.1cm shifted (1/2[AA,BB]);
+      draw fullcircle scaled 0.1cm shifted (1/2[CC,DD]);
+    elseif n=4 :
+      pair v,w;
+      v=1/2[AA,BB];
+      w=1/2[CC,DD];
+      draw codemil(AA,BB,60);
+      draw codemil(AA,BB,120);
+      draw codemil(CC,DD,60);
+      draw codemil(CC,DD,120);
+    elseif n=3 :
+      draw codemil(AA,BB,60);
+      draw codemil(AA,BB,60) shifted (2*unitvector(AA-BB));
+      draw codemil(AA,BB,60) shifted (2*unitvector(BB-AA));
+      draw codemil(CC,DD,60);
+      draw codemil(CC,DD,60) shifted (2*unitvector(CC-DD));
+      draw codemil(CC,DD,60) shifted (2*unitvector(DD-CC));
+    elseif n=2 :
+      draw codemil(AA,BB,60) shifted unitvector(AA-BB);
+      draw codemil(AA,BB,60) shifted unitvector(BB-AA);
+      draw codemil(CC,DD,60) shifted unitvector(CC-DD);
+      draw codemil(CC,DD,60) shifted unitvector(DD-CC);
+    elseif n=1 :
+      draw codemil(AA,BB,60);
+      draw codemil(CC,DD,60);
+    fi;
+    );
+    $
+  enddef;
+
+%Codage de plusieurs segments de meme longueur
+  vardef Codelongueur(text t)=
+  save result;
+  picture result;
+  pair tt[];
+  k:=0;
+  for p_=t:
+    if pair p_:
+      k:=k+1;
+      tt[k]=p_;
+    elseif color p_:
+      k:=k+1;
+      tt[k]=Projette(p_);
+    elseif numeric p_:
+      co:=p_;
+    fi;
+  endfor;
+  result=image(
+    if co=5:
+      for j=1 upto (k div 2):
+	draw fullcircle scaled 0.1cm shifted (1/2[tt[2*j-1],tt[2*j]]);
+      endfor;
+    elseif co=4:
+      for j=1 upto (k div 2):
+	draw codemil(tt[2*j-1],tt[2*j],60);
+	draw codemil(tt[2*j-1],tt[2*j],120);
+      endfor;
+    elseif co=3:
+      for j=1 upto (k div 2):
+	draw codemil(tt[2*j-1],tt[2*j],60);
+	draw codemil(tt[2*j-1],tt[2*j],60) shifted (2*unitvector(tt[2*j-1]-tt[2*j]));
+	draw codemil(tt[2*j-1],tt[2*j],60) shifted (2*unitvector(tt[2*j]-tt[2*j-1]));
+      endfor;
+    elseif co=2:
+      for j=1 upto (k div 2):
+	draw codemil(tt[2*j-1],tt[2*j],60) shifted unitvector(tt[2*j-1]-tt[2*j]);
+	draw codemil(tt[2*j-1],tt[2*j],60) shifted unitvector(tt[2*j]-tt[2*j-1]);
+      endfor;
+    elseif co=1:
+      for j=1 upto (k div 2):
+	draw codemil(tt[2*j-1],tt[2*j],60);
+      endfor;
+    fi;
+    );
+  result
+enddef;
+
+%Codage de l'angle abc non oriente (mais donne dans le sens direct) n fois avec des mesures differentes
+vardef codeangle@#(expr aa,bb,cc,nb,nom)=
+  save s,p,$;
+  path p;
+  picture $;
+  $=image(
+    trace marqueangle(aa,bb,cc,nb);
+    label.@#(nom,w);
+    );
+  $
+enddef;
+
+vardef Marqueangle(expr aa,bb,mark)=%codage d'un angle forme par les demi-droites aa et bb dans le sens direct avec la marque mark
+  save $;
+  picture $;
+  path conf,rr;
+  pair w,tangent;
+  numeric t,tt;
+  conf=fullcircle scaled (2*marque_a) shifted (aa intersectionpoint bb);
+  numeric te;
+  te=angle((conf intersectionpoint aa)-(aa intersectionpoint bb));
+  rr=(conf intersectionpoint aa){dir(90+angle((conf intersectionpoint aa)-(aa intersectionpoint bb)))}..(conf intersectionpoint bb);
+  t=length rr/2;
+  w=point(t) of rr;
+  tangent=unitvector(direction t of rr);
+  $=image(
+    trace rr;
+    if mark=1:
+      trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90);
+    elseif mark=2:
+      trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90) shifted tangent;
+      trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90) shifted(-tangent);
+    elseif mark=3:
+      trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90);
+      trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90) shifted(1.5*tangent);
+      trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,90) shifted(-1.5*tangent);
+    elseif mark=4:
+      trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,45);
+      trace rotation((w shifted(5*tangent))--(w shifted(-5*tangent)),w,-45);
+    fi;
+    );
+  $
+enddef;
+
+vardef marqueangle(expr aa,bb,cc,mark)=%codage d'un angle de sommet bb dans le sens direct par la marque mark.
+  save $;
+  picture $;
+  path conf,rr;
+  pair w,tangent;
+  numeric t;
+  if typetrace="mainlevee":
+    conf=fullcircle scaled (2*marque_a) shifted bb;
+    rr=(conf intersectionpoint demidroite(bb,aa)){dir(90+angle(aa-bb))}..(conf intersectionpoint demidroite(bb,cc));
+    w=rr intersectionpoint droite(bb,CentreCercleI(aa,bb,cc));
+    t=length rr/2;
+    tangent=unitvector(direction t of rr);
+    $=image(
+	trace rr;
+      if mark=1:
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90);
+      elseif mark=2:
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90) shifted tangent;
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90) shifted(-tangent);
+      elseif mark=3:
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90);
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90) shifted(1.marque_s*tangent);
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90) shifted(-1.marque_s*tangent);
+      elseif mark=4:
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,45);
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,-45);
+      fi;
+      );
+  else:
+    rr=arccercle(bb+marque_a*unitvector(aa-bb),bb+marque_a*unitvector(cc-bb),bb);
+    w=rr intersectionpoint droite(bb,CentreCercleI(aa,bb,cc));
+    t=length rr/2;
+    tangent=unitvector(direction t of rr);
+    $=image(
+	if mark=5:
+	drawarrow rr;
+      else:
+	trace rr;
+      fi;
+      if mark=1:
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90);
+      elseif mark=2:
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90) shifted tangent;
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90) shifted(-tangent);
+      elseif mark=3:
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90);
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90) shifted(1.marque_s*tangent);
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,90) shifted(-1.marque_s*tangent);
+      elseif mark=4:
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,45);
+	trace rotation((w shifted(marque_s*tangent))--(w shifted(-marque_s*tangent)),w,-45);
+      fi;
+      );
+  fi;
+  $
+enddef;
+
+vardef coloreangle(expr aa,bb,cc)=arccercle(bb+marque_a*unitvector(aa-bb),bb+marque_a*unitvector(cc-bb),bb)--bb--cycle
+enddef;
+
+vardef Codeangle(expr aa,bb,cc,nb,nom)=
+  save s,p,$;
+  path p;
+  picture $;
+  $=image(
+    trace marqueangle(aa,bb,cc,nb);
+    label(nom,w shifted(marque_ang*unitvector(w-bb)));
+    );
+  $
+enddef;
+
+vardef marquesegment(expr aa,bb)=
+  save tr;
+  picture tr;
+  if typetrace="3D":
+    tr=image(%
+	typetrace:="normal";
+      trace rotation(segment(Projette(aa)-marque_s*unitvector(Projette(bb)-Projette(aa)),Projette(aa)+marque_s*unitvector(Projette(bb)-Projette(aa))),Projette(aa),90);
+      trace rotation(segment(Projette(bb)-marque_s*unitvector(Projette(bb)-Projette(aa)),Projette(bb)+marque_s*unitvector(Projette(bb)-Projette(aa))),Projette(bb),90);
+      typetrace:="3D";
+      );
+  else:
+    tr=image(%
+	trace rotation(segment(aa-marque_s*unitvector(bb-aa),aa+marque_s*unitvector(bb-aa)),aa,90);
+      trace rotation(segment(bb-marque_s*unitvector(bb-aa),bb+marque_s*unitvector(bb-aa)),bb,90);
+      );
+  fi;
+  tr
+enddef;
+
+vardef marquedemidroite(expr aa,bb)=
+  save tr;
+  picture tr;
+  tr=image(
+    trace rotation(segment(aa-marque_s*unitvector(bb-aa),aa+marque_s*unitvector(bb-aa)),aa,90);
+    );
+  tr
+enddef;
+
+%------------------------------------------------
+% Transformations
+%------------------------------------------------
+vardef projection(expr m,a,b) =
+  save h; pair h;
+  h - m = whatever * (b-a) rotated 90;
+  h = whatever [a,b];
+  if typetrace="mainlevee":
+    h:=h shifted((-2+uniformdeviate(4))*unitvector(a-b))
+  fi;
+  h
+enddef;
+  
+vardef homothetie(expr objet,CTR,rapport)=
+  ((objet shifted (-CTR)) scaled rapport) shifted CTR
+enddef;
+
+vardef rotation(expr p,c,a)=
+  p rotatedaround(c,a)
+enddef;
+
+vardef symetrie(expr x)(text t)=
+  save n;
+  n:=0;
+  for p_=t: if pair p_:
+      n:=n+1;
+      _t[n]:=p_;
+    elseif color p_:
+      n:=n+1;
+      _T[n]:=p_;
+    fi;
+  endfor;
+  if n=1:
+    if typetrace="3D":
+      2[x,_T[1]]
+    else:
+      rotation(x,_t[1],180)
+    fi
+  elseif n=2:
+    x reflectedabout(_t[1],_t[2])
+  elseif n=3:%Par rapport a un plan
+    2[x,ProjectionsurPlan(x,_T[1],_T[2],_T[3])]
+  fi
+enddef;
+
+%------------------------------------------------
+% Droites
+%------------------------------------------------
+vardef segment(expr aa,bb)=
+  save Seg;
+  path Seg;
+  if typetrace="mainlevee":
+    Seg=aa{dir(angle(bb-aa)+5)}..bb{dir(angle(bb-aa)+5)}
+  elseif typetrace="3D":
+    Seg=Projette(aa)--Projette(bb)
+  else:
+    Seg=aa--bb
+  fi;
+  Seg
+enddef;
+
+vardef droite(expr AA,BB)=
+  save Dro;
+  path Dro;
+  if typetrace="mainlevee":
+    Dro=(_tfig/abs(AA-BB))[BB,AA]{dir(angle(BB-AA)+10)}..segment(AA,BB)..(_tfig/abs(AA-BB))[AA,BB]{dir(angle(BB-AA)+10)}
+  elseif typetrace="3D":
+    Dro=(_tfig/abs(Projette(AA)-Projette(BB)))[Projette(BB),Projette(AA)]--(_tfig/abs(Projette(AA)-Projette(BB)))[Projette(AA),Projette(BB)]
+  else:
+    Dro=(_tfig/abs(AA-BB))[BB,AA]--(_tfig/abs(AA-BB))[AA,BB]
+  fi;
+  Dro
+enddef;
+vardef demidroite(expr AA,BB)=
+  save Dem;
+  path Dem;
+  if typetrace="mainlevee":
+    Dem=segment(AA,BB)..(_tfig/abs(AA-BB))[AA,BB]{dir(angle(BB-AA)+10)}
+  elseif typetrace="3D":
+    Dem=Projette(AA)--(_tfig/abs(Projette(AA)-Projette(BB)))[Projette(AA),Projette(BB)]
+  else:
+    Dem=AA--(_tfig/abs(AA-BB))[AA,BB]
+  fi;
+  Dem
+enddef;
+
+vardef bissectrice(expr AA,BB,CC)=
+  save $;
+  path $;
+  if typetrace="mainlevee":
+    $=rotation(demidroite(BB,CentreCercleI(AA,BB,CC)),BB,-5+uniformdeviate(10))
+  else:
+    $=demidroite(BB,CentreCercleI(AA,BB,CC))
+  fi;
+  $
+enddef;
+
+vardef mediatrice(expr AA,BB)=droite(iso(AA,BB),rotation(BB,iso(AA,BB),90))
+enddef;
+%main levee : passer par la perpendiculaire passant par le milieu.
+
+vardef perpendiculaire(expr AA,BB,II)=droite(iso(AA,BB),rotation(BB,iso(AA,BB),90)) shifted (II-iso(AA,BB))
+enddef;
+
+vardef parallele(expr AA,BB,II)=droite(AA,BB) shifted (II-(projection(II,AA,BB)))
+enddef;
+
+%%%%%%%%%%
+%Polygone/Ligne brisée
+%%%%%%%%%
+vardef polygone(text t)=
+  pair aaa[];
+  j:=0;
+  for p_=t: if pair p_:
+      j:=j+1;
+      aaa[j]=p_;
+    elseif color p_:
+      j:=j+1;
+      aaa[j]=Projette(p_);
+    fi;
+  endfor;
+  aaa[j+1]:=aaa[1];
+  save $;
+  path $;
+  $=aaa1--
+    for k=2 upto j:
+    aaa[k]--
+  endfor
+  cycle;
+  $
+enddef;
+
+vardef chemin(text t)=
+  pair aaa[];
+  j:=0;
+  for p_=t: if pair p_:
+      j:=j+1;
+      aaa[j]=p_;
+    elseif color p_:
+      j:=j+1;
+      aaa[j]=Projette(p_);
+    fi;
+  endfor;
+  if typetrace="mainlevee":
+    save $;
+    picture $;
+    $=image(
+      for k=1 upto (j-1):
+	trace segment(aaa[k],aaa[k+1]);
+      endfor;
+      );
+  else:
+    save $;
+    path $;
+    $=aaa1
+    for k=2 upto j:
+      --aaa[k]
+    endfor;
+  fi;
+  $
+enddef;
+
+%------------------------------------------------
+%Sucres
+%------------------------------------------------
+vardef hachurage(expr chemin, angle, ecart, trace)=
+  save $;
+  picture $;
+  path support;
+  support=((u*(-37,0))--(u*(37,0))) rotated angle;
+  if trace=1:
+    drawoptions(dashed evenly);
+  elseif trace=2:
+    drawoptions(dashed dashpattern(on12bp off6bp on3bp off6bp));
+  elseif trace=3:
+    drawoptions(dashed withdots);
+  fi;
+  $ = image(
+    for j=-200 upto 200:
+      if ((support shifted (ecart*j*(u,0))) intersectiontimes chemin)<>(-1,-1):
+	draw support shifted (ecart*j*(u,0));
+      fi
+    endfor;
+    );
+  clip $ to chemin;
+  drawoptions();
+  $
+enddef;
+%fleche pour coter un segment [AB] (Jacques Marot)
+vardef cotation(expr aa,bb,ecart,decalage,cote)=
+  pair m[] ;
+  save $;
+  picture $;
+  m3=unitvector(bb-aa) rotated 90;
+  m1=aa+ecart*m3;
+  m2=bb+ecart*m3;
+  $=image(
+    pickup pencircle scaled 0.2bp;
+    drawdblarrow m1--m2 ;
+    draw aa--m1 dashed evenly;
+    draw bb--m2 dashed evenly;
+    label(cote rotated angle(m2-m1),(m1+m2)/2+decalage*m3);
+    );
+  $
+enddef;
+
+vardef appelation(expr aa,bb,decalage,cote)=
+  save $;
+  pair m[],AA,BB;
+  if color aa:
+    AA=Projette(aa);
+  else:
+    AA=aa;
+  fi;
+  if color bb:
+    BB=Projette(bb);
+  else:
+    BB=bb;
+  fi;
+  m3=unitvector(BB-AA) rotated 90;
+  picture $;
+  $=image(
+    label(cote rotated angle(BB-AA),(BB+AA)/2+decalage*m3);
+    );
+  $
+enddef;
+
+vardef cotationmil(expr aa,bb,ecart,decalage,cote)= %Christophe
+  pair m[],AA,BB;
+  save $;
+  picture cot;
+   if color aa:
+    AA=Projette(aa)
+  else:
+    AA=aa
+  fi;
+  if color bb:
+    BB=Projette(bb)
+  else:
+    BB=bb
+  fi;
+  m3=unitvector(BB-AA) rotated 90;
+  m1=AA+ecart*m3;
+  m2=BB+ecart*m3;
+  cot=image(
+    pickup pencircle scaled 0.2bp;
+    drawarrow (1/2[m1,m2]+decalage*unitvector(m1-m2))--m1;
+    drawarrow (1/2[m1,m2]-decalage*unitvector(m1-m2))--m2;
+    draw AA--m1 dashed evenly;
+    draw BB--m2 dashed evenly;
+    label(cote rotated angle(m2-m1),(m1+m2)/2);
+    );
+  cot
+enddef;
+
+%%%%%%%%%%
+%francisation
+%%%%%%%%%
+def trace expr o =
+    if path o: draw o else: draw o fi
+enddef;
+def remplis expr o =
+    if path o: fill o else: fill o fi
+enddef;
+
+%3D - basé sur donymodule
+color Sommet[];
+
+color Co[];
+Co0=jaune;
+Co1=violet;
+Co2=orange;
+Co3=ciel;
+Co4=vert;
+Co5=bleu;
+Co6=rouge;
+
+string pointilles;
+
+string typerepre;
+typerepre:="proj";
+
+%generalite
+vardef Projette(expr X)=
+  pair $;
+  Xobs := -redpart(X)*Aux1 + greenpart(X)*Aux3;
+  Yobs := -redpart(X)*Aux5 - greenpart(X)*Aux6 + bluepart(X)*Aux4;
+  if typerepre="proj":
+    Zobs := -redpart(X)*Aux7 - greenpart(X)*Aux8 - bluepart(X)*Aux2 + Rho;
+    XProj := DE*Xobs/Zobs;
+    YProj := DE*Yobs/Zobs;
+  elseif typerepre="persp":
+    XProj := DE*Xobs;
+    YProj := DE*Yobs;
+  fi;
+  $=(XProj,YProj);
+  $
+enddef;
+
+vardef Initialisation(expr r,t,p,d)=
+  Rho:=r;
+  Theta:=t;
+  Phi:=p;
+  DE:=d;
+  Aux1:=sind(Theta);
+  Aux2:=sind(Phi);
+  Aux3:=cosd(Theta);
+  Aux4:=cosd(Phi);
+  Aux5:=Aux3*Aux2;
+  Aux6:=Aux1*Aux2;
+  Aux7:=Aux3*Aux4;
+  Aux8:=Aux1*Aux4;
+  pointilles:="oui";
+enddef;
+
+%vues cachees
+
+vardef Face(text t)=
+  j:=0;
+  for p_=t :
+    if numeric p_:
+      a[j]:=p_;
+      j:=j+1;
+    fi;
+  endfor;
+  for k=1 upto (j-1):
+    Fc[a0*100+(k-1)]:=a[k];
+  endfor;
+enddef;
+
+vardef Oeil=(Rho*Aux7,Rho*Aux8,Rho*Aux2)
+enddef;
+
+vardef Vision(expr num)=
+  save bb;
+  color bb;
+  bb=(redpart(Oeil-Sommet[num]),greenpart(Oeil-Sommet[num]),bluepart(Oeil-Sommet[num]));  
+  bb
+enddef;
+
+vardef Normal(expr vecun,vecde,vectr)=
+  save aa;
+  color aa;
+  P1:=redpart(vecde-vecun);
+  P2:=greenpart(vecde-vecun);
+  P3:=bluepart(vecde-vecun);
+  Q1:=redpart(vectr-vecun);
+  Q2:=greenpart(vectr-vecun);
+  Q3:=bluepart(vectr-vecun);
+  aa=(P2*Q3-Q2*P3,P3*Q1-Q3*P1,P1*Q2-Q1*P2);
+  aa
+enddef;
+
+vardef ProduitScalaire(expr wec,mor)=
+  redpart(wec)*redpart(mor)+greenpart(wec)*greenpart(mor)+bluepart(wec)*bluepart(mor)
+enddef;
+
+vardef Distance(expr aa,bb)=%Entre deux points
+  sqrt((redpart(bb)-redpart(aa))*(redpart(bb)-redpart(aa))+(greenpart(bb)-greenpart(aa))*(greenpart(bb)-greenpart(aa))+(bluepart(bb)-bluepart(aa))*(bluepart(bb)-bluepart(aa)))
+enddef;
+
+vardef Module(expr aa)=%module d'un vecteur
+sqrt((redpart(aa))**2+(greenpart(aa))**2+(bluepart(aa)**2))
+enddef;
+
+color CoulTrace;
+CoulTrace=black;
+
+vardef DessineObjet=
+  for l=1 upto NF:
+    color cc,dd;
+    dd=Vision(Fc[l*100+1]);
+    cc=Normal(Sommet[Fc[l*100+1]],Sommet[Fc[l*100+2]],Sommet[Fc[l*100+3]]);
+    if (ProduitScalaire(dd,cc)<0):
+      if pointilles="oui":
+	drawoptions(dashed dashpattern(on3pt off6pt) withcolor CoulTrace);
+	trace for k=1 upto Fc[100*l]:
+	  Projette(Sommet[Fc[100*l+k]])--
+	endfor
+	cycle;
+      fi;
+    else:
+      trace for k=1 upto Fc[100*l]:
+	Projette(Sommet[Fc[100*l+k]])--
+      endfor
+      cycle withcolor CoulTrace;
+    fi;
+    drawoptions();
+  endfor;
+enddef;
+
+%%Transformations
+
+%Translations
+
+vardef TranslateSommets(expr v)=
+  for k=1 upto NbS:
+    Sommet[k]:=Sommet[k]+v;
+  endfor;
+enddef;
+
+vardef SymetriePlanZ(expr vv)=
+  for k=1 upto NbS:
+    w:=vv-bluepart(Sommet[k]);
+    Sommet[k]:=(redpart(Sommet[k]),greenpart(Sommet[k]),w);
+  endfor;
+enddef;
+
+vardef IntersectionDroite(expr aa,bb,cc,dd)=
+  save tt;
+  color tt;
+  tt=whatever[aa,bb];
+  tt=whatever[cc,dd];
+  tt
+enddef;
+
+%%denis Roegel----------
+vardef Intersectionplandroite(expr aa,bb,cc,dd,ee)=
+  save int;
+  boolean int;
+  color gg,caaa[];
+  caaa3=Normal(aa,bb,cc)/Module(Normal(aa,bb,cc));
+  caaa1=aa-dd;
+  caaa2=ee-dd;
+  if ProduitScalaire(caaa2,caaa3)<>0:
+    caaa4=caaa2*(ProduitScalaire(caaa1,caaa3)/ProduitScalaire(caaa2,caaa3));
+    int:=true;
+  else: % the line is parallel to the plane
+    int:=false;
+  fi;
+  int
+enddef;
+
+vardef IntersectionPlanDroite(expr aa,bb,cc,dd,ee)=%plan (aa,bb,cc) droite(dd,ee)
+  if Intersectionplandroite(aa,bb,cc,dd,ee):
+    gg=dd+caaa4;
+  fi;
+  gg
+enddef;
+
+vardef ProjectionsurPlan(expr aa,bb,cc,dd)=%Projection du point aa sur le plan (bbccdd)
+  save di,vc;
+  color va,vb,vc;
+  va=Normal(bb,cc,dd)/Module(Normal(bb,cc,dd));
+  vb=aa-bb;
+  di=-ProduitScalaire(vb,va);
+  va:=di*va;
+  vb:=vb+va;
+  vc=bb+vb;
+  vc
+enddef;
+
+vardef Intersectionplanplan(expr AA,BB,CC,DD,EE,FF)=%besoin pour la suite
+  color trial[];
+  path INTer;
+  if Intersectionplandroite(DD,EE,FF,AA,BB):
+    trial1=IntersectionPlanDroite(DD,EE,FF,AA,BB);
+  else:% there is no intersection or the intersection is the line
+    trial1=IntersectionPlanDroite(DD,EE,FF,AA,1/2[BB,CC]);
+  fi;
+  if Intersectionplandroite(DD,EE,FF,AA,CC):
+    trial2=IntersectionPlanDroite(DD,EE,FF,AA,CC);
+  else:% there is no intersection or the intersection is the line
+    trial2=IntersectionPlanDroite(DD,EE,FF,CC,1/2[BB,AA]);%modif de cp
+  fi;
+  %INTer=segment(10[trial1,trial2],10[trial2,trial1]);
+  INTer=droite(trial1,trial2);
+  INTer
+enddef;
+
+vardef IntersectionPlanPlan(expr aa,bb,cc,dd,ee,ff)=
+  %a verifier
+  save da,db,dc,int,INTER;
+  boolean int;
+  path INTER;
+  da=Module(aa-ProjectionsurPlan(aa,dd,ee,ff));
+  %show da;
+  db=Module(bb-ProjectionsurPlan(bb,dd,ee,ff));
+  %show db;
+  dc=Module(cc-ProjectionsurPlan(cc,dd,ee,ff));
+  %show dc;
+  if (da=db) and (db=dc): % the two planes are parallel
+    int:=false;
+  else:
+    int:=true;
+    if (da=db):
+      INTER=droite(aa,bb);
+    elseif (db=dc):
+      INTER=droite(bb,cc);
+    elseif (dc=da):
+      INTER=droite(cc,aa);
+    elseif (da>=db) and (da>=dc):
+      INTER=Intersectionplanplan(aa,bb,cc,dd,ee,ff);
+    elseif (db>=da) and (db>=dc):
+      INTER=Intersectionplanplan(bb,cc,aa,dd,ee,ff);
+    elseif (dc>=da) and (dc>=db):
+      INTER=Intersectionplanplan(cc,aa,bb,dd,ee,ff);
+    fi;
+  fi;
+  INTER
+enddef;
+%%---------------------
+
+%Cube
+numeric arete;
+arete=1;
+
+vardef Cube(text t)=
+  picture cub;
+  cub=image(
+  NbS:=8;
+  Sommet1:=(arete,0,0);
+  Sommet2:=(arete,arete,0);
+  Sommet3:=(0,arete,0);
+  Sommet4:=(0,0,0);
+  Sommet5:=(0,0,arete);
+  Sommet6:=(arete,0,arete);
+  Sommet7:=(arete,arete,arete);
+  Sommet8:=(0,arete,arete);
+%%Faces
+  NF:=6;
+  Fc[100]:=4;Fc[101]:=1;Fc[102]:=4;Fc[103]:=3;Fc[104]:=2;
+  Fc[200]:=4;Fc[201]:=4;Fc[202]:=5;Fc[203]:=8;Fc[204]:=3;
+  Fc[300]:=4;Fc[301]:=1;Fc[302]:=6;Fc[303]:=5;Fc[304]:=4;
+  Fc[400]:=4;Fc[401]:=5;Fc[402]:=6;Fc[403]:=7;Fc[404]:=8;
+  Fc[500]:=4;Fc[501]:=2;Fc[502]:=3;Fc[503]:=8;Fc[504]:=7;
+  Fc[600]:=4;Fc[601]:=1;Fc[602]:=2;Fc[603]:=7;Fc[604]:=6;
+  DessineObjet;
+  k:=1;
+  for p_=t:
+    if color p_:
+      p_=Sommet[k];
+      k:=k+1;
+    fi
+  endfor;
+  );
+cub
+enddef;
+
+vardef cube=
+  typetrace:="3D";
+  typerepre:="persp";
+  Initialisation(1500,30,20,100);
+  picture cub;
+  cub=image(
+      NbS:=8;
+    Sommet1:=(arete,0,0);
+    Sommet2:=(arete,arete,0);
+    Sommet3:=(0,arete,0);
+    Sommet4:=(0,0,0);
+    Sommet5:=(0,0,arete);
+    Sommet6:=(arete,0,arete);
+    Sommet7:=(arete,arete,arete);
+    Sommet8:=(0,arete,arete);
+%%Faces
+    NF:=6;
+    Fc[100]:=4;Fc[101]:=1;Fc[102]:=4;Fc[103]:=3;Fc[104]:=2;
+    Fc[200]:=4;Fc[201]:=4;Fc[202]:=5;Fc[203]:=8;Fc[204]:=3;
+    Fc[300]:=4;Fc[301]:=1;Fc[302]:=6;Fc[303]:=5;Fc[304]:=4;
+    Fc[400]:=4;Fc[401]:=5;Fc[402]:=6;Fc[403]:=7;Fc[404]:=8;
+    Fc[500]:=4;Fc[501]:=2;Fc[502]:=3;Fc[503]:=8;Fc[504]:=7;
+    Fc[600]:=4;Fc[601]:=1;Fc[602]:=2;Fc[603]:=7;Fc[604]:=6;
+    DessineObjet;
+    );
+  cub
+enddef;
+
+%Cube
+vardef Paveh(text t)=
+  picture paveh;
+  paveh=image(
+  NbS:=8;
+  Sommet1:=(0.75,0,0);
+  Sommet2:=(0.75,1.5,0);
+  Sommet3:=(0,1.5,0);
+  Sommet4:=(0,0,0);
+  Sommet5:=(0,0,1);
+  Sommet6:=(0.75,0,1);
+  Sommet7:=(0.75,1.5,1);
+  Sommet8:=(0,1.5,1);
+%%Faces
+  NF:=6;
+  Fc[100]:=4;Fc[101]:=1;Fc[102]:=4;Fc[103]:=3;Fc[104]:=2;
+  Fc[200]:=4;Fc[201]:=4;Fc[202]:=5;Fc[203]:=8;Fc[204]:=3;
+  Fc[300]:=4;Fc[301]:=1;Fc[302]:=6;Fc[303]:=5;Fc[304]:=4;
+  Fc[400]:=4;Fc[401]:=5;Fc[402]:=6;Fc[403]:=7;Fc[404]:=8;
+  Fc[500]:=4;Fc[501]:=2;Fc[502]:=3;Fc[503]:=8;Fc[504]:=7;
+  Fc[600]:=4;Fc[601]:=1;Fc[602]:=2;Fc[603]:=7;Fc[604]:=6;
+  DessineObjet;
+  k:=1;
+  for p_=t:
+    if color p_:
+      p_=Sommet[k];
+      k:=k+1;
+    fi
+  endfor;
+  );
+paveh
+enddef;
+
+%Cube
+vardef Pavev(text t)=
+  picture pavev;
+  pavev=image(
+  NbS:=8;
+  Sommet1:=(1,0,0);
+  Sommet2:=(1,0.75,0);
+  Sommet3:=(0,0.75,0);
+  Sommet4:=(0,0,0);
+  Sommet5:=(0,0,1.5);
+  Sommet6:=(1,0,1.5);
+  Sommet7:=(1,0.75,1.5);
+  Sommet8:=(0,0.75,1.5);
+%%Faces
+  NF:=6;
+  Fc[100]:=4;Fc[101]:=1;Fc[102]:=4;Fc[103]:=3;Fc[104]:=2;
+  Fc[200]:=4;Fc[201]:=4;Fc[202]:=5;Fc[203]:=8;Fc[204]:=3;
+  Fc[300]:=4;Fc[301]:=1;Fc[302]:=6;Fc[303]:=5;Fc[304]:=4;
+  Fc[400]:=4;Fc[401]:=5;Fc[402]:=6;Fc[403]:=7;Fc[404]:=8;
+  Fc[500]:=4;Fc[501]:=2;Fc[502]:=3;Fc[503]:=8;Fc[504]:=7;
+  Fc[600]:=4;Fc[601]:=1;Fc[602]:=2;Fc[603]:=7;Fc[604]:=6;
+  DessineObjet;
+  k:=1;
+  for p_=t:
+    if color p_:
+      p_=Sommet[k];
+      k:=k+1;
+    fi
+  endfor;
+  );
+pavev
+enddef;
+
+vardef Pave(text t)(expr aa,bb,cc)=
+  picture pave;
+  pave=image(
+  NbS:=8;
+  Sommet1:=(aa,0,0);
+  Sommet2:=(aa,bb,0);
+  Sommet3:=(0,bb,0);
+  Sommet4:=(0,0,0);
+  Sommet5:=(0,0,cc);
+  Sommet6:=(aa,0,cc);
+  Sommet7:=(aa,bb,cc);
+  Sommet8:=(0,bb,cc);
+%%Faces
+  NF:=6;
+  Fc[100]:=4;Fc[101]:=4;Fc[102]:=3;Fc[103]:=2;Fc[104]:=1;
+  Fc[200]:=4;Fc[201]:=4;Fc[202]:=5;Fc[203]:=8;Fc[204]:=3;
+  Fc[300]:=4;Fc[301]:=4;Fc[302]:=1;Fc[303]:=6;Fc[304]:=5;
+  Fc[400]:=4;Fc[401]:=5;Fc[402]:=6;Fc[403]:=7;Fc[404]:=8;
+  Fc[500]:=4;Fc[501]:=2;Fc[502]:=3;Fc[503]:=8;Fc[504]:=7;
+  Fc[600]:=4;Fc[601]:=1;Fc[602]:=2;Fc[603]:=7;Fc[604]:=6;
+  DessineObjet;
+  k:=1;
+  for p_=t:
+    if color p_:
+      p_=Sommet[k];
+      k:=k+1;
+    fi
+  endfor;
+  );
+pave
+enddef;
+
+vardef pave(expr aa,bb,cc)=
+  typetrace:="3D";
+  typerepre:="persp";
+  Initialisation(1500,30,20,100);
+  picture PAVE;
+  PAVE=image(
+      NbS:=8;
+    Sommet1:=(aa,0,0);
+    Sommet2:=(aa,bb,0);
+    Sommet3:=(0,bb,0);
+    Sommet4:=(0,0,0);
+    Sommet5:=(0,0,cc);
+    Sommet6:=(aa,0,cc);
+    Sommet7:=(aa,bb,cc);
+    Sommet8:=(0,bb,cc);
+%%Faces
+    NF:=6;
+    Fc[100]:=4;Fc[101]:=4;Fc[102]:=3;Fc[103]:=2;Fc[104]:=1;
+    Fc[200]:=4;Fc[201]:=4;Fc[202]:=5;Fc[203]:=8;Fc[204]:=3;
+    Fc[300]:=4;Fc[301]:=4;Fc[302]:=1;Fc[303]:=6;Fc[304]:=5;
+    Fc[400]:=4;Fc[401]:=5;Fc[402]:=6;Fc[403]:=7;Fc[404]:=8;
+    Fc[500]:=4;Fc[501]:=2;Fc[502]:=3;Fc[503]:=8;Fc[504]:=7;
+    Fc[600]:=4;Fc[601]:=1;Fc[602]:=2;Fc[603]:=7;Fc[604]:=6;
+    DessineObjet;
+    );
+  PAVE
+enddef;
+
+vardef Tetraedrer(text t)=
+  picture tetrar;
+  tetrar=image(
+    %Sommets
+    NbS:=4;
+    Sommet1:=(0,0,1);
+    Sommet2:=(-0.4714045,-0.8164965,-1/3);
+    Sommet3:=(0.942809,0,-1/3);
+    Sommet4:=(-0.4714045,0.8164965,-1/3);
+    %Faces
+    NF:=4;
+    Fc[100]:=3;Fc[101]:=1;Fc[102]:=2;Fc[103]:=3;
+    Fc[200]:=3;Fc[201]:=1;Fc[202]:=3;Fc[203]:=4;
+    Fc[300]:=3;Fc[301]:=1;Fc[302]:=4;Fc[303]:=2;
+    Fc[400]:=3;Fc[401]:=2;Fc[402]:=4;Fc[403]:=3;
+    DessineObjet;
+    k:=1;
+    for p_=t:
+      if color p_:
+	p_=Sommet[k];
+	k:=k+1;
+      fi
+    endfor;
+    );
+  tetrar
+enddef;
+
+endinput;
diff --git a/Master/texmf-dist/metapost/profcollege/PfC-LaTeX.mp b/Master/texmf-dist/metapost/profcollege/PfC-LaTeX.mp
new file mode 100644
index 00000000000..daa206a603d
--- /dev/null
+++ b/Master/texmf-dist/metapost/profcollege/PfC-LaTeX.mp
@@ -0,0 +1,20 @@
+%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[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";
+  write "btex "&s&" etex" to "mptextmp.mp";
+  write EOF to "mptextmp.mp";
+  scantokens "input mptextmp"
+enddef;
diff --git a/Master/texmf-dist/metapost/profcollege/PfC-Svgnames.mp b/Master/texmf-dist/metapost/profcollege/PfC-Svgnames.mp
new file mode 100644
index 00000000000..3af1336dc33
--- /dev/null
+++ b/Master/texmf-dist/metapost/profcollege/PfC-Svgnames.mp
@@ -0,0 +1,156 @@
+%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);
+color Aqua; Aqua = (0,1,1);
+color Aquamarine; Aquamarine = (.498,1,.83);
+color Azure; Azure = (.94,1,1);
+color Beige; Beige = (.96,.96,.864);
+color Bisque; Bisque = (1,.894,.77);
+color Black; Black = (0,0,0);
+color BlanchedAlmond; BlanchedAlmond = (1,.92,.804);
+color Blue; Blue = (0,0,1);
+color BlueViolet; BlueViolet = (.54,.17,.888);
+color Brown; Brown = (.648,.165,.165);
+color BurlyWood; BurlyWood = (.87,.72,.53);
+color CadetBlue; CadetBlue = (.372,.62,.628);
+color Chartreuse; Chartreuse = (.498,1,0);
+color Chocolate; Chocolate = (.824,.41,.116);
+color Coral; Coral = (1,.498,.312);
+color CornflowerBlue; CornflowerBlue = (.392,.585,.93);
+color Cornsilk; Cornsilk = (1,.972,.864);
+color Crimson; Crimson = (.864,.08,.235);
+color Cyan; Cyan = (0,1,1);
+color DarkBlue; DarkBlue = (0,0,.545);
+color DarkCyan; DarkCyan = (0,.545,.545);
+color DarkGoldenrod; DarkGoldenrod = (.72,.525,.044);
+color DarkGray; DarkGray = (.664,.664,.664);
+color DarkGreen; DarkGreen = (0,.392,0);
+color DarkGrey; DarkGrey = (.664,.664,.664);
+color DarkKhaki; DarkKhaki = (.74,.716,.42);
+color DarkMagenta; DarkMagenta = (.545,0,.545);
+color DarkOliveGreen; DarkOliveGreen = (.332,.42,.185);
+color DarkOrange; DarkOrange = (1,.55,0);
+color DarkOrchid; DarkOrchid = (.6,.196,.8);
+color DarkRed; DarkRed = (.545,0,0);
+color DarkSalmon; DarkSalmon = (.912,.59,.48);
+color DarkSeaGreen; DarkSeaGreen = (.56,.736,.56);
+color DarkSlateBlue; DarkSlateBlue = (.284,.24,.545);
+color DarkSlateGray; DarkSlateGray = (.185,.31,.31);
+color DarkSlateGrey; DarkSlateGrey = (.185,.31,.31);
+color DarkTurquoise; DarkTurquoise = (0,.808,.82);
+color DarkViolet; DarkViolet = (.58,0,.828);
+color DeepPink; DeepPink = (1,.08,.576);
+color DeepSkyBlue; DeepSkyBlue = (0,.75,1);
+color DimGray; DimGray = (.41,.41,.41);
+color DimGrey; DimGrey = (.41,.41,.41);
+color DodgerBlue; DodgerBlue = (.116,.565,1);
+color FireBrick; FireBrick = (.698,.132,.132);
+color FloralWhite; FloralWhite = (1,.98,.94);
+color ForestGreen; ForestGreen = (.132,.545,.132);
+color Fuchsia; Fuchsia = (1,0,1);
+color Gainsboro; Gainsboro = (.864,.864,.864);
+color GhostWhite; GhostWhite = (.972,.972,1);
+color Gold; Gold = (1,.844,0);
+color Goldenrod; Goldenrod = (.855,.648,.125);
+color Gray; Gray = (.5,.5,.5);
+color Green; Green = (0,.5,0);
+color GreenYellow; GreenYellow = (.68,1,.185);
+color Grey; Grey = (.5,.5,.5);
+color Honeydew; Honeydew = (.94,1,.94);
+color HotPink; HotPink = (1,.41,.705);
+color IndianRed; IndianRed = (.804,.36,.36);
+color Indigo; Indigo = (.294,0,.51);
+color Ivory; Ivory = (1,1,.94);
+color Khaki; Khaki = (.94,.9,.55);
+color Lavender; Lavender = (.9,.9,.98);
+color LavenderBlush; LavenderBlush = (1,.94,.96);
+color LawnGreen; LawnGreen = (.488,.99,0);
+color LemonChiffon; LemonChiffon = (1,.98,.804);
+color LightBlue; LightBlue = (.68,.848,.9);
+color LightCoral; LightCoral = (.94,.5,.5);
+color LightCyan; LightCyan = (.88,1,1);
+color LightGoldenrod; LightGoldenrod = (.933,.867,.51);
+color LightGoldenrodYellow; LightGoldenrodYellow = (.98,.98,.824);
+color LightGray; LightGray = (.828,.828,.828);
+color LightGreen; LightGreen = (.565,.932,.565);
+color LightGrey; LightGrey = (.828,.828,.828);
+color LightPink; LightPink = (1,.712,.756);
+color LightSalmon; LightSalmon = (1,.628,.48);
+color LightSeaGreen; LightSeaGreen = (.125,.698,.668);
+color LightSkyBlue; LightSkyBlue = (.53,.808,.98);
+color LightSlateBlue; LightSlateBlue = (.518,.44,1);
+color LightSlateGray; LightSlateGray = (.468,.532,.6);
+color LightSlateGrey; LightSlateGrey = (.468,.532,.6);
+color LightSteelBlue; LightSteelBlue = (.69,.77,.87);
+color LightYellow; LightYellow = (1,1,.88);
+color Lime; Lime = (0,1,0);
+color LimeGreen; LimeGreen = (.196,.804,.196);
+color Linen; Linen = (.98,.94,.9);
+color Magenta; Magenta = (1,0,1);
+color Maroon; Maroon = (.5,0,0);
+color MediumAquamarine; MediumAquamarine = (.4,.804,.668);
+color MediumBlue; MediumBlue = (0,0,.804);
+color MediumOrchid; MediumOrchid = (.73,.332,.828);
+color MediumPurple; MediumPurple = (.576,.44,.86);
+color MediumSeaGreen; MediumSeaGreen = (.235,.7,.444);
+color MediumSlateBlue; MediumSlateBlue = (.484,.408,.932);
+color MediumSpringGreen; MediumSpringGreen = (0,.98,.604);
+color MediumTurquoise; MediumTurquoise = (.284,.82,.8);
+color MediumVioletRed; MediumVioletRed = (.78,.084,.52);
+color MidnightBlue; MidnightBlue = (.098,.098,.44);
+color MintCream; MintCream = (.96,1,.98);
+color MistyRose; MistyRose = (1,.894,.884);
+color Moccasin; Moccasin = (1,.894,.71);
+color NavajoWhite; NavajoWhite = (1,.87,.68);
+color Navy; Navy = (0,0,.5);
+color NavyBlue; NavyBlue = (0,0,.5);
+color OldLace; OldLace = (.992,.96,.9);
+color Olive; Olive = (.5,.5,0);
+color OliveDrab; OliveDrab = (.42,.556,.136);
+color Orange; Orange = (1,.648,0);
+color OrangeRed; OrangeRed = (1,.27,0);
+color Orchid; Orchid = (.855,.44,.84);
+color PaleGoldenrod; PaleGoldenrod = (.932,.91,.668);
+color PaleGreen; PaleGreen = (.596,.985,.596);
+color PaleTurquoise; PaleTurquoise = (.688,.932,.932);
+color PaleVioletRed; PaleVioletRed = (.86,.44,.576);
+color PapayaWhip; PapayaWhip = (1,.936,.835);
+color PeachPuff; PeachPuff = (1,.855,.725);
+color Peru; Peru = (.804,.52,.248);
+color Pink; Pink = (1,.752,.796);
+color Plum; Plum = (.868,.628,.868);
+color PowderBlue; PowderBlue = (.69,.88,.9);
+color Purple; Purple = (.5,0,.5);
+color Red; Red = (1,0,0);
+color RosyBrown; RosyBrown = (.736,.56,.56);
+color RoyalBlue; RoyalBlue = (.255,.41,.884);
+color SaddleBrown; SaddleBrown = (.545,.27,.075);
+color Salmon; Salmon = (.98,.5,.448);
+color SandyBrown; SandyBrown = (.956,.644,.376);
+color SeaGreen; SeaGreen = (.18,.545,.34);
+color Seashell; Seashell = (1,.96,.932);
+color Sienna; Sienna = (.628,.32,.176);
+color Silver; Silver = (.752,.752,.752);
+color SkyBlue; SkyBlue = (.53,.808,.92);
+color SlateBlue; SlateBlue = (.415,.352,.804);
+color SlateGray; SlateGray = (.44,.5,.565);
+color SlateGrey; SlateGrey = (.44,.5,.565);
+color Snow; Snow = (1,.98,.98);
+color SpringGreen; SpringGreen = (0,1,.498);
+color SteelBlue; SteelBlue = (.275,.51,.705);
+color Tan; Tan = (.824,.705,.55);
+color Teal; Teal = (0,.5,.5);
+color Thistle; Thistle = (.848,.75,.848);
+color Tomato; Tomato = (1,.39,.28);
+color Turquoise; Turquoise = (.25,.88,.815);
+color Violet; Violet = (.932,.51,.932);
+color VioletRed; VioletRed = (.816,.125,.565);
+color Wheat; Wheat = (.96,.87,.7);
+color White; White = (1,1,1);
+color WhiteSmoke; WhiteSmoke = (.96,.96,.96);
+color Yellow; Yellow = (1,1,0);
+color YellowGreen; YellowGreen = (.604,.804,.196);
+endinput
diff --git a/Master/texmf-dist/tex/latex/profcollege/PfC-EquationComposition1.tex b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationComposition1.tex
new file mode 100644
index 00000000000..b513a6b1163
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationComposition1.tex
@@ -0,0 +1,277 @@
+% 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 a<c              % Autre cas délicat
+              \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}{\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 a<c              % Autre cas délicat
+              \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}{\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-EquationLaurent1.tex b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationLaurent1.tex
new file mode 100644
index 00000000000..347afc0e8d9
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationLaurent1.tex
@@ -0,0 +1,226 @@
+% Licence    : Released under the LaTeX Project Public License v1.3c
+% or later, see http://www.latex-project.org/lppl.txtf
+\newcommand{\EquaBaseLaurent}[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*}%
+        \xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{#2}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{#2}}}}&=\xintifboolexpr{#2=1}{\num{#5}}{\color{Cdecomp}\frac{\color{black}\num{#5}}{\num{#2}}}
+        \xintifboolexpr{#2=1}{}{\\\useKV[ClesEquation]{Lettre}&=\frac{\num{#5}}{\num{#2}}}%\\
+        \ifboolKV[ClesEquation]{Entier}{%
+        \SSimpliTest{#5}{#2}%
+        \ifboolKV[ClesEquation]{Simplification}{%
+        \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{#5}{#2}}{}%\\
+        }{}
+        }{}
+      \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{\EquaDeuxLaurent}[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
+  \EquaDeuxLaurent[#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
+      \EquaBaseLaurent[#1]{#2}{}{}{#5}%
+    }{%ax+b=d$ Ici
+      \begin{align*}
+        \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{-\num{\fpeval{0-#3}}\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}&=\num{#5}\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}\\
+        \xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}%\\
+        \xintifboolexpr{\Coeffa=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{\Coeffa}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{\Coeffa}}}}&=\xintifboolexpr{\Coeffa=1}{\num{\Coeffb}}{\color{Cdecomp}\frac{\color{black}\num{\Coeffb}}{\num{\Coeffa}}}%\\
+        \xintifboolexpr{\Coeffa=1}{}{\\}
+        \xintifboolexpr{\Coeffa=1}{% 
+        }{%\ifnum\cmtd>1
+        \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+        \ifboolKV[ClesEquation]{Entier}{%
+        \SSimpliTest{\Coeffb}{\Coeffa}%
+        \ifboolKV[ClesEquation]{Simplification}{%
+        \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+        }{}
+        }{}
+        }
+      \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}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
+      }{}
+    }
+  }
+}
+
+\newcommand{\EquaTroisLaurent}[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
+      \EquaTroisLaurent[#1]{#4}{#5}{#2}{}%
+    \fi
+  \else
+  \xintifboolexpr{#2=0}{%b=cx
+    \EquaBaseLaurent[#1]{#4}{}{}{#3}
+  }{%
+    \xintifboolexpr{#4=0}{%ax+b=0
+      \EquaDeuxLaurent[#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*}
+            \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{-\num{\fpeval{0-#3}}\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}\\
+            \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}\\
+            \xdef\Coeffa{\fpeval{#2-#4}}\xdef\Coeffb{\fpeval{0-#3}}%\\
+            \xintifboolexpr{\Coeffa=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{\Coeffa}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{\Coeffa}}}}&=\xintifboolexpr{\Coeffa=1}{\num{\Coeffb}}{\color{Cdecomp}\frac{\color{black}\num{\Coeffb}}{\num{\Coeffa}}}%\\
+            \xintifboolexpr{\Coeffa=1}{}{\\}
+            \xintifboolexpr{\Coeffa=1}{% 
+            }{%\ifnum\cmtd>1
+            \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+            \ifboolKV[ClesEquation]{Entier}{%
+            \SSimpliTest{\Coeffb}{\Coeffa}%
+            \ifboolKV[ClesEquation]{Simplification}{%
+            \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+            }{}
+            }{}
+            }
+          \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 avec a<c              % Autre cas délicat
+          \begin{align*}%
+            \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}\\
+            \xdef\Coeffa{\fpeval{#2-#4}}\xdef\Coeffb{\fpeval{0-#3}}%\\
+            \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{-\num{\fpeval{0-#3}}\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}&=0\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}\\
+            \xintifboolexpr{\Coeffa=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{\Coeffa}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{\Coeffa}}}}&=\xintifboolexpr{\Coeffa=1}{\num{\Coeffb}}{\color{Cdecomp}\frac{\color{black}\num{\Coeffb}}{\num{\Coeffa}}}%\\
+            \xintifboolexpr{\Coeffa=1}{}{\\}
+            \xintifboolexpr{\Coeffa=1}{% 
+            }{%\ifnum\cmtd>1
+            \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+            \ifboolKV[ClesEquation]{Entier}{%
+            \SSimpliTest{\Coeffb}{\Coeffa}%
+            \ifboolKV[ClesEquation]{Simplification}{%
+            \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+            }{}
+            }{}
+            }
+          \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{\ResolEquationLaurent}[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
+      \EquaDeuxLaurent[#1]{#4}{#5}{}{#3}%
+    }%
+  }{%
+    \xintifboolexpr{#4=0}{%ax+b=0x+d
+      \EquaDeuxLaurent[#1]{#2}{#3}{}{#5}%
+    }
+    {%ax+b=cx+d
+      \xintifboolexpr{#3=0}{%
+        \xintifboolexpr{#5=0}{%ax=cx
+          \EquaTroisLaurent[#1]{#2}{0}{#4}{}%
+        }%
+        {%ax=cx+d
+          \EquaTroisLaurent[#1]{#4}{#5}{#2}{}%
+        }%
+      }%
+      {\xintifboolexpr{#5=0}{%ax+b=cx
+          \EquaTroisLaurent[#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*}
+                \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{-\num{\fpeval{0-#3}}\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}\\
+                \xdef\Coeffa{\fpeval{#2-#4}}\xdef\Coeffb{\fpeval{#5-#3}}%\\
+                \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}\xintifboolexpr{\Coeffb>0}{+\num{\Coeffb}}{-\num{\fpeval{0-\Coeffb}}}\\
+                \xintifboolexpr{\Coeffa=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{\Coeffa}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{\Coeffa}}}}&=\xintifboolexpr{\Coeffa=1}{\num{\Coeffb}}{\color{Cdecomp}\frac{\color{black}\num{\Coeffb}}{\num{\Coeffa}}}%\\
+                \xintifboolexpr{\Coeffa=1}{}{\\}
+                \xintifboolexpr{\Coeffa=1}{% 
+                }{%\ifnum\cmtd>1
+                \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+                \ifboolKV[ClesEquation]{Entier}{%
+                \SSimpliTest{\Coeffb}{\Coeffa}%
+                \ifboolKV[ClesEquation]{Simplification}{%
+                \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+                }{}
+                }{}
+                }
+              \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 a<c              % Autre cas délicat
+              \begin{align*}%
+                \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}} {}}\stackText}%
+                &=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}} {}}\stackText}
+                \\
+                \xdef\Coeffa{\fpeval{#2-#4}}\xdef\Coeffb{\fpeval{#5-#3}}%\\
+                \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}\xintifboolexpr{\Coeffb>0}{+\num{\Coeffb}}{-\num{\fpeval{0-\Coeffb}}}\\
+                \xintifboolexpr{\Coeffa=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{\Coeffa}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{\Coeffa}}}}&=\xintifboolexpr{\Coeffa=1}{\num{\Coeffb}}{\color{Cdecomp}\frac{\color{black}\num{\Coeffb}}{\num{\Coeffa}}}%\\
+                \xintifboolexpr{\Coeffa=1}{}{\\}
+                \xintifboolexpr{\Coeffa=1}{% 
+                }{%\ifnum\cmtd>1
+                \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+                \ifboolKV[ClesEquation]{Entier}{%
+                \SSimpliTest{\Coeffb}{\Coeffa}%
+                \ifboolKV[ClesEquation]{Simplification}{%
+                \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+                }{}
+                }{}
+                }
+              \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}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
+              }{}%
+            }%
+          }%
+        }%
+      }%
+    }%
+  }%
+}%
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/latex/profcollege/PfC-EquationPose1.tex b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationPose1.tex
new file mode 100644
index 00000000000..e34d382a588
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationPose1.tex
@@ -0,0 +1,246 @@
+% Licence    : Released under the LaTeX Project Public License v1.3c
+% or later, see http://www.latex-project.org/lppl.txtf
+\newcommand{\EquaBaseL}[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...
+  \EquaBaseL[#1]{#4}{}{}{#3}
+  \else
+  % si non, on est dans le cas ax=d
+  \xintifboolexpr{#2=0}{%
+    \xintifboolexpr{#5=0}{%
+      L'équation $0\useKV[ClesEquation]{Lettre}=0$ 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*}%
+        \xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}}{\num{#2}\useKV[ClesEquation]{Lettre}}&=\num{#5}\\
+        \xintifboolexpr{#2=1}{}{%
+        \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\phantom{\useKV[ClesEquation]{Lettre}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\\}
+        \useKV[ClesEquation]{Lettre}&=\frac{\num{#5}}{\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{\EquaDeuxL}[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
+    \EquaDeuxL[#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
+        \EquaBaseL[#1]{#2}{}{}{#5}%
+      }{%ax+b=d$ Ici
+        \begin{align*}
+          \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\\
+          \phantom{\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&\phantom{\mathrel{=}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
+          \xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\num{\Coeffb}%\\
+          \xintifboolexpr{\Coeffa=1}{}{\\}
+          \xintifboolexpr{\Coeffa=1}{% 
+          }{%\ifnum\cmtd>1
+          \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\phantom{\useKV[ClesEquation]{Lettre}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\\
+          \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+          }
+          \ifboolKV[ClesEquation]{Entier}{%
+          \SSimpliTest{\Coeffb}{\Coeffa}%
+          \ifboolKV[ClesEquation]{Simplification}{%
+          \ifthenelse{\boolean{Simplification}}{%
+          \\\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\SSimplifie{\Coeffb}{\Coeffa}%
+                                                                                                                   }{}%\\
+          }{}
+          }{}
+        \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{\EquaTroisL}[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
+      \EquaTroisL[#1]{#4}{#5}{#2}{}%
+    \fi
+  \else
+  \xintifboolexpr{#2=0}{%b=cx
+    \EquaBaseL[#1]{#4}{}{}{#3}
+  }{%
+    \xintifboolexpr{#4=0}{%ax+b=0
+      \EquaDeuxL[#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*}
+              \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}\\
+                \mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{{}-{}\num{#4}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{{}={}}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\
+              \xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\\
+              \phantom{\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}&\phantom{\mathrel{=}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}\\
+              \xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\num{\Coeffb}%\\
+              \xintifboolexpr{\Coeffa=1}{}{\\}
+              \xintifboolexpr{\Coeffa=1}{% 
+              }{%\ifnum\cmtd>1
+              \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\phantom{\useKV[ClesEquation]{Lettre}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
+              \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+              }
+              \ifboolKV[ClesEquation]{Entier}{%
+              \SSimpliTest{\Coeffb}{\Coeffa}%
+              \ifboolKV[ClesEquation]{Simplification}{%
+              \ifthenelse{\boolean{Simplification}}{\\%
+              \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\SSimplifie{\Coeffb}{\Coeffa}%\\
+              }{}
+              }{}
+              }{}
+            \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 a<c              % Autre cas délicat
+              \begin{align*}%
+                \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}\\
+                \mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{{}={}}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
+                \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}%\\
+                \xintifboolexpr{\Coeffa=1}{}{\\}
+                \xintifboolexpr{\Coeffa=1}{% 
+                }{%\ifnum\cmtd>1
+                \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
+              \frac{\num{\Coeffb}}{\num{\Coeffa}}&=\phantom{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%\\
+              }
+              \ifboolKV[ClesEquation]{Entier}{%
+              \SSimpliTest{\Coeffb}{\Coeffa}%
+              \ifboolKV[ClesEquation]{Simplification}{%
+              \ifthenelse{\boolean{Simplification}}{\\%
+              \SSimplifie{\Coeffb}{\Coeffa}&=\phantom{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%\\
+              }{}
+              }{}
+              }{}
+              \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{\ResolEquationL}[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$
+      \EquaDeuxL[#1]{#4}{#5}{}{#3}%
+    }%
+  }{%
+    \xintifboolexpr{#4=0}{%ax+b=0x+d
+      \EquaDeuxL[#1]{#2}{#3}{}{#5}%
+    }
+    {%ax+b=cx+d$
+      \xintifboolexpr{#3=0}{%
+        \xintifboolexpr{#5=0}{%ax=cx
+          \EquaTroisL[#1]{#2}{0}{#4}{}%
+        }%
+        {%ax=cx+d
+          \EquaTroisL[#1]{#4}{#5}{#2}{}%
+        }%
+      }%
+      {\xintifboolexpr{#5=0}{%ax+b=cx
+          \EquaTroisL[#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*}
+                \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}}}\\
+                \mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{{}-{}\num{#4}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{{}-{}\num{#4}\useKV[ClesEquation]{Lettre}}{\phantom{{}={}}+{}\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\
+                \xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{\phantom{{}+{}}\num{#5}}{-\num{\fpeval{0-#5}}}\\
+                \mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}&\phantom{{}={}\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}\\
+                \xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{\Coeffb>0}{\phantom{{}+{}}\num{\Coeffb}}{{}-{}\num{\fpeval{0-\Coeffb}}}%\\
+                \xintifboolexpr{\Coeffa=1}{}{\\}
+                \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+                \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\phantom{\useKV[ClesEquation]{Lettre}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{{}={}}\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
+                \phantom{\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{\Coeffb>0}{{}+{}}{}}\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+                }
+                \ifboolKV[ClesEquation]{Entier}{%
+                \SSimpliTest{\Coeffb}{\Coeffa}%
+                \ifboolKV[ClesEquation]{Simplification}{%
+                \ifthenelse{\boolean{Simplification}}{\\%
+                \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{\Coeffb>0}{{}+{}}{}}\SSimplifie{\Coeffb}{\Coeffa}%\\
+                }{}
+                }{}
+                }{}
+              \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 a<c              % Autre cas délicat
+              \begin{align*}%
+                \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}}}\\
+                \mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\xintifboolexpr{#4<0}{\phantom{={}}}{}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
+                \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}}}\\
+                \mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{{}-{}\num{#5}}{{}+{}\num{\fpeval{0-#5}}}}&\phantom{{}={}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}\\
+                \xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%\\
+                \xintifboolexpr{\Coeffa=1}{}{\\}
+                \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+                \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}&\xintifboolexpr{\Coeffa<0}{\phantom{{}={}}}{\phantom{=}}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
+                \frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}%\\
+                }
+                \ifboolKV[ClesEquation]{Entier}{%
+                \SSimpliTest{\Coeffb}{\Coeffa}%
+                \ifboolKV[ClesEquation]{Simplification}{%
+                \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
+                }{}
+                }{}
+              \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-EquationSoustraction1.tex b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationSoustraction1.tex
new file mode 100644
index 00000000000..034aa7e2ed4
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationSoustraction1.tex
@@ -0,0 +1,332 @@
+% 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 a<c              % Autre cas délicat
+              \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{#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 a<c              % Autre cas délicat
+              \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{#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-EquationSymbole1.tex b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationSymbole1.tex
new file mode 100644
index 00000000000..4faec4767ae
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationSymbole1.tex
@@ -0,0 +1,225 @@
+% Licence    : Released under the LaTeX Project Public License v1.3c
+% or later, see http://www.latex-project.org/lppl.txtf
+\newcommand{\EquaBaseSymbole}[5][]{%type ax=d ou b=cx
+  \useKVdefault[ClesEquation]%
+  \setKV[ClesEquation]{#1}%
+  \setKV[ClesEquation]{Fleches=false,FlecheDiv=false,Terme=false,Decomposition=false}
+  \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...
+    \ifx\bla#4\bla
+  %% il manque un paramètre
+    \else
+      \EquaBaseSymbole[#1]{#4}{}{}{#3}
+    \fi
+  \else
+  % si non, on est dans le cas ax=d
+  \xintifboolexpr{#2=0}{%
+    \xintifboolexpr{#5=0}{%
+      L'équation $0\times\useKV[ClesEquation]{Lettre}=0$ a une infinité de solution.}{L'équation $0\times\useKV[ClesEquation]{Lettre}=\num{#5}$ n'a aucune solution.}%
+  }{%\else
+    \xintifboolexpr{#5=0}{L'équation $\num{#2}\times\useKV[ClesEquation]{Lettre}=0$ a une unique solution : $\useKV[ClesEquation]{Lettre}=0$.}{%\else
+      \begin{align*}%
+         \xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}}{\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}&=\num{#5}\\
+        \useKV[ClesEquation]{Lettre}&=\frac{\num{#5}}{\num{#2}}%\\
+        \ifboolKV[ClesEquation]{Entier}{%
+                \SSimpliTest{#5}{#2}%
+                \ifboolKV[ClesEquation]{Simplification}{%
+                \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{#5}{#2}}{}%\\
+                }{}
+                }{}
+      \end{align*}
+    }
+  }
+  \fi
+}
+
+\newcommand{\EquaDeuxSymbole}[5][]{%type ax+b=d ou b=cx+d$
+  \useKVdefault[ClesEquation]%
+  \setKV[ClesEquation]{#1}%
+  \setKV[ClesEquation]{Fleches=false,FlecheDiv=false,Terme=false,Decomposition=false}
+  \ifx\bla#2\bla%On échange en faisant attention à ne pas boucler : c doit être non vide
+    \EquaDeuxSymbole[#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
+        \EquaBaseSymbole[#1]{#2}{}{}{#5}%
+      }{%ax+b=d$ Ici
+        \begin{align*}
+          \xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}}{\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\\
+          \ifboolKV[ClesEquation]{Bloc}{\Fdash{$\xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}}{\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}$}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\\}{}%
+          \xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{\useKV[ClesEquation]{Lettre}}{\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}&=\num{\Coeffb}%\\
+          \xintifboolexpr{\Coeffa=1}{% 
+          }{%\ifnum\cmtd>1
+          \\
+          \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+          \ifboolKV[ClesEquation]{Entier}{%
+          \SSimpliTest{\Coeffb}{\Coeffa}%
+          \ifboolKV[ClesEquation]{Simplification}{%
+          \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+          }{}
+          }{}
+          }
+        \end{align*}
+      }
+    }
+  \fi
+}
+
+\newcommand{\EquaTroisSymbole}[5][]{%ax+b=cx ou ax=cx+d
+  \useKVdefault[ClesEquation]%
+  \setKV[ClesEquation]{#1}%
+  \setKV[ClesEquation]{Fleches=false,FlecheDiv=false,Terme=false,Decomposition=false}
+  \ifx\bla#3\bla%on inverse en faisant attention à la boucle #3<->#5
+    \ifx\bla#5\bla%
+      %% paramètre oublié
+    \else
+      \EquaTroisSymbole[#1]{#4}{#5}{#2}{}%
+    \fi
+  \else
+  \xintifboolexpr{#2=0}{%b=cx
+    \EquaBaseSymbole[#1]{#4}{}{}{#3}
+  }{%
+    \xintifboolexpr{#4=0}{%ax+b=0
+      \EquaDeuxSymbole[#1]{#2}{#3}{}{0}
+      }{%ax+b=cx
+        \xintifboolexpr{#2=#4}{%
+          \xintifboolexpr{#3=0}{%ax=ax
+            L'équation $\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}=\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}$ a une infinité de solution.}%
+          {%ax+b=ax
+            L'équation $\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}$ n'a aucune solution.%
+          }%
+        }{%% Cas délicat
+          \xintifboolexpr{#2>#4}{%ax+b=cx avec a>c
+            \begin{align*}
+              \multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\\
+              \mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{#4-1}}{+\useKV[ClesEquation]{Lettre}}}\multido{\i=1+1}{\fpeval{#2-#4}}{+\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Csymbole}{\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}\\              
+              \xdef\Coeffa{\fpeval{#2-#4}}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\\
+              \ifboolKV[ClesEquation]{Bloc}{\Fdash{\mathcolor{Csymbole!30}{$\multido{\i=1+1}{\fpeval{\Coeffa-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}$}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\\}{}
+              \xdef\Coeffb{\fpeval{0-#3}}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}%\\
+              \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+              \\\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+                \ifboolKV[ClesEquation]{Entier}{%
+                \SSimpliTest{\Coeffb}{\Coeffa}%
+                \ifboolKV[ClesEquation]{Simplification}{%
+                \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+                }{}
+                }{}
+                }
+              \end{align*}
+            }{%ax+b=cx+d avec a<c              % Autre cas délicat
+              \begin{align*}%
+                \multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\\
+                \mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{#2-1}}{+\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{#2-1}}{+\useKV[ClesEquation]{Lettre}}}\multido{\i=1+1}{\fpeval{#4-#2}}{+\useKV[ClesEquation]{Lettre}}\\
+                \xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\multido{\i=1+1}{\fpeval{\Coeffa-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}% \\
+                \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+                \\\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}%\\
+                \ifboolKV[ClesEquation]{Entier}{%
+                \SSimpliTest{\Coeffb}{\Coeffa}%
+                \ifboolKV[ClesEquation]{Simplification}{%
+                \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
+                }{}
+                }{}
+                }
+              \end{align*}
+            }%
+          }%
+        }%
+      }%
+    \fi
+  }%
+
+
+\newcommand{\ResolEquationSymbole}[5][]{%
+  \useKVdefault[ClesEquation]%
+  \setKV[ClesEquation]{#1}%
+  \setKV[ClesEquation]{Fleches=false,FlecheDiv=false,Terme=false,Decomposition=false}
+  \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$
+      \EquaDeuxSymbole[#1]{#4}{#5}{#2}{#3}%
+    }%
+  }{%
+    \xintifboolexpr{#4=0}{%ax+b=0x+d
+      \EquaDeuxSymbole[#1]{#2}{#3}{}{#5}%
+    }
+    {%ax+b=cx+d$
+      \xintifboolexpr{#3=0}{%
+        \xintifboolexpr{#5=0}{%ax=cx
+          \EquaTroisSymbole[#1]{#2}{0}{#4}{}%
+        }%
+        {%ax=cx+d
+          \EquaTroisSymbole[#1]{#4}{#5}{#2}{}%
+        }%
+      }%
+      {\xintifboolexpr{#5=0}{%ax+b=cx
+          \EquaTroisSymbole[#1]{#2}{#3}{#4}{}%
+        }%
+        {%ax+b=cx+d -- ici
+          \xintifboolexpr{#2=#4}{%
+            \xintifboolexpr{#3=#5}{%b=d
+              L'équation $\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une infinité de solution.}%
+            {%b<>d
+              L'équation $\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ n'a aucune solution.%
+            }%
+          }{
+            %% Cas délicat
+            \xintifboolexpr{#2>#4}{%ax+b=cx+d avec a>c
+              \begin{align*}
+                \multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+                \mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{#4-1}}{+\useKV[ClesEquation]{Lettre}}}\multido{\i=1+1}{\fpeval{#2-#4}}{+\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Csymbole}{\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+                \xdef\Coeffa{\fpeval{#2-#4}}\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\\
+                \ifboolKV[ClesEquation]{Bloc}{%
+                \Fdash{$\mathcolor{Csymbole!30}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}}$}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\\
+                }{}%
+                \xdef\Coeffb{\fpeval{#5-#3}}\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}&=\num{\Coeffb}%\\
+                \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+                \\\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
+                \ifboolKV[ClesEquation]{Entier}{%
+                \SSimpliTest{\Coeffb}{\Coeffa}%
+                \ifboolKV[ClesEquation]{Simplification}{%
+                \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+                }{}
+                }{}
+                }
+              \end{align*}
+            }{%ax+b=cx+d avec a<c              % Autre cas délicat
+              \begin{align*}%
+                \multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+                \mathcolor{Csymbole}{\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{#2-1}}{+\useKV[ClesEquation]{Lettre}}}\multido{\i=1+1}{\fpeval{#4-#2}}{+\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+                \xdef\Coeffa{\fpeval{#4-#2}}\num{#3}&=\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+                \ifboolKV[ClesEquation]{Bloc}{%
+                \num{#3}&=\Fdash{$\mathcolor{Csymbole!30}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}}$}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+                }{}%
+                \xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}%\\
+                \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+                \\\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}%\\
+                \ifboolKV[ClesEquation]{Entier}{%
+                \SSimpliTest{\Coeffb}{\Coeffa}%
+                \ifboolKV[ClesEquation]{Simplification}{%
+                \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
+                }{}
+                }{}
+                }
+              \end{align*}
+            }%
+          }%
+        }%
+      }%
+    }%
+  }%
+}%
+
+
diff --git a/Master/texmf-dist/tex/latex/profcollege/PfC-EquationTerme1.tex b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationTerme1.tex
new file mode 100644
index 00000000000..f3930d0408b
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+++ b/Master/texmf-dist/tex/latex/profcollege/PfC-EquationTerme1.tex
@@ -0,0 +1,276 @@
+% Licence    : Released under the LaTeX Project Public License v1.3c
+% or later, see http://www.latex-project.org/lppl.txtf
+\newcommand{\EquaDeuxTerme}[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
+    \EquaDeuxTerme[#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{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
+        \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}\\
+          \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}&=\num{#5}\mathcolor{Cterme}{\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{\EquaTroisTerme}[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
+      \EquaTroisTerme[#1]{#4}{#5}{#2}{}%
+    \fi
+  \else
+  \xintifboolexpr{#2=0}{%b=cx
+    \EquaBase[#1]{#4}{}{}{#3}
+  }{%
+    \xintifboolexpr{#4=0}{%ax+b=0
+      \EquaDeuxTerme[#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{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
+            \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}\\
+                \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\\
+              \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}\\
+              \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=0\mathcolor{Cterme}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
+              \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 a<c              % Autre cas délicat
+              \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
+              \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}\\
+                \xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\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{\ResolEquationTerme}[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$
+      \EquaDeuxTerme[#1]{#4}{#5}{#2}{#3}%
+    }%
+  }{%
+    \xintifboolexpr{#4=0}{%ax+b=0x+d
+      \EquaDeuxTerme[#1]{#2}{#3}{}{#5}%
+    }
+    {%ax+b=cx+d$
+      \xintifboolexpr{#3=0}{%
+        \xintifboolexpr{#5=0}{%ax=cx
+          \EquaTroisTerme[#1]{#2}{0}{#4}{}%
+        }%
+        {%ax=cx+d
+          \EquaTroisTerme[#1]{#4}{#5}{#2}{}%
+        }%
+      }%
+      {\xintifboolexpr{#5=0}{%ax+b=cx
+          \EquaTroisTerme[#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{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
+              \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}\\
+                \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\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{#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}\tikzmark{F-\theNbequa}\\
+                \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{#5}\mathcolor{Cterme}{\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 a<c              % Autre cas délicat
+              \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
+              \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}\\
+                \xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\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}\\
+                \num{#3}\mathcolor{Cterme}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\\
+                \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/ProfCollege.sty b/Master/texmf-dist/tex/latex/profcollege/ProfCollege.sty
new file mode 100644
index 00000000000..30aa5d3e9d2
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/profcollege/ProfCollege.sty
@@ -0,0 +1,10542 @@
+% Author     : Christophe Poulain
+% Licence    : Released under the LaTeX Project Public License v1.3c
+% or later, see http://www.latex-project.org/lppl.txtf
+%%%%%%%
+% 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}[2021/01/18 v0.89 Aide pour l'utilisation de LaTeX au collège]
+
+\RequirePackage{mathtools}%Amélioration des rendus
+\RequirePackage{amssymb}
+
+% mathématiques
+\RequirePackage{siunitx}%unités SI
+\sisetup{%
+  locale=FR,
+  detect-all,%
+  output-decimal-marker={,},%
+  group-four-digits%
+}
+
+\DeclareSIUnit{\kmh}{\km\per\hour}
+\newcommand\speed[1]{\SI{#1}{\kmh}}
+\newcommand\Speed[1]{\SI[per-mode=symbol]{#1}{\kmh}}
+
+\RequirePackage[table,svgnames]{xcolor}%Gestion des couleurs
+\RequirePackage{xstring}%Gestion de chaines de caractères
+\RequirePackage{simplekv}%Gestion de paramètres sous forme de clés
+\RequirePackage{ifthen}
+\RequirePackage{modulus}%Pour certains calculs arithmétiques.
+\RequirePackage{xinttools}%Pour la création dynamique d'un tableau
+
+\newif\if@shellescape \@shellescapetrue
+\DeclareOption{nonshellescape}{\@shellescapefalse}
+\ProcessOptions\relax
+
+\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;}}
+\usempxclass{article}
+\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;}}
+\usempxclass{article}
+\usempxpackage[utf8]{inputenc}
+\usempxpackage[T1]{fontenc}
+\usempxpackage{fourier}
+\usempxpackage[french]{babel}
+\usempxpackage{pifont}
+\usempxpackage[locale=FR]{siunitx}
+\fi
+
+\RequirePackage{xintexpr}
+\RequirePackage{listofitems}%pour définir simplement la liste des données.
+\RequirePackage{datatool}
+\RequirePackage{multido}
+
+\RequirePackage{xlop}%Pour effectuer les calculs nécessaires.
+\opset{decimalsepsymbol={,}}%
+
+\RequirePackage{xfp}%Pour les calculs trigonométriques
+
+\RequirePackage[most]{tcolorbox}
+
+\RequirePackage{tikz}
+% https://tex.stackexchange.com/questions/349259/curved-arrow-describing-a-step-in-a-equation-derivation
+%https://tex.stackexchange.com/questions/58656/best-way-to-draw-a-chevron-diagram-using-tikz
+\usetikzlibrary{calc,arrows,tikzmark,chains,positioning,shapes.symbols}
+
+\RequirePackage{suffix}%pour la commande étoilée
+
+\RequirePackage{multicol}
+
+\RequirePackage{hhline}% Pour la cohabitation de cline avec les couleurs
+
+\RequirePackage{iftex}
+
+\RequirePackage{stackengine}
+\RequirePackage[thicklines]{cancel}
+
+\ifpdftex
+\RequirePackage[babel=true,kerning=true]{microtype}%Pour gérer le souci du ; dans tikz avec pdftex...
+\fi
+
+% 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);}
+\everyendmplib{endfig;}
+\fi
+
+%%%%% Quelques besoins particuliers
+
+\def\bla{}%JCC :) Pour les tests sur arguments vides
+
+%% Colorer en mode mathématique. \color ne gère pas les espaces propres au mode mathématique. Donc besoin de changer
+% https://tex.stackexchange.com/questions/21598/how-to-color-math-symbols
+\makeatletter
+\def\mathcolor#1#{\@mathcolor{#1}}
+\def\@mathcolor#1#2#3{%
+  \protect\leavevmode
+  \begingroup
+    \color#1{#2}#3%
+  \endgroup
+}
+\makeatother
+
+% Colorer uniquement la barre de soulignement
+% https://tex.stackexchange.com/questions/9466/color-underline-a-formula/153884
+\def\mathunderline#1#2{\color{#1}\underline{{\color{black}#2}}\color{black}}
+
+% Ecrire des lignes d'équations
+\catcode`\@=11
+\def\Eqalign#1{\null\,\vcenter{\openup\jot\m@th\ialign{
+      \strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil
+      &&\quad\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$
+      \hfil\crcr #1\crcr}}\,}
+\catcode`\@=12
+
+%%%%%%%%%%%%%%%%%%%%%
+%% Commandes "utiles"
+%%%%%%%%%%%%%%%%%%%%%
+%encadrer avec des "sommets arrondis"
+\newsavebox{\logobox}
+
+\newcommand{\Logo}[2]{%
+\setbox1=\hbox{\includegraphics[scale=#2]{#1}}
+\begin{tikzpicture}%
+\clip[rounded corners=5mm] (0,0) rectangle (\wd1,\ht1);
+\node[xshift=0.5\wd1, yshift=0.5\ht1, inner xsep=0pt, inner ysep=0pt] (box) {%
+\includegraphics[scale=#2]{#1}%
+};%
+\end{tikzpicture}%
+}
+
+\makeatletter
+\def\Dotfill{%
+\leavevmode
+\cleaders \hb@xt@ .44em{\hss\xleaders\hrule width0.33em\hss}\hfill
+\kern\z@}
+\makeatother
+
+\newcommand\pointilles[1][]{%
+  \ifx\bla#1\bla%
+  \Dotfill%
+  \else%
+  \hbox to#1{\Dotfill}%
+  \fi
+}
+
+\newcommand\Lignespointilles[1]{%
+  \xintFor* ##1 in {\xintSeq {1}{#1}}\do{
+    \pointilles\par%
+  }
+}
+
+%%%%%%%%%%%%%%%%%
+% Tables Addition-Multiplication
+%%%%%%%%%%%%%%%%%
+\setKVdefault[Tables]{Addition=false,Multiplication=true,Seul=false,Debut=0,Fin=10,Couleur=white}
+
+% pour mémoire
+\newcommand\TableMultiplicationComplete{%
+  \xdef\NbColTabMul{\fpeval{\useKV[Tables]{Fin}+1-\useKV[Tables]{Debut}}}%
+  \begin{tabular}{|>{\columncolor{gray!15}\centering\arraybackslash}p{1.5em}|*{\NbColTabMul}{>{\centering\arraybackslash}p{1.5em}|}}%
+    \hline
+    $\times$\xintFor* ##1 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
+    &\cellcolor{gray!15}\fpeval{##1}
+      }
+    \\
+    \hline
+    \xintFor* ##1 in {\xintSeq {0}{10}}\do{%
+    ##1\xintFor* ##2 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
+    &\fpeval{##2*##1}
+      }
+    \\
+    \hline
+    }
+  \end{tabular}%
+}
+%%%%
+
+\newcommand\TableMultiplicationCompleteColore{%
+  \xdef\NbColTabMul{\fpeval{\useKV[Tables]{Fin}+1-\useKV[Tables]{Debut}}}%
+  \begin{tabular}{|>{\columncolor{gray!15}\centering\arraybackslash}p{1.5em}|*{\NbColTabMul}{>{\centering\arraybackslash}p{1.5em}|}}%
+    \hline
+    $\times$\xintFor* ##1 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
+    &\cellcolor{gray!15}\fpeval{##1}
+      }
+    \\
+    \hline
+    \xintFor* ##1 in {\xintSeq {0}{10}}\do{%
+    ##1\xintFor* ##2 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
+    &\xintifboolexpr{##2<##1}{\cellcolor{\useKV[Tables]{Couleur}!\fpeval{##1*10}}}{\xintifboolexpr{##2>##1}{\cellcolor{\useKV[Tables]{Couleur}!\fpeval{##2*10}}}{}}\fpeval{##2*##1}
+      }
+    \\
+    \hline
+    }
+  \end{tabular}%
+}
+
+\newcommand\TableAdditionComplete{%
+  \xdef\NbColTabMul{\fpeval{\useKV[Tables]{Fin}+1-\useKV[Tables]{Debut}}}%
+  \begin{tabular}{|>{\columncolor{gray!15}\centering\arraybackslash}p{1.5em}|*{\NbColTabMul}{>{\centering\arraybackslash}p{1.5em}|}}%
+    \hline
+    $+$\xintFor* ##1 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
+    &\cellcolor{gray!15}\fpeval{##1}
+      }
+    \\
+    \hline
+    \xintFor* ##1 in {\xintSeq {0}{10}}\do{%
+    ##1\xintFor* ##2 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
+    &\fpeval{##2+##1}
+      }
+    \\
+    \hline
+    }
+  \end{tabular}%
+}
+
+\newcommand\TableMultiplicationSeule[1]{%
+  \ensuremath{%
+    \begin{array}{ccccc}%
+      \xintFor* ##1 in {\xintSeq
+      {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{
+      ##1&\times&#1&=&\fpeval{##1*#1}\\
+      }
+    \end{array}
+  }%
+}%
+
+\newcommand\TableAdditionSeule[1]{%
+  \ensuremath{%
+    \begin{array}{ccccc}
+      \xintFor* ##1 in {\xintSeq
+      {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{
+      ##1&+&#1&=&\fpeval{##1+#1}\\
+      }
+    \end{array}
+  }%
+}%
+
+
+\newcommand\Tables[2][]{%
+  \useKVdefault[Tables]%
+  \setKV[Tables]{#1}%
+  \ifboolKV[Tables]{Seul}{%
+    \ifboolKV[Tables]{Addition}{%
+      \TableAdditionSeule{#2}%
+    }{%
+      \TableMultiplicationSeule{#2}%
+    }%
+  }{
+    \ifboolKV[Tables]{Addition}{%
+      \TableAdditionComplete%
+    }{%
+      \TableMultiplicationCompleteColore%
+    }%
+  }%
+}%
+
+%%%%%%%%%%%%%%
+% 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%
+  \readlist*\ListeLaby{#2}%
+  \ifboolKV[Labyrinthe]{Passages}{%
+    \readlist*\ListeLabySol{#3}%
+  }{}%
+  \xdef\LabyLong{\useKV[Labyrinthe]{Longueur}}%
+  \xdef\LabyHaut{\useKV[Labyrinthe]{Hauteur}}%
+  \xdef\TotalLaby{\fpeval{3*\useKV[Labyrinthe]{Colonnes}-2}}%
+  \xdef\CouleurF{\useKV[Labyrinthe]{CouleurF}}%
+  \xdef\MotifTexte{\useKV[Labyrinthe]{Texte}}%
+  \xintifboolexpr{\ListeLabylen=\fpeval{\useKV[Labyrinthe]{Lignes}*\useKV[Labyrinthe]{Colonnes}}}{%
+    \begin{tikzpicture}[remember picture]
+      % on dessine les cadres
+      \foreach \compteurv in {1,...,\useKV[Labyrinthe]{Lignes}}{%
+        \foreach \compteurh in {1,...,\useKV[Labyrinthe]{Colonnes}}{%
+          \xdef\ColorFill{\ListeLaby[\fpeval{\useKV[Labyrinthe]{Colonnes}*(\compteurv-1)+\compteurh},2]}%
+          \node[fill=\ColorFill,draw,minimum height=\LabyHaut*1cm,minimum width=\LabyLong*1cm,name=A-\compteurh-\compteurv] at
+          (\fpeval{\LabyLong+\useKV[Labyrinthe]{EcartH}}*\compteurh,-\fpeval{\LabyHaut+\useKV[Labyrinthe]{EcartV}}*\compteurv) {\ListeLaby[\fpeval{\useKV[Labyrinthe]{Colonnes}*(\compteurv-1)+\compteurh},1]};%
+        }%
+      }%
+      % on dessine les flèches
+      \foreach \compteurv in {1,...,\fpeval{\useKV[Labyrinthe]{Lignes}-1}}{%
+        \foreach \compteurh in {1,...,\useKV[Labyrinthe]{Colonnes}}{%
+          \ifboolKV[Labyrinthe]{Passages}{%
+            \xdef\NomNode{\ListeLabySol[1,\fpeval{\TotalLaby*(\compteurv-1)+\useKV[Labyrinthe]{Colonnes}+2*(\compteurh-1)}]}%
+            \draw[\CouleurF,line width=1pt,stealth-stealth] (A-\compteurh-\compteurv) -- node[fill=white,midway]{\MotifTexte\NomNode}(A-\compteurh-\fpeval{\compteurv+1});%
+          }{%
+            \draw[\CouleurF,line width=1pt,stealth-stealth] (A-\compteurh-\compteurv) -- (A-\compteurh-\fpeval{\compteurv+1});%
+          }%
+        }
+      }
+      \foreach \compteurv in {1,...,\useKV[Labyrinthe]{Lignes}}{%
+        \foreach \compteurh in {1,...,\fpeval{\useKV[Labyrinthe]{Colonnes}-1}}{%
+          \ifboolKV[Labyrinthe]{Passages}{%
+            \xdef\NomNode{\ListeLabySol[1,\fpeval{\TotalLaby*(\compteurv-1)+\compteurh}]}%
+            \draw[\CouleurF,line width=1pt,stealth-stealth]
+            (A-\compteurh-\compteurv) -- node[fill=white,midway]{\MotifTexte\NomNode}(A-\fpeval{\compteurh+1}-\compteurv);
+          }{%
+            \draw[\CouleurF,line width=1pt,stealth-stealth]
+            (A-\compteurh-\compteurv) -- (A-\fpeval{\compteurh+1}-\compteurv);
+          }%
+        }
+      }
+      \foreach \compteurv in {2,...,\fpeval{\useKV[Labyrinthe]{Lignes}}}{%
+        \foreach \compteurh in {1,...,\fpeval{\useKV[Labyrinthe]{Colonnes}-1}}{%
+          \draw[\CouleurF,line width=1pt,stealth-stealth] (A-\compteurh-\compteurv) -- (A-\fpeval{\compteurh+1}-\fpeval{\compteurv-1});
+        }
+      }
+      \foreach \compteurv in {1,...,\fpeval{\useKV[Labyrinthe]{Lignes}-1}}{%
+        \foreach \compteurh in {1,...,\fpeval{\useKV[Labyrinthe]{Colonnes}-1}}{%
+          \ifboolKV[Labyrinthe]{Passages}{%
+            \xdef\NomNode{\ListeLabySol[1,\fpeval{\TotalLaby*(\compteurv-1)+\useKV[Labyrinthe]{Colonnes}+2*(\compteurh-1)+1}]}%
+            \draw[\CouleurF,line width=1pt,stealth-stealth] (A-\compteurh-\compteurv) -- node[fill=white,midway]{\MotifTexte\NomNode}(A-\fpeval{\compteurh+1}-\fpeval{\compteurv+1});
+          }{%
+            \draw[\CouleurF,line width=1pt,stealth-stealth] (A-\compteurh-\compteurv) -- (A-\fpeval{\compteurh+1}-\fpeval{\compteurv+1});
+          }%          
+        }%
+      }%
+    \end{tikzpicture}
+  }{\textbf{! Le nombre d'informations n'est pas compatible avec les
+      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}
+
+\tcbset{calbackground/.style={
+    enhanced,
+    leftright skip=0.25cm,beforeafter skip=0pt,
+    toptitle=0mm,bottomtitle=0mm,
+    right=2mm,left=2mm,
+    top=1pt,
+    bottom=0.25cm,
+    boxsep=0pt,
+    boxrule=0mm,
+    sharp corners,
+    sidebyside,
+    sidebyside gap=2mm,
+    lefthand ratio=0.6,
+    bicolor,
+    colback=black!10!white,
+    colbacklower=greenish,
+    colframe=white,
+    autoparskip,
+  }}
+
+\newtcbox{\KY}[1][]{
+  enhanced,
+  on line,
+  arc=2pt,outer arc=2pt,
+  boxrule=0pt,bottomrule=0.25mm,rightrule=0.2mm,
+  boxsep=0pt,left=0pt,right=0pt,top=1pt,bottom=1pt,
+  interior style={top color=blackish,bottom color=blackened},
+  colframe=greyish,
+  width=2.5em,
+  tcbox width=forced center,
+  equal height group=K,
+  valign=center,
+  fontupper=\footnotesize\sffamily,
+  coltext=orangeish,
+  before upper=\vrule width 0pt height 2ex depth 1ex\relax,
+}
+
+\newtcbox{\KYm}[1][]{
+  enhanced,
+  on line,
+  arc=2pt,outer arc=2pt,
+  boxrule=0pt,bottomrule=0.25mm,rightrule=0.2mm,
+  boxsep=0pt,left=0pt,right=0pt,top=1pt,bottom=1pt,
+  interior style={top color=blackish,bottom color=blackened},
+  colframe=greyish,
+  width=2.5em,
+  tcbox width=forced center,
+  equal height group=K,
+  valign=center,
+  fontupper=\footnotesize\sffamily,
+  coltext=orangeish,
+  before upper=\vrule width 0pt height 2ex depth 1ex\relax$,
+  after upper=$,
+}
+
+\newtcbox{\KN}{
+  enhanced,
+  on line,
+  arc=2pt,outer arc=2pt,
+  boxrule=0pt,bottomrule=0.25mm,rightrule=0.2mm,
+  boxsep=0pt,left=0pt,right=0pt,top=1pt,bottom=1pt,
+  interior style={top color=blackish,bottom color=blackened},
+  colframe=greyish,
+  width=1.5em,
+  tcbox width=forced center,
+  equal height group=K,
+  valign=center,
+  fontupper=\footnotesize\sffamily,
+  coltext=whiteish,
+  before upper=\vrule width 0pt height 2ex depth 1ex\relax,
+}
+
+\parindent0pt
+
+\newtcolorbox{calc}[1][]{%
+  enhanced,bicolor,
+  boxsep=0pt,
+  boxrule=0pt,
+  top=6pt,bottom=0pt,left=6pt,right=0pt,
+  sharp corners,
+  frame empty,
+  colback=black!10,
+  colbacklower=greenish,
+  sidebyside,
+  sidebyside align=top seam,
+  sidebyside gap=0pt,
+  righthand width=50.7mm,
+  before lower=\begin{tabular}{@{}l@{}},
+  after lower=\end{tabular},
+  overlay={\node[inner sep=0pt, outer sep=0pt, text height=5pt, text
+    depth=1pt, text width=50.7mm, fill=greenish, anchor=north
+    east, font=\sffamily\tiny\bfseries, align=flush right]
+    at (frame.north east) {#1};}
+}
+
+\def\MPCalculatrice#1#2{
+  % #1 Calcul %2 réponse
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    input PfC-Calculatrice;
+    LCD(#1)(#2);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Calculatrice;}]
+    LCD(#1)(#2);    
+  \end{mpost}
+  \fi
+}
+
+\setKVdefault[ClesCalculatrice]{Ecran=false}
+
+\newcommand\Calculatrice[2][]{%
+  \setstackgap{L}{0.775\baselineskip}%
+  \useKVdefault[ClesCalculatrice]%
+  \setKV[ClesCalculatrice]{#1}%
+  \ifboolKV[ClesCalculatrice]{Ecran}{%
+    \setsepchar[*]{,*/}%
+    \readlist\ListeCalc{#2}%
+    \MPCalculatrice{\ListeCalc[1,1]}{\ListeCalc[1,2]}%
+  }{%
+    \setsepchar[*]{,*/}%
+    \readlist\ListeCalc{#2}%
+    \foreachitem\compteur\in\ListeCalc{\xintifboolexpr{\listlen\ListeCalc[\compteurcnt]=2}{\Longstack{{\tiny\ListeCalc[\compteurcnt,1]} \KN{\ListeCalc[\compteurcnt,2]}}}{\Longstack{{\tiny\ListeCalc[\compteurcnt,2]} \KY{\ListeCalc[\compteurcnt,3]}}}%
+    }%
+  }%
+  \setstackgap{L}{\baselineskip}%
+}%
+
+
+%%%%%%%%%%%%%%%%
+%%% 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}}
+\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}
+
+\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\MPHorloge#1#2#3{
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+  marque_horloge=1;
+  save Hor;
+  picture Hor;
+  path gdeaig,pteaig,trot;
+  pair centrehorloge;
+  centrehorloge=(0,0);
+  path tourhorloge;
+  tourhorloge=cercles(centrehorloge,marque_horloge*cm);
+  Hor=image(
+  %% dessin de l'horloge
+  draw tourhorloge;
+  for i=0 upto 59:
+  if (i mod 5)=0:
+  if (i mod 15)=0:
+  draw pointarc(tourhorloge,6*i)--(pointarc(tourhorloge,6*i) shifted (7*unitvector(centrehorloge-pointarc(tourhorloge,6*i)))) withpen pencircle scaled 2bp;
+  else:
+  draw pointarc(tourhorloge,6*i)--(pointarc(tourhorloge,6*i) shifted (5*unitvector(centrehorloge-pointarc(tourhorloge,6*i)))) withpen pencircle scaled 1.5bp;
+  fi;
+  else:
+  draw pointarc(tourhorloge,6*i)--(pointarc(tourhorloge,6*i) shifted (3*unitvector(centrehorloge-pointarc(tourhorloge,6*i))));
+  fi;
+  endfor;
+  path graduhorloge;
+  graduhorloge=cercles(centrehorloge,marque_horloge*cm+5*abs(unitvector(centrehorloge-pointarc(tourhorloge,0))));
+  % 
+  marque_p:="plein";
+  pointe(centrehorloge);
+  marque_p:="rien";
+  %% placement des aiguilles
+  gdeaig=centrehorloge--(pointarc(tourhorloge,0) shifted (7*unitvector(centrehorloge-pointarc(tourhorloge,0))));
+  pteaig=centrehorloge--(pointarc(tourhorloge,0) shifted (18*unitvector(centrehorloge-pointarc(tourhorloge,0))));
+  trot=centrehorloge--(pointarc(tourhorloge,0) shifted (10*unitvector(centrehorloge-pointarc(tourhorloge,0))));
+  draw rotation(trot,centrehorloge,90-6*#3) withpen pencircle scaled0.4;
+  draw rotation(gdeaig,centrehorloge,90-6*#2) withpen pencircle scaled1.25;
+  draw rotation(pteaig,centrehorloge,90-30*(#1+#2/60)) withpen pencircle scaled 2bp;
+  );
+  draw Hor;
+  \end{mplibcode}
+\else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    marque_horloge=1;
+    save Hor;
+    picture Hor;
+    path gdeaig,pteaig,trot;
+    pair centrehorloge;
+    centrehorloge=(0,0);
+    path tourhorloge;
+    tourhorloge=cercles(centrehorloge,marque_horloge*cm);
+    Hor=image(
+    %% dessin de l'horloge
+    draw tourhorloge;
+    for i=0 upto 59:
+    if (i mod 5)=0:
+    if (i mod 15)=0:
+    draw pointarc(tourhorloge,6*i)--(pointarc(tourhorloge,6*i) shifted (7*unitvector(centrehorloge-pointarc(tourhorloge,6*i)))) withpen pencircle scaled 2bp;
+    else:
+    draw pointarc(tourhorloge,6*i)--(pointarc(tourhorloge,6*i) shifted (5*unitvector(centrehorloge-pointarc(tourhorloge,6*i)))) withpen pencircle scaled 1.5bp;
+    fi;
+    else:
+    draw pointarc(tourhorloge,6*i)--(pointarc(tourhorloge,6*i) shifted (3*unitvector(centrehorloge-pointarc(tourhorloge,6*i))));
+    fi;
+    endfor;
+    path graduhorloge;
+    graduhorloge=cercles(centrehorloge,marque_horloge*cm+5*abs(unitvector(centrehorloge-pointarc(tourhorloge,0))));
+    %
+    marque_p:="plein";
+    pointe(centrehorloge);
+    marque_p:="rien";
+    %% placement des aiguilles
+    gdeaig=centrehorloge--(pointarc(tourhorloge,0) shifted (7*unitvector(centrehorloge-pointarc(tourhorloge,0))));
+    pteaig=centrehorloge--(pointarc(tourhorloge,0) shifted (18*unitvector(centrehorloge-pointarc(tourhorloge,0))));
+    trot=centrehorloge--(pointarc(tourhorloge,0) shifted (10*unitvector(centrehorloge-pointarc(tourhorloge,0))));
+    draw rotation(trot,centrehorloge,90-6*#3) withpen pencircle scaled0.4;
+    draw rotation(gdeaig,centrehorloge,90-6*#2) withpen pencircle scaled1.25;
+    draw rotation(pteaig,centrehorloge,90-30*(#1+#2/60)) withpen pencircle scaled 2bp;
+    );
+    draw Hor;
+  \end{mpost}
+  \fi
+}
+
+\newcommand\QFNumeration{%
+  \begin{CadreNombre}
+    {\Large LE NOMBRE DU JOUR est : }
+    \tcbox[BoiteExpression]{\num{\ListeFlash[1,1]}}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie1]
+      $\square$ \textbf{Le chiffre des \ListeFlash[1,2] est :}
+      \tcbox[BoiteExpression]{\phantom{1500000}}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie2]
+      $\square$ \textbf{Le chiffre \ListeFlash[1,3] représente le
+        chiffre des :}
+      \tcbox[BoiteExpression]{\phantom{1500000}}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie3]
+      $\square$ \textbf{Le nombre de \ListeFlash[1,4] est :}
+      \tcbox[BoiteExpression]{\phantom{1500000}}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie4]
+      $\square$ \textbf{Le nombre de \ListeFlash[1,5] est :}
+      \tcbox[BoiteExpression]{\phantom{1500000}}
+    \end{tcolorbox}
+  \end{CadreNombre}
+}
+
+\newcommand\QFHeure{%
+  \begin{CadreNombre}
+    {\Large L'HEURE DU JOUR est : }\raisebox{-0.9cm}{\MPHorloge{\NbHeures}{\NbMinutes}{\NbSecondes}}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie1]
+      $\square$ \textbf{\ListeFlash[1,2] :}
+      \tcbox[BoiteExpression]{\phantom{1500000000}}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie2]
+      $\square$ \textbf{\ListeFlash[1,3] :}
+      \tcbox[BoiteExpression]{\phantom{1500000000}}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie3]
+      $\square$ \textbf{\ListeFlash[1,4] :}
+      \tcbox[BoiteExpression]{\phantom{\hbox to4.5em{15}}}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie4]
+      $\square$ \textbf{\ListeFlash[1,5] :}
+      \tcbox[BoiteExpression]{\phantom{\hbox to4.5em{1500000}}}
+    \end{tcolorbox}
+  \end{CadreNombre}
+}
+
+\newcommand\QFMesure{%
+  \begin{CadreNombre}
+    {\Large LA MESURE DU JOUR est : }
+    \tcbox[BoiteExpression]{\ListeFlash[1,1]}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie1]
+      $\square$ \textbf{Convertis la en \ListeFlash[1,2] :}
+      \tcbox[BoiteExpression]{\phantom{1500000000}}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie2]
+      $\square$ \textbf{Convertis la en \ListeFlash[1,3] :}
+      \tcbox[BoiteExpression]{\phantom{1500000000}}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie3]
+      $\square$ \textbf{Ajoute lui \ListeFlash[1,4] :}
+      \tcbox[BoiteExpression]{\phantom{\hbox to5em{1500000}}}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie4]
+      $\square$ \textbf{Enlève lui \ListeFlash[1,5] :}
+      \tcbox[BoiteExpression]{\phantom{\hbox to5em{1500000}}}
+    \end{tcolorbox}
+  \end{CadreNombre}
+}
+
+\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}{}
+          }{%
+            \xintifboolexpr{\s = \ListeFlashlen}{%
+              \node[arrow,on chain] {\Huge\bfseries?};
+            }{%
+              \node[arrow,on chain] {\ListeFlash[\s]};
+              \ifboolKV[ClesFlash]{Pause}{\pause}{}
+            }
+          }
+        }
+      \end{scope}
+    \end{tikzpicture}
+}
+
+\newcommand\QFDecimal{%
+  \begin{CadreNombre}
+    {\Large LE NOMBRE DU JOUR est : }
+    \tcbox[BoiteExpression]{\num{\ListeFlash[1,1]}}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie1]
+      \textbf{\'Ecriture en fraction décimale :}
+      \tcbox[BoiteExpression]{$\dfrac{\phantom{1000000}}{\phantom{1000000}}$}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie2]
+      \begin{tabular}{c}
+        \textbf{Partie}\\
+        \textbf{entière}
+      \end{tabular} \textbf{: }
+      \tcbox[BoiteExpression]{\phantom{100000}}\hfill%
+      \begin{tabular}{c}
+        \textbf{Partie}\\
+        \textbf{décimale}
+      \end{tabular} \textbf{: }
+      \tcbox[BoiteExpression]{\phantom{100000}}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie3]
+      \textbf{\useKV[ClesFlash]{Operation} le par
+        \ListeFlash[1,2] :} \tcbox[BoiteExpression]{\phantom{1000000000}}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie4]
+      \textbf{Trouve le nombre entier le plus proche :} \tcbox[BoiteExpression]{\phantom{10000000}}
+    \end{tcolorbox}
+  \end{CadreNombre}
+}
+
+\newcommand\QFMental{%
+  \begin{CadreNombre}
+    {\Large LE NOMBRE DU JOUR est : }
+    \tcbox[BoiteExpression]{\ListeFlash[1,1]}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie1]
+      $\square$ \textbf{Ajoute lui}
+      \tcbox[BoiteExpression]{\ListeFlash[1,2]}\hfill$\square$
+      \textbf{Soustrais lui}  \tcbox[BoiteExpression]{\ListeFlash[1,3]}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie2]
+      $\square$ \textbf{Multiplie le par }
+      \tcbox[BoiteExpression]{\ListeFlash[1,4]}\hfill$\square$
+      \textbf{Divise le par } \tcbox[BoiteExpression]{\ListeFlash[1,5]}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie3]
+      $\square$ \textbf{Trouve}
+      \tcbox[BoiteExpression]{\ListeFlash[1,6]}
+      \textbf{\% de ce nombre.}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie4]
+      $\square$ \textbf{Trouve } \tcbox[BoiteExpression]{\ListeFlash[1,7]}
+      \textbf{de ce nombre.}
+    \end{tcolorbox}
+  \end{CadreNombre}
+}
+
+\newcommand\QFExpression{%
+  \begin{CadreNombre}
+    {\Large L'EXPRESSION DU JOUR est : }
+    \tcbox[BoiteExpression]{\ListeFlash[1,1]}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie1]
+      $\square$ \textbf{Ajoute lui}
+      \tcbox[BoiteExpression]{\ListeFlash[1,2]}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie2]
+      $\square$ \textbf{Soustrais lui}
+      \tcbox[BoiteExpression]{\ListeFlash[1,3]}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie3]
+      $\square$ \textbf{Multiplie la par}
+      \tcbox[BoiteExpression]{\ListeFlash[1,4]}
+    \end{tcolorbox}
+    \ifboolKV[ClesFlash]{Pause}{\pause}{}
+    \begin{tcolorbox}[ExpressionSerie4]
+      $\square$ \textbf{\'Evalue la lorsque} \tcbox[BoiteExpression]{\ListeFlash[1,5]}
+    \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}}
+  \ifboolKV[ClesFlash]{Evaluation}{%
+    \ifboolKV[ClesFlash]{Numeration}{%
+      \setsepchar[*]{,*/}%
+      \readlist*\ListeFlash{#2}%
+      \QFNumeration%
+    }{%
+      \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]%
+        \QFHeure%
+      }{%
+        \ifboolKV[ClesFlash]{Mesure}{%
+          \setsepchar[*]{,*/}%
+          \readlist*\ListeFlash{#2}%
+          \QFMesure%
+        }{%
+          \ifboolKV[ClesFlash]{Daily}{%
+            \setsepchar[*]{/}%
+            \readlist*\ListeFlash{#2}%
+            \QFDaily%
+          }{%
+            \ifboolKV[ClesFlash]{Decimal}{%
+              \setsepchar[*]{,*/}%
+              \readlist*\ListeFlash{#2}%
+              \begin{frame}
+                \QFDecimal%
+              \end{frame}
+            }{%
+              \ifboolKV[ClesFlash]{Mental}{%
+                \setsepchar[*]{,*/}%
+                \readlist*\ListeFlash{#2}%
+                \QFMental%
+              }{%
+                \ifboolKV[ClesFlash]{Expression}{%
+                  \setsepchar[*]{,*/}%
+                  \readlist*\ListeFlash{#2}%
+                  \QFExpression%
+                }{%
+                  \setsepchar[*]{/}%
+                  \readlist*\ListeFlash{#2}%
+                  \ifboolKV[ClesFlash]{Simple}{%
+                    \ListeFlash[1]
+                    \begin{tcolorbox}[valign=center]
+                      \ListeFlash[2]
+                    \end{tcolorbox}
+                  }{%
+                    \setsepchar[*]{*/}%
+                    \readlist*\ListeFlash{#2}%
+                    \ifboolKV[ClesFlash]{Kahout}{%
+                      \setsepchar[*]{*/}%
+                      \readlist*\ListeFlash{#2}%
+                      \begin{tcolorbox}[halign=center,valign=center]
+                        \ListeFlash[1,1]
+                      \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]
+                        \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[*]{,*/}%
+      \readlist*\ListeFlash{#2}%
+      \begin{frame}
+        \QFNumeration%
+      \end{frame}
+    }{%
+      \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}
+          \QFHeure%
+        \end{frame}
+      }{%
+        \ifboolKV[ClesFlash]{Mesure}{%
+          \setsepchar[*]{,*/}%
+          \readlist*\ListeFlash{#2}%
+          \begin{frame}
+            \QFMesure%
+          \end{frame}
+        }{%
+          \ifboolKV[ClesFlash]{Daily}{%
+            \setsepchar[*]{/}%
+            \readlist*\ListeFlash{#2}%
+            \begin{frame}
+              \QFDaily
+            \end{frame}
+          }{%
+            \ifboolKV[ClesFlash]{Decimal}{%
+              \setsepchar[*]{,*/}%
+              \readlist*\ListeFlash{#2}%
+              \begin{frame}
+                \QFDecimal%
+              \end{frame}
+            }{%
+              \ifboolKV[ClesFlash]{Mental}{%
+                \setsepchar[*]{,*/}%
+                \readlist*\ListeFlash{#2}%
+                \begin{frame}
+                  \QFMental%
+                \end{frame}
+              }{
+                \ifboolKV[ClesFlash]{Expression}{%
+                  \setsepchar[*]{,*/}%
+                  \readlist*\ListeFlash{#2}%
+                  \begin{frame}
+                    \QFExpression%
+                  \end{frame}
+                }{%
+                  \setsepchar[*]{/}%
+                  \readlist*\ListeFlash{#2}%
+                  \ifboolKV[ClesFlash]{Simple}{%
+                    \begin{frame}
+                      \ListeFlash[1]
+                      \begin{tcolorbox}[valign=center]
+                        \ListeFlash[2]
+                      \end{tcolorbox}
+                    \end{frame}
+                  }{%
+                    \setsepchar[*]{,*/}%
+                    \readlist*\ListeFlash{#2}%
+                    \ifboolKV[ClesFlash]{Kahout}{%
+                      \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=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[*]{*/}%
+                      \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}
+                    }%
+                  }%
+                }%
+              }%
+            }
+          }%
+        }%
+      }%
+    }%
+  }%
+}%
+
+%%%%%%%%%%%%%
+%%% Fractions
+%%%%%%%%%%%%%
+\setKVdefault[ClesFraction]{Rayon=2cm,Disque,Regulier=false,Segment=false,Rectangle=false,Longueur=5cm,Largeur=2cm,Cotes=5,Couleur=green,Reponse=false,Multiple=1}
+
+\def\MPFractionRegulier#1#2#3#4#5{
+  % #1 rayon, #2 nb côtés, #3 num, #4 deno, #5 couleur
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    pair O,A[],B[];
+    O=u*(0,0);
+    path cc,cd;
+    cc=cercles(O,#1);
+    for k=0 upto #2:
+    A[k]=pointarc(cc,k*(360/#2));
+    endfor;
+    cd=polygone(A0 for k=1 upto #2-1:,A[k] endfor);
+    for k=0 upto #4-1:
+    B[k]=point(k*(#2/#4)) of cd;
+    endfor;
+    remplis O--arccercle(B[0],B[#3],O)--cycle withcolor #5;
+    %fi;
+    clip currentpicture to cd;
+    draw polygone(A0 for k=1 upto #2:,A[k] endfor);
+    if #4>1:
+    for k=0 upto #4-1:
+    draw segment(O,B[k]) cutafter cd;
+    endfor;
+    fi;
+  \end{mplibcode}
+  \else
+\begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    pair O,A[],B[];
+    O=u*(0,0);
+    path cc,cd;
+    cc=cercles(O,#1);
+    for k=0 upto #2:
+    A[k]=pointarc(cc,k*(360/#2));
+    endfor;
+    cd=polygone(A0 for k=1 upto #2-1:,A[k] endfor);
+    for k=0 upto #4-1:
+    B[k]=point(k*(#2/#4)) of cd;
+    endfor;
+    remplis O--arccercle(B[0],B[#3],O)--cycle withcolor #5;
+    %fi;
+    clip currentpicture to cd;
+    draw polygone(A0 for k=1 upto #2:,A[k] endfor);
+    if #4>1:
+    for k=0 upto #4-1:
+    draw segment(O,B[k]) cutafter cd;
+    endfor;
+    fi;
+  \end{mpost}
+  \fi
+}
+
+\def\MPFractionRectangle#1#2#3#4#5#6{%
+  % #1 longueur, #2 largeur, #3 num, #4 deno, #5 couleur, #6 multiple
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    pair A,B,C,D,M[],N[],R[],S[];
+    A=(1,1);
+    B-A=(#1,0);
+    C-B=(0,#2);
+    D-C=A-B;
+    numeric parts;
+    parts=(#4 div #6);
+    for k=0 upto parts:
+    M[k]=(k/parts)[A,B];
+    N[k]=(k/parts)[D,C];
+    endfor;
+    if #6>1:
+    for k=0 upto #6:
+    R[k]=(k/#6)[A,D];
+    S[k]=(k/#6)[B,C];
+    endfor;
+    fi;
+    if #6=1:
+    remplis polygone(A,M[#3],N[#3],D) withcolor #5;
+    else:
+    DDiv=#3 div parts;
+    MMod=#3 mod parts;
+    remplis polygone(A,B,S[DDiv],R[DDiv]) withcolor #5;
+    remplis
+    polygone(R[DDiv],(xpart(M[MMod]),ypart(R[DDiv])),(xpart(M[MMod]),ypart(R[DDiv+1])),R[DDiv+1]) withcolor #5;
+    fi;
+    draw polygone(A,B,C,D);
+    for k=1 upto (parts-1):
+    draw segment(M[k],N[k]);
+    endfor;
+    if #6>1:
+    for k=1 upto (#6-1):
+    draw segment(R[k],S[k]);
+    endfor;
+    fi;
+  \end{mplibcode}
+  \else
+\begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    pair A,B,C,D,M[],N[],R[],S[];
+    A=(1,1);
+    B-A=(#1,0);
+    C-B=(0,#2);
+    D-C=A-B;
+    numeric parts;
+    parts=(#4 div #6);
+    for k=0 upto parts:
+    M[k]=(k/parts)[A,B];
+    N[k]=(k/parts)[D,C];
+    endfor;
+    if #6>1:
+    for k=0 upto #6:
+    R[k]=(k/#6)[A,D];
+    S[k]=(k/#6)[B,C];
+    endfor;
+    fi;
+    if #6=1:
+    remplis polygone(A,M[#3],N[#3],D) withcolor #5;
+    else:
+    DDiv=#3 div parts;
+    MMod=#3 mod parts;
+    remplis polygone(A,B,S[DDiv],R[DDiv]) withcolor #5;
+    remplis
+    polygone(R[DDiv],(xpart(M[MMod]),ypart(R[DDiv])),(xpart(M[MMod]),ypart(R[DDiv+1])),R[DDiv+1]) withcolor #5;
+    fi;
+    draw polygone(A,B,C,D);
+    for k=1 upto (parts-1):
+    draw segment(M[k],N[k]);
+    endfor;
+    if #6>1:
+    for k=1 upto (#6-1):
+    draw segment(R[k],S[k]);
+    endfor;
+    fi;
+  \end{mpost}
+  \fi
+}
+
+\def\MPFractionDisque#1#2#3#4{%
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    pair A,B[];
+    A=(0,0);
+    path cc;
+    cc=cercles(A,#1);
+    for k=0 upto (#3-1):
+    B[k]=pointarc(cc,(360/#3)*k);
+    endfor;
+    fill (A--B0--arccercle(B[0],B[#2],A)--cycle) withcolor #4;
+    draw cc;
+    for k=0 upto (#3-1):
+    draw segment(A,B[k]);
+    endfor;
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    pair A,B[];
+    A=(0,0);
+    path cc;
+    cc=cercles(A,#1);
+    for k=0 upto (#3-1):
+    B[k]=pointarc(cc,(360/#3)*k);
+    endfor;
+    fill (A--B0--arccercle(B[0],B[#2],A)--cycle) withcolor #4;
+    draw cc;
+    for k=0 upto (#3-1):
+    draw segment(A,B[k]);
+    endfor;
+  \end{mpost}
+  \fi
+}
+
+\def\MPFractionSegment#1#2#3#4{
+  \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;
+    draw segment(B[0],B[#2]) withpen pencircle scaled 2 withcolor #4;
+    draw segment(A,C);
+    marque_p:="tiretv";
+    for k=0 upto #3:
+    pointe(B[k]);
+    endfor;
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    pair A,C,B[];
+    A=(0,0);
+    C-A=(#1,0);
+    for k=0 upto #3:
+    B[k]=(k/#3)[A,C];
+    endfor;
+    draw segment(B[0],B[#2]) withpen pencircle scaled 2 withcolor #4;
+    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]{Reponse}{}{\setKV[ClesFraction]{Couleur=white}}%
+    \MPFractionRegulier{\useKV[ClesFraction]{Rayon}}{\useKV[ClesFraction]{Cotes}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}%
+  }{%
+    \ifboolKV[ClesFraction]{Segment}{%
+      \ifboolKV[ClesFraction]{Reponse}{}{\setKV[ClesFraction]{Couleur=white}}%
+      \MPFractionSegment{\useKV[ClesFraction]{Longueur}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}%
+    }{
+      \ifboolKV[ClesFraction]{Rectangle}{%rectangle
+        \ifboolKV[ClesFraction]{Reponse}{}{\setKV[ClesFraction]{Couleur=white}}%
+        \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}}%
+        \MPFractionDisque{\useKV[ClesFraction]{Rayon}}{\ListeFraction[1]}{\ListeFraction[2]}{\useKV[ClesFraction]{Couleur}}%
+      }%
+    }%
+  }%
+}%
+
+%%%%%%%%%%%%%%%%
+%%% Réponses à relier
+%%%%%%%%%%%%%%%%
+\setKVdefault[ClesRelie]{Solution=false,LargeurG=5cm,LargeurD=2cm,Stretch=1.5,Ecart=2cm}
+
+\newcommand\Relie[2][]{%
+  \useKVdefault[ClesRelie]%
+  \setKV[ClesRelie]{#1}%
+  \setsepchar[*]{,*/}%
+  \readlist*\ListeRelie{#2}%
+  \buildtabrelie%
+  \ifboolKV[ClesRelie]{Solution}{%
+    \xintFor* ##1 in {\xintSeq {1}{\ListeRelielen}}\do{%
+      \itemtomacro\ListeRelie[##1,1]\untest
+      \ifx\bla\untest\bla%
+      \else
+      \tikz[remember picture,overlay]{\draw (RelieG-##1) -- (RelieD-\ListeRelie[##1,3]);}%
+      \fi
+    }%
+  }{%
+  }%
+}
+
+\newcounter{NbRelie}
+
+\def\buildtabrelie{%
+  \setcounter{NbRelie}{0}%
+  \renewcommand{\arraystretch}{\useKV[ClesRelie]{Stretch}}%
+  \begin{tabular}{p{\useKV[ClesRelie]{LargeurG}}cp{\useKV[ClesRelie]{Ecart}}>{\tikz[remember
+    picture]{\node[name=RelieD-\theNbRelie,inner
+    sep=0pt]{};\fill[] (RelieD-\theNbRelie) circle[radius=1.5pt]}}cp{\useKV[ClesRelie]{LargeurD}}}%
+    \xintFor* ##1 in {\xintSeq {1}{\ListeRelielen}}\do{\ListeRelie[##1,1]\itemtomacro\ListeRelie[##1,1]\untest%
+\ifx\bla\untest\bla%                                       
+    \uppercase{&}\stepcounter{NbRelie}%
+      \else
+      \uppercase{&}\stepcounter{NbRelie}\tikz[remember
+                   picture,overlay]{\node[name=RelieG-\theNbRelie,inner
+                   sep=0pt]{};\fill[]
+                   (RelieG-\theNbRelie) circle[radius=1.5pt];}
+\fi&&&\ListeRelie[##1,2]\\}%
+  \end{tabular}%
+  \setcounter{NbRelie}{0}%
+}%
+
+\def\buildtabrelieold{%
+  \setcounter{NbRelie}{0}%
+  \renewcommand{\arraystretch}{\useKV[ClesRelie]{Stretch}}%
+  \begin{tabular}{p{\useKV[ClesRelie]{LargeurG}}cp{\useKV[ClesRelie]{Ecart}}>{\tikz[remember
+    picture,baseline]{\node[name=RelieD-\theNbRelie]{\Large\textbullet};}}cp{\useKV[ClesRelie]{LargeurD}}}%
+    \xintFor* ##1 in {\xintSeq {1}{\ListeRelielen}}\do{\ListeRelie[##1,1]\itemtomacro\ListeRelie[##1,1]\untest%
+\ifx\bla\untest\bla%                                       
+    \uppercase{&}\stepcounter{NbRelie}%
+      \else
+      \uppercase{&}\stepcounter{NbRelie}\tikz[remember picture,baseline]{\node[name=RelieG-\theNbRelie]{\Large\textbullet};}
+\fi&&&\ListeRelie[##1,2]\\}%
+  \end{tabular}%
+  \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}
+\newlength{\LargeurQCM}
+\newcounter{QuestionQCM}
+\newcommand\QCM[2][]{%
+  \setcounter{QuestionQCM}{0}
+  \useKVdefault[ClesQCM]%
+  \setKV[ClesQCM]{#1}%
+  \setsepchar[*]{,*&}\ignoreemptyitems%
+  \readlist*\ListeQCM{#2}%
+  \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|}{}&Vrai&Faux\\
+      \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}{\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}%
+      \\
+      }{}
+      \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]%
+        }\\
+      }%
+      \hline%
+    \end{tabular}%
+  }%
+}
+
+
+
+%%%%%%%%%%%%%%%%%%%%%
+%%%% Somme des angles
+%%%%%%%%%%%%%%%%%%%%%
+
+\setKVdefault[ClesSommeAngle]{Detail=true,Figure=false,Isocele=false}%
+
+% On définit la figure à utiliser
+\def\MPFigureSommeAngle#1#2#3#4#5#6{
+    % #1 Premier sommet
+    % #2 Deuxième sommet
+    % #3 Troisième sommet
+    % #4 1er angle
+    % #5 2eme angle
+    % #6 0 isocèle / 1 pas isocèle
+  \ifluatex
+  \mplibcodeinherit{enable}
+  \mplibforcehmode
+  \begin{mplibcode}
+    pair A,B,C,O,I;%
+    % On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=u*(1,1);
+    B-A=u*(4,0);
+    C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]);
+    % On définit le centre du cercle circonscrit
+    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 :)
+    path triangle;
+    triangle=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}--B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}--C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}--cycle;
+    % pour marquer les angles
+    path cc;
+    cc=fullcircle scaled 1u;
+    % on marque les angles
+    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
+    label(btex #1 etex,1.2[O,A]);
+    label(btex #2 etex,1.2[O,B]);
+    label(btex #3 etex,1.2[O,C]);
+    if #6=0:
+    if #4=#5:
+    marque_s:=marque_s/2;
+    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));
+    label(btex $\ang{#5}$ etex,C+0.95u*unitvector(I-C));
+    label(btex ? etex,A+0.95u*unitvector(I-A));
+    fi;
+    %fi;
+  \end{mplibcode}
+  \mplibcodeinherit{disable}
+  \else
+  \begin{mpost}
+    input PfC-Geometrie;
+    u:=1cm;
+    pair A,B,C,O,I;%
+    % On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=u*(1,1);
+    B-A=u*(4,0);
+    C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]);
+    % On définit le centre du cercle circonscrit
+    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 :)
+    path triangle;
+    triangle=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}--B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}--C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}--cycle;
+    % pour marquer les angles
+    path cc;
+    cc=fullcircle scaled 1u;
+    % on marque les angles
+    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
+    label(btex #1 etex,1.2[O,A]);
+    label(btex #2 etex,1.2[O,B]);
+    label(btex #3 etex,1.2[O,C]);
+    if #6=0:
+    if #4=#5:
+    marque_s:=marque_s/2;
+    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));
+    label(btex $\ang{#5}$ etex,C+0.95u*unitvector(I-C));
+    label(btex ? etex,A+0.95u*unitvector(I-A));
+    fi;
+    %fi;
+  \end{mpost}
+  \fi
+}
+
+\newcommand\RedactionSomme[4][]{%
+  % #1 : nom du triangle pA pB pC
+  % #2 : mesure de l'angle pApBpC
+  % #3 : mesure de l'angle pBpCpA
+  % la macro calculant la mesure de l'angle pCpApB
+  \useKVdefault[ClesSommeAngle]%obligatoire car la macro n'est pas dans un groupe.
+  \setKV[ClesSommeAngle]{#1}%On lit les arguments optionnels
+  % On récupère les noms des sommets.
+  \StrMid{#2}{1}{1}[\NomA]%
+  \StrMid{#2}{2}{2}[\NomB]%
+  \StrMid{#2}{3}{3}[\NomC]%
+  % On rédige
+  Dans le triangle $\NomA\NomB\NomC$,\ifboolKV[ClesSommeAngle]{Isocele}{ isocèle en \NomA,}{} on a :%
+      \ifboolKV[ClesSommeAngle]{Isocele}{%
+        \ifx#4\bla\bla%
+        \begin{align*}%
+        \widehat{\NomA\NomB\NomC}+\widehat{\NomB\NomC\NomA}+\widehat{\NomC\NomA\NomB}&=\ang{180}\\%
+        2\times\ang{#3}+\widehat{\NomC\NomA\NomB}&=\ang{180}\\%
+        \xdef\sommeangle{\fpeval{2*#3}}\xdef\totalangle{\fpeval{180-\sommeangle}}\ang{\sommeangle}+\widehat{\NomC\NomA\NomB}&=\ang{180}\\%
+        \ifboolKV[ClesSommeAngle]{Detail}{\widehat{\NomC\NomA\NomB}&=\ang{180}-\ang{\sommeangle}\\}{\widehat{\NomC\NomA\NomB}&=\ang{\totalangle}}%
+        \ifboolKV[ClesSommeAngle]{Detail}{\widehat{\NomC\NomA\NomB}&=\ang{\totalangle}}{}%
+        \end{align*}%
+        \xdef\ResultatAngle{\totalangle}%
+        \else%
+        \begin{align*}%
+          \widehat{\NomA\NomB\NomC}+\widehat{\NomB\NomC\NomA}+\widehat{\NomC\NomA\NomB}&=\ang{180}\\%
+          2\times\widehat{\NomA\NomB\NomC}+\ang{#4}&=\ang{180}\\%
+          \xdef\totalangle{\fpeval{180-#4}}%
+          \ifboolKV[ClesSommeAngle]{Detail}{2\times\widehat{\NomA\NomB\NomC}&=\ang{180}-\ang{#4}\\}{2\times\widehat{\NomA\NomB\NomC}&=\ang{\totalangle}\\}%
+          \ifboolKV[ClesSommeAngle]{Detail}{2\times\widehat{\NomA\NomB\NomC}&=\ang{\totalangle}\\}{\widehat{\NomA\NomB\NomC}&=\frac{\ang{\totalangle}}{2}\\}%
+          \ifboolKV[ClesSommeAngle]{Detail}{\widehat{\NomA\NomB\NomC}&=\frac{\ang{\totalangle}}{2}\\}{\widehat{\NomA\NomB\NomC}&=\ang{\fpeval{0.5*(180-#4)}}}%\\
+          \ifboolKV[ClesSommeAngle]{Detail}{\widehat{\NomA\NomB\NomC}&=\ang{\fpeval{0.5*(180-#4)}}\\}{}%
+        \end{align*}%
+        \xdef\ResultatAngle{\fpeval{0.5*(180-#4)}}%
+        \fi%
+      }{%
+      \begin{align*}%
+        \widehat{\NomA\NomB\NomC}+\widehat{\NomB\NomC\NomA}+\widehat{\NomC\NomA\NomB}&=\ang{180}\\%
+        \ang{#3}+\ang{#4}+\widehat{\NomC\NomA\NomB}&=\ang{180}\\%
+        \xdef\sommeangle{\fpeval{#3+#4}}\xdef\totalangle{\fpeval{180-\sommeangle}}\ang{\sommeangle}+\widehat{\NomC\NomA\NomB}&=\ang{180}\\%
+        \ifboolKV[ClesSommeAngle]{Detail}{\widehat{\NomC\NomA\NomB}&=\ang{180}-\ang{\sommeangle}\\}{\widehat{\NomC\NomA\NomB}&=\ang{\totalangle}}%\\
+        \ifboolKV[ClesSommeAngle]{Detail}{\widehat{\NomC\NomA\NomB}&=\ang{\totalangle}}{}%
+      \end{align*}%
+      \xdef\ResultatAngle{\totalangle}%
+    }%
+}%
+
+\newcommand\SommeAngles[4][]{%
+  % #1 : nom du triangle pA pB pC
+  % #2 : mesure de l'angle pApBpC
+  % #3 : mesure de l'angle pBpCpA
+  % la macro calculant la mesure de l'angle pCpApB
+  \useKVdefault[ClesSommeAngle]%obligatoire car la macro n'est pas dans un groupe.
+  \setKV[ClesSommeAngle]{#1}%On lit les arguments optionnels
+  % On récupère les noms des sommets.
+  \StrMid{#2}{1}{1}[\NomA]%
+  \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
+      \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}
+
+% On définit les figures à utiliser
+\def\MPFigurePytha#1#2#3#4#5#6{%
+  % #1 Premier sommet
+  % #2 Sommet de l'angle droit
+  % #3 troisième sommet
+  % #4 1ere longueur
+  % #5 2eme longueur
+  % #6 angle de rotation de la figure
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    u:=1cm;
+    pair A,B,C,O,D,E,F;%B est le sommet de l'angle droit
+    O=u*(2.5,2.5);
+    path cc;
+    cc=(fullcircle scaled 4u) shifted O;
+    % On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=point(0.9*length cc) of cc;
+    B=A rotatedabout(O,-120);
+    C=2[A,O];
+    % On tourne pour éventuellement moins de lassitude :)
+    A:=A rotatedabout(O,#6);
+    B:=B rotatedabout(O,#6);
+    C:=C rotatedabout(O,#6);
+    % 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 #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
+    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)));
+      fi;
+    fi;
+    label(btex #3 etex,1.2[O,A]);
+    label(btex #2 etex,1.2[O,B]);
+    label(btex #1 etex,1.2[O,C]);
+  \end{mplibcode}
+  \else
+  \begin{mpost}
+    u:=1cm;
+    pair A,B,C,O,D,E,F;%B est le sommet de l'angle droit
+    O=u*(2.5,2.5);
+    path cc;
+    cc=(fullcircle scaled 4u) shifted O;
+    % On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=point(0.9*length cc) of cc;
+    B=A rotatedabout(O,-120);
+    C=2[A,O];
+    % On tourne pour éventuellement moins de lassitude :)
+    A:=A rotatedabout(O,#6);
+    B:=B rotatedabout(O,#6);
+    C:=C rotatedabout(O,#6);
+    % 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 #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
+    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)));
+      fi;
+    fi;
+    label(btex #3 etex,1.2[O,A]);
+    label(btex #2 etex,1.2[O,B]);
+    label(btex #1 etex,1.2[O,C]);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureReciPytha#1#2#3#4#5#6#7{%
+  % #1 Premier sommet
+    % #2 Sommet de l'angle droit
+    % #3 troisième sommet
+    % #4 1ere longueur
+    % #5 2eme longueur
+    % #6 3eme longueur
+    % #7 angle de rotation de la figure
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    u:=1cm;
+    pair A,B,C,O,D,E,F;%B est le sommet de l'angle droit
+    O=u*(2.5,2.5);
+    path cc;
+    cc=(fullcircle scaled 4u) shifted O;
+    % On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=point(0.8*length cc) of cc;
+    B=A rotatedabout(O,-100);
+    C=2[A,O];
+    % On tourne pour éventuellement moins de lassitude :)
+    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)));
+    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)));
+    fi;
+    label(btex #1 etex,1.2[O,A]);
+    label(btex #2 etex,1.2[O,B]);
+    label(btex #3 etex,1.2[O,C]);
+  \end{mplibcode}
+  \else
+  \begin{mpost}
+    u:=1cm;
+    pair A,B,C,O,D,E,F;%B est le sommet de l'angle droit
+    O=u*(2.5,2.5);
+    path cc;
+    cc=(fullcircle scaled 4u) shifted O;
+    % On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=point(0.8*length cc) of cc;
+    B=A rotatedabout(O,-100);
+    C=2[A,O];
+    % On tourne pour éventuellement moins de lassitude :)
+    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));
+    label(LATEX("\num{"&decimal(#5)&"}") rotated(angle(C-B)),1/2[C,B]-decalage*(unitvector(C-B)));
+    label(LATEX("\num{"&decimal(#6)&"}") rotated(angle(B-A)),1/2[A,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(LATEX("\num{"&decimal(#6)&"}") rotated angle(C-B),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]);
+    label(btex #3 etex,1.2[O,C]);
+  \end{mpost}
+  \fi
+}
+
+\newcommand{\Pythagore}[5][]{%
+  % #1 Paramètres sous forme de clés
+  % #2 Nom "complet" du triangle : ABC par exemple
+  % #3 Première longueur
+  % #4 Deuxième longueur
+  % #5 Troisième longueur (éventuellement vide)
+  \useKVdefault[ClesPythagore]%obligatoire car la macro n'est pas dans un groupe.
+  \setKV[ClesPythagore]{#1}%On lit les arguments optionnels
+  \ifboolKV[ClesPythagore]{Reciproque}{%
+    % On retient les noms des sommets
+    \StrMid{#2}{1}{1}[\NomA]%
+    \StrMid{#2}{2}{2}[\NomB]%
+    \StrMid{#2}{3}{3}[\NomC]%
+    % on stocke les valeurs données
+    \opcopy{#3}{A1}%
+    \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
+        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}{%
+        \[
+          \begin{array}{cccc|cccc}
+            \NomA\NomC^2&&&&&\NomA\NomB^2&+&\NomB\NomC^2\\
+            \opexport{A1}{\Aun}\num{\Aun}^2&&&&&\opexport{A2}{\Adeux}\num{\Adeux}^2&+&\opexport{A3}{\Atrois}\num{\Atrois}^2\\
+            \opmul*{A1}{A1}{a1}&&&&&\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}&+&\opmul*{A3}{A3}{a3}\opexport{a3}{\Atrois}\num{\Atrois}\\
+            \opexport{a1}{\Aun}\num{\Aun}&&&&&\multicolumn{3}{c}{\opadd*{a2}{a3}{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}}\\
+          \end{array}
+        \]
+      }{%
+        \[\left.
+            \begin{array}{l}
+              \NomA\NomC^2=\opexport{A1}{\Aun}\num{\Aun}^2=\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\num{\Aun}\\
+              \\
+              \NomA\NomB^2+\NomB\NomC^2=\opexport{A2}{\Adeux}\num{\Adeux}^2+\opexport{A3}{\Atrois}\num{\Atrois}^2=\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\num{\Adeux}+\opmul*{A3}{A3}{a3}\opexport{a3}{\Atrois}\num{\Atrois}=\opadd*{a2}{a3}{a4}\opexport{a4}{\Aquatre}\num{\Aquatre}\\
+            \end{array}
+          \right\}\opcmp{a1}{a4}\ifopeq\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2\fi\opcmp{a1}{a4}\ifopneq\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2\fi
+        \]
+      }
+      \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}%
+    \opcopy{#4}{A2}%
+    \opcopy{\useKV[ClesPythagore]{Precision}}{pres}%
+    % On retient les noms des sommets
+    \StrMid{#2}{1}{1}[\NomA]%
+    \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%
+        % 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})}}%
+        \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*}
+              \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}}}}%\\
+            }
+            \end{align*}
+          }{%
+            \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%
+    }%
+  }%
+}%
+
+%%%%%%%%%%%%%%%%%
+%% 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]{%
+    \node[name=Distri-\theNbDistri,anchor=base] {${#1}$};}%
+  \stepcounter{NbDistri}%
+}%
+
+\newcommand{\DrawArrow}{%
+  \begin{tikzpicture}[overlay,remember picture]
+    \draw[-stealth,out=50,in=140,DCFlechesh,transform canvas={yshift=2pt}] (Distri-0.north) to (Distri-2.north);
+    \draw[-stealth,out=50,in=140,DCFlechesh!50,transform canvas={yshift=2pt}] (Distri-0.north) to (Distri-3.north);
+    \draw[-stealth,out=-50,in=-140,DCFlechesb,transform canvas={yshift=-2pt}] (Distri-1.south) to (Distri-2.south);
+    \draw[-stealth,out=-50,in=-140,DCFlechesb!50,transform canvas={yshift=-2pt}] (Distri-1.south) to (Distri-3.south);
+  \end{tikzpicture}
+}
+
+\newcommand{\DrawArrowSimple}[1]{%
+  \begin{tikzpicture}[overlay,remember picture]
+    \draw[-stealth,out=50,in=140,DCFlechesh,transform canvas={yshift=2pt}] (Distri-#1.north) to (Distri-2.north);
+    \draw[-stealth,out=50,in=140,DCFlechesh!50,transform canvas={yshift=2pt}] (Distri-#1.north) to (Distri-3.north);
+  \end{tikzpicture}
+}
+
+\newcommand{\DrawArrowSimpleRenverse}[1]{%
+  \begin{tikzpicture}[overlay,remember picture]
+    \draw[-stealth,out=140,in=50,DCFlechesh,transform canvas={yshift=2pt}] (Distri-#1.north) to (Distri-0.north);
+    \draw[-stealth,out=140,in=50,DCFlechesh!50,transform canvas={yshift=2pt}] (Distri-#1.north) to (Distri-1.north);
+  \end{tikzpicture}
+}
+
+\newcounter{NbDistri}%
+\setcounter{NbDistri}{0}%
+
+\newcounter{NbCalculDistri}%Pour compter combien de distributivité il
+% 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 ?
+
+\newcommand\Affichage[4][]{%
+  \setKV[ClesDistributivite]{#1}%On lit les arguments optionnels
+  \def\LETTRE{\useKV[ClesDistributivite]{Lettre}}%
+  \ensuremath{%
+    % partie du x^2
+    \xintifboolexpr{#2=0}{}{\xintifboolexpr{#2=1}{}{\xintifboolexpr{#2=-1}{-}{\num{#2}}}\LETTRE^2}%
+    % partie du x
+    \xintifboolexpr{#3=0}{}{\xintifboolexpr{#3>0}{\xintifboolexpr{#2=0}{}{+}\xintifboolexpr{#3=1}{}{\num{#3}}}{%
+        \xintifboolexpr{#2=0}{\xintifboolexpr{#3=-1}{-}{\num{#3}}}{\xintifboolexpr{#3=-1}{-}{-\num{\fpeval{abs(#3)}}}}%
+      }\LETTRE}%
+    % partie du nombre
+    \xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{\xintifboolexpr{#2=0}{\xintifboolexpr{#3=0}{}{+}}{+}\num{#4}}{%
+        \xintifboolexpr{#2=0}{\xintifboolexpr{#3=0}{\num{#4}}{-\num{\fpeval{abs(#4)}}}}{-\num{\fpeval{abs(#4)}}}}}%
+    % 
+  }%
+}%
+
+\xdef\SommeA{0}%
+\xdef\SommeB{0}%
+\xdef\SommeC{0}%
+
+\newcommand{\Distri}[5][]{%
+  \ensuremath{%
+    \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}}%
+    \colorlet{DCFlechesh}{\useKV[ClesDistributivite]{CouleurFH}}%
+    \colorlet{DCFlechesb}{\useKV[ClesDistributivite]{CouleurFB}}%
+    \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)}}%
+          }{%
+            \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}}}{}%
+          }%
+        }%
+      }{%
+        \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}{%
+              \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}{)}{}%
+            }%
+            \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}{)}{}}%
+              }%
+            }{%
+              \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
+              \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}}}%\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}}}{}%
+          }{}%
+        }%
+      }%
+    }%
+  }%
+  }%
+}%
+
+\newcommand{\Resultat}[1][]{%
+  \setKV[ClesDistributivite]{#1}%On lit les arguments optionnels
+  \ensuremath{%
+    \Affichage{\SommeA}{\SommeB}{\SommeC}
+  }
+}
+
+\newcommand\AffichageEchange[4][]{%
+  \setKV[ClesDistributivite]{#1}%On lit les arguments optionnels
+  \def\LETTRE{\useKV[ClesDistributivite]{Lettre}}%
+  \ensuremath{%
+    % partie du nombre
+    \xintifboolexpr{#2=0}{}{\num{#2}}%
+    % partie du x
+    \xintifboolexpr{#3=0}{}{\xintifboolexpr{#3>0}{\xintifboolexpr{#2=0}{}{+}\xintifboolexpr{#3=1}{}{\num{#3}}}{%
+        \xintifboolexpr{#2=0}{\xintifboolexpr{#3=-1}{-}{\num{#3}}}{\xintifboolexpr{#3=-1}{-}{-\num{\fpeval{abs(#3)}}}}
+      }\LETTRE}%
+    % partie du x^2
+    \xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{\xintifboolexpr{#2=0}{\xintifboolexpr{#3=0}{}{+}}{+}\xintifboolexpr{#4=1}{}{\num{#4}}}{%
+        \xintifboolexpr{#2=0}{\xintifboolexpr{#3=0}{\num{#4}}{-\num{\fpeval{abs(#4)}}}}{-\num{\fpeval{abs(#4)}}}}\LETTRE^2}%
+  }%
+}%
+
+\newcommand{\DistriEchange}[5][]{%
+  \ensuremath{%
+    \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}}%
+    \colorlet{DCFlechesh}{\useKV[ClesDistributivite]{CouleurFH}}%
+    \colorlet{DCFlechesb}{\useKV[ClesDistributivite]{CouleurFB}}%
+    \ifboolKV[ClesDistributivite]{Remarquable}{%
+      \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=1}{\ifx\bla#4\bla(\AffichageEchange{#2}{#3}{0})^2\else(\AffichageEchange{#2}{#3}{0})(\AffichageEchange{#4}{#5}{0})\fi
+      }{}
+      \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=2}{%
+        \ifx\bla#4\bla\xintifboolexpr{#3>0}{%
+          \num{#2}^2+2\times\num{#2}\times\xintifboolexpr{#3=1}{}{\num{#3}}\useKV[ClesDistributivite]{Lettre}+
+          \xintifboolexpr{#3=1}{}{(\num{#3}}\useKV[ClesDistributivite]{Lettre}\xintifboolexpr{#3=1}{}{)}^2%
+        }{%
+          \num{#2}^2-2\times\num{#2}\times\xintifboolexpr{#3=-1}{}{\num{\fpeval{0-#3}}}\useKV[ClesDistributivite]{Lettre}+
+          \xintifboolexpr{#3=-1}{}{(\num{\fpeval{0-#3}}}\useKV[ClesDistributivite]{Lettre}\xintifboolexpr{#3=-1}{}{)}^2%
+        }%
+        \else\num{#2}^2-\xintifboolexpr{#3=1}{}{(\num{#3}}\useKV[ClesDistributivite]{Lettre}\xintifboolexpr{#3=1}{}{)}^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}{(}{}\AffichageEchange{\Multi}{0}{0}\xintifboolexpr{\Multi<0}{)}{}}%
+          \xintifboolexpr{\Multim=0}{}{\xintifboolexpr{\Multim>0}{+}{+(}\AffichageEchange{0}{\Multim}{0}\xintifboolexpr{\Multim<0}{)}{}}%
+          \xintifboolexpr{\Multil=0}{}{\xintifboolexpr{\Multil>0}{+}{+(}\AffichageEchange{0}{0}{\Multil}\xintifboolexpr{\Multil<0}{)}{}}%
+        }{%
+          \AffichageEchange{\Multi}{\Multim}{\Multil}%
+        }
+        \ifboolKV[ClesDistributivite]{Somme}{\xdef\SommeA{\fpeval{\SommeA+#3*#3}}\xdef\SommeB{\fpeval{\SommeB+#2*#3+#3*#2}}\xdef\SommeC{\fpeval{\SommeC+#2*#2}}}{}%
+        \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-#3*#3}}\xdef\SommeB{\fpeval{\SommeB-#2*#3-#3*#2}}\xdef\SommeC{\fpeval{\SommeC-#2*#2}}}{}%
+        \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}{(}{}\AffichageEchange{\Multi}{0}{0}\xintifboolexpr{\Multi<0}{)}{}}%
+          \xintifboolexpr{\Multim=0}{}{\xintifboolexpr{\Multim>0}{+}{+(}\AffichageEchange{0}{\Multim}{0}\xintifboolexpr{\Multim<0}{)}{}}%
+          \xintifboolexpr{\Multil=0}{}{\xintifboolexpr{\Multil>0}{+}{+(}\AffichageEchange{0}{0}{\Multil}\xintifboolexpr{\Multil<0}{)}{}}%
+        }{%
+          \AffichageEchange{\Multi}{\Multim}{\Multil}%
+        }
+        % à faire
+        \ifboolKV[ClesDistributivite]{Somme}{\xdef\SommeA{\fpeval{\SommeA+#3*#5}}\xdef\SommeB{\fpeval{\SommeB+#2*#5+#3*#4}}\xdef\SommeC{\fpeval{\SommeC+#2*#4}}}{}%
+        \ifboolKV[ClesDistributivite]{Difference}{\xdef\SommeA{\fpeval{\SommeA-#3*#5}}\xdef\SommeB{\fpeval{\SommeB-#2*#5-#3*#4}}\xdef\SommeC{\fpeval{\SommeC-#2*#4}}}{}%
+        % 
+        \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)}}%
+        % }{%
+        %   \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}}}{}%
+        % }%
+        % }%
+      }{%
+        \ifboolKV[ClesDistributivite]{All}{%
+           \xdef\NomLettre{\useKV[ClesDistributivite]{NomExpression}}%
+           \xdef\NomFin{\useKV[ClesDistributivite]{Fin}}%
+           \xdef\ValeurEchange{\useKV[ClesDistributivite]{Echange}}
+           \xintFor* ##1 in {\xintSeq {1}{\useKV[ClesDistributivite]{Fin}-1}}\do
+           {\NomLettre&=\DistriEchange[Echange=\ValeurEchange,Etape=##1]{#2}{#3}{#4}{#5}\\}%
+           \NomLettre&=\DistriEchange[Echange=\ValeurEchange,Etape=\NomFin]{#2}{#3}{#4}{#5}%
+        }{%
+          % Etape 1
+          \xintifboolexpr{\useKV[ClesDistributivite]{Etape}=1}{%
+            \xintifboolexpr{\useKV[ClesDistributivite]{Echange}=1||\useKV[ClesDistributivite]{Echange}=3}{%
+              \xintifboolexpr{#2=0}{%
+              }{\xintifboolexpr{#3=0}{%
+                }{(}}\Tikzmark{\Affichage[#1]{0}{0}{#2}}%
+              \ifboolKV[ClesDistributivite]{AideAdda}{\mathcolor{DCAide}{+(}}{}%
+              \xintifboolexpr{#3>0}{\xintifboolexpr{#2=0}{}{+}}{\xintifboolexpr{#3<0}{-}{}}\Tikzmark{\Affichage[#1]{0}{\fpeval{abs(#3)}}{0}}%
+              \ifboolKV[ClesDistributivite]{AideAdda}{\mathcolor{DCAide}{)}}{}%
+              \xintifboolexpr{#2=0}{%
+              }{\xintifboolexpr{#3=0}{%
+                }{)}}%
+            }{
+              \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{\useKV[ClesDistributivite]{Echange}=2||\useKV[ClesDistributivite]{Echange}=3}{%
+              \xintifboolexpr{\Multi=0}{\times%
+                \xintifboolexpr{#4<0}{(}{\xintifboolexpr{#5<0}{(}{}}}{(}%
+              \Tikzmark{\AffichageEchange[#1]{#4}{0}{0}}%
+              \ifboolKV[ClesDistributivite]{AideAddb}{\mathcolor{DCAide}{+(}}{}%
+              \xintifboolexpr{#5>0}{\xintifboolexpr{#4=0}{}{+}}{\xintifboolexpr{#5<0}{-}{}}\Tikzmark{\AffichageEchange[#1]{0}{\fpeval{abs(#5)}}{0}}%
+              \ifboolKV[ClesDistributivite]{AideAddb}{\mathcolor{DCAide}{)}}{}%
+              \xintifboolexpr{\Multi=0}{%
+                \xintifboolexpr{#4<0}{)}{\xintifboolexpr{#5<0}{)}{}}}{)}%
+            }{%
+              \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}}%
+             \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}{%
+            \xintifboolexpr{\useKV[ClesDistributivite]{Echange}=1}{%
+              \xdef\Multi{\fpeval{#2*#4}}%
+              \xintifboolexpr{\Multi=0}{}{%
+                \xintifboolexpr{#2<0}{(}{}\AffichageEchange[#1]{#2}{0}{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}{(}{}\AffichageEchange[#1]{#2}{0}{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}{(}{}\AffichageEchange[#1]{0}{#3}{0}\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}{(}{}\AffichageEchange[#1]{0}{#3}{0}\xintifboolexpr{#3<0}{)}{}\times\xintifboolexpr{#5<0}{(}{}\Affichage[#1]{0}{0}{#5}\xintifboolexpr{#5<0}{)}{}%
+              }%
+            }{}%
+            \xintifboolexpr{\useKV[ClesDistributivite]{Echange}=2}{%
+              \xdef\Multi{\fpeval{#2*#4}}%
+              \xintifboolexpr{\Multi=0}{}{%
+                \xintifboolexpr{#2<0}{(}{}\Affichage[#1]{0}{#2}{0}\xintifboolexpr{#2<0}{)}{}\times\xintifboolexpr{#4<0}{(}{}\AffichageEchange[#1]{#4}{0}{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}{(}{}\AffichageEchange[#1]{0}{#5}{0}\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}{(}{}\AffichageEchange[#1]{#4}{0}{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}{(}{}\AffichageEchange[#1]{0}{#5}{0}\xintifboolexpr{#5<0}{)}{}%
+              }%
+            }{}%
+            \xintifboolexpr{\useKV[ClesDistributivite]{Echange}=3}{%
+              \xdef\Multi{\fpeval{#2*#4}}%
+              \xintifboolexpr{\Multi=0}{}{%
+                \xintifboolexpr{#2<0}{(}{}\AffichageEchange[#1]{#2}{0}{0}\xintifboolexpr{#2<0}{)}{}\times\xintifboolexpr{#4<0}{(}{}\AffichageEchange[#1]{#4}{0}{0}\xintifboolexpr{#4<0}{)}{}%
+              }%
+              \xdef\Multij{\fpeval{#2*#5}}%
+              \xintifboolexpr{\Multij=0}{}{%
+                \xintifboolexpr{\Multi=0}{}{+}%
+                \xintifboolexpr{#2<0}{(}{}\AffichageEchange[#1]{#2}{0}{0}\xintifboolexpr{#2<0}{)}{}\times\xintifboolexpr{#5<0}{(}{}\AffichageEchange[#1]{0}{#5}{0}\xintifboolexpr{#5<0}{)}{}%
+              }%
+              \xdef\Multik{\fpeval{#3*#4}}%
+              \xintifboolexpr{\Multik=0}{}{%
+                \xintifboolexpr{\Multi=0}{}{+}%
+                \xintifboolexpr{#3<0}{(}{}\AffichageEchange[#1]{0}{#3}{0}\xintifboolexpr{#3<0}{)}{}\times\xintifboolexpr{#4<0}{(}{}\AffichageEchange[#1]{#4}{0}{0}\xintifboolexpr{#4<0}{)}{}%
+              }%
+              \xdef\Multil{\fpeval{#3*#5}}%
+              \xintifboolexpr{\Multil=0}{}{+%
+                \xintifboolexpr{#3<0}{(}{}\AffichageEchange[#1]{0}{#3}{0}\xintifboolexpr{#3<0}{)}{}\times\xintifboolexpr{#5<0}{(}{}\AffichageEchange[#1]{0}{#5}{0}\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
+            \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}{)}{}%
+              \xdef\Multim{\fpeval{#2*#4+#3*#5}}%              
+              \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}}}{}%              
+            }{}%
+            \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}{)}{}%
+              \xdef\Multim{\fpeval{#2*#4+#3*#5}}%
+              \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}}}{}%
+            }{}%
+            \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}{)}{}%
+              \xdef\Multim{\fpeval{#2*#5+#3*#4}}%
+              \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}}}{}%
+            }{}%
+          }{}%fin etape3
+          % 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
+            % 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}{%
+                \xdef\Multiko{\fpeval{-\Multik}}%
+                \xdef\Multimo{\fpeval{-\Multim}}%
+                \xdef\Multijo{\fpeval{-\Multij}}%
+                 \xintifboolexpr{\Multiko=0}{}{\xintifboolexpr{\Multiko<0}{(}{}\Affichage{\Multiko}{0}{0}\xintifboolexpr{\Multiko<0}{)}{}}%
+                 \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}}}{}%
+            }{}%
+            \xintifboolexpr{\useKV[ClesDistributivite]{Echange}=2}{%
+              \xdef\Multim{\fpeval{#2*#4+#3*#5}}%
+              \ifboolKV[ClesDistributivite]{Oppose}{%
+                \xdef\Multijo{\fpeval{-\Multij}}%
+                \xdef\Multimo{\fpeval{-\Multim}}%
+                \xdef\Multiko{\fpeval{-\Multik}}%
+                 \xintifboolexpr{\Multijo=0}{}{\xintifboolexpr{\Multijo<0}{(}{}\Affichage{\Multijo}{0}{0}\xintifboolexpr{\Multijo<0}{)}{}}%
+                 \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}}}{}%
+            }{}%
+            \xintifboolexpr{\useKV[ClesDistributivite]{Echange}=3}{%
+              \xdef\Multim{\fpeval{#2*#5+#3*#4}}%
+              \ifboolKV[ClesDistributivite]{Oppose}{%
+                \xdef\Multilo{\fpeval{-\Multil}}%
+                \xdef\Multimo{\fpeval{-\Multim}}%
+                \xdef\Multio{\fpeval{-\Multi}}%
+                 \xintifboolexpr{\Multilo=0}{}{\xintifboolexpr{\Multilo<0}{(}{}\Affichage{\Multilo}{0}{0}\xintifboolexpr{\Multilo<0}{)}{}}%
+                 \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}}}{}%
+            }{}%
+          }{}%
+        }%
+      }%
+    }%
+  }%
+}%
+
+%%%%%%%%%%%%%%%
+%Nombre Premier
+%%%%%%%%%%%%%%%
+\setKVdefault[ClesNombrePremier]{Tableau=false,TableauVertical=false,TableauVerticalVide=false,Exposant=false,Longue=false,All=false,Arbre=false,ArbreVide=false,ArbreComplet=false,Diviseurs=false}
+
+\newcommand\Decomposition[2][]{%
+  \useKVdefault[ClesNombrePremier]%
+  \setKV[ClesNombrePremier]{#1}%
+  \ifboolKV[ClesNombrePremier]{Tableau}{\NombrePremier{#2}}{}%
+  \ifboolKV[ClesNombrePremier]{TableauVertical}{\NombrePremierVertical{#2}}{}%
+  \ifboolKV[ClesNombrePremier]{TableauVerticalVide}{\NombrePremierVerticalVide{#2}}{}%
+  \ifboolKV[ClesNombrePremier]{Exposant}{\PremierExposant{#2}}{}%
+  \ifboolKV[ClesNombrePremier]{Longue}{\PremierLong{#2}}{}%
+  \ifboolKV[ClesNombrePremier]{All}{\NombrePremierExposant{#2}}{}%
+  \ifboolKV[ClesNombrePremier]{Arbre}{\MPArbre{#2}}{}%
+  \ifboolKV[ClesNombrePremier]{ArbreComplet}{\MPArbreComplet{#2}}{}%
+  \ifboolKV[ClesNombrePremier]{Diviseurs}{\ListeDiviseur{#2}}{}%
+  \ifboolKV[ClesNombrePremier]{ArbreVide}{\MPArbreVide{#2}}{}%
+}
+
+\def\MPArbre#1{%
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    numeric depart;
+    pair Ancre[];
+    numeric decalage;
+    decalage=10mm;
+    
+    vardef PremierSimple(expr NB)=
+    b:=2;
+    depart:=NB;
+    if Estcepremier(depart)=false:
+    forever:
+      if (depart mod b)=0:
+	Ancre[k+1]-Ancre[k]=(-decalage*0.5,-decalage);
+	Ancre[k+2]-Ancre[k+1]=(decalage,0);
+	depart:=depart div b;
+	label(TEX("\num{"&decimal(b)&"}"),Ancre[k+1]);
+	label(TEX("\num{"&decimal(depart)&"}"),Ancre[k+2]);
+	draw 1/5[Ancre[k],Ancre[k+1]]--4/5[Ancre[k],Ancre[k+1]];
+	draw 1/5[Ancre[k],Ancre[k+2]]--4/5[Ancre[k],Ancre[k+2]];
+	k:=k+2;
+	racine:=depart;
+	depart:=1;
+      else:
+	b:=b+1;
+      fi;
+      exitif depart=1;
+    endfor;
+  else:
+    racine:=1;
+  fi;
+enddef;
+
+vardef Estcepremier(expr NBa)=
+  boolean $;
+  c:=2;
+  departa:=NBa;
+  test:=1;
+  $=true;
+  if departa=1:
+    $:=false;
+  else:
+    forever:
+      if (departa mod c)=0:
+	departa:=departa div c;
+	test:=test+1;
+      else:
+	c:=c+1;
+      fi;
+      exitif departa=1;
+    endfor;
+  fi;
+  if test=2:
+    $:=true
+  else:
+    $:=false;
+  fi;
+  $
+  enddef;
+  k:=0;
+  Ancre0:=(0,0);
+  racine:=#1;
+
+  label(btex \num{#1} etex,(0,0));
+  forever:
+   PremierSimple(racine);
+  exitif racine=1;
+  endfor;
+  \end{mplibcode}
+  \else
+  \begin{mpost}
+    numeric depart;
+    pair Ancre[];
+    numeric decalage;
+    decalage=10mm;
+    
+    vardef PremierSimple(expr NB)=
+    b:=2;
+    depart:=NB;
+    if Estcepremier(depart)=false:
+    forever:
+      if (depart mod b)=0:
+	Ancre[k+1]-Ancre[k]=(-decalage*0.5,-decalage);
+	Ancre[k+2]-Ancre[k+1]=(decalage,0);
+	depart:=depart div b;
+	label(LATEX("\num{"&decimal(b)&"}"),Ancre[k+1]);
+	label(LATEX("\num{"&decimal(depart)&"}"),Ancre[k+2]);
+	draw 1/5[Ancre[k],Ancre[k+1]]--4/5[Ancre[k],Ancre[k+1]];
+	draw 1/5[Ancre[k],Ancre[k+2]]--4/5[Ancre[k],Ancre[k+2]];
+	k:=k+2;
+	racine:=depart;
+	depart:=1;
+      else:
+	b:=b+1;
+      fi;
+      exitif depart=1;
+    endfor;
+  else:
+    racine:=1;
+  fi;
+enddef;
+
+vardef Estcepremier(expr NBa)=
+  boolean $;
+  c:=2;
+  departa:=NBa;
+  test:=1;
+  $=true;
+  if departa=1:
+    $:=false;
+  else:
+    forever:
+      if (departa mod c)=0:
+	departa:=departa div c;
+	test:=test+1;
+      else:
+	c:=c+1;
+      fi;
+      exitif departa=1;
+    endfor;
+  fi;
+  if test=2:
+    $:=true
+  else:
+    $:=false;
+  fi;
+  $
+  enddef;
+
+  k:=0;
+  Ancre0:=(0,0);
+  racine:=#1;
+  label(LATEX("\num{"&decimal(racine)&"}"),(0,0));
+  forever:
+    PremierSimple(racine);    
+    exitif racine=1;
+  endfor;
+\end{mpost}
+\fi
+}
+
+\def\MPArbreComplet#1{%
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    beginfig(1);
+    numeric depart;
+    pair Ancre[];
+    numeric decalage;
+    decalage=7.5mm;
+    
+vardef NbEtape(expr nb)=
+  b:=2;
+  depart:=nb;
+  etape:=0;
+  Stock[0][0]=depart;
+  forever:
+    if (depart mod b)=0:
+      etape:=etape+1;
+      if etape=1:
+	Stock[etape][0]=b;
+	Stock[etape][etape]:=depart div b;
+      else:
+	for k=0 upto etape-2:
+	  Stock[etape][k]:=Stock[etape-1][k];
+	endfor;
+	Stock[etape][etape-1]:=b;
+	Stock[etape][etape]:=depart div b;
+      fi;
+      depart:=depart div b;
+    else:
+      b:=b+1;
+    fi;
+    exitif depart=1;
+  endfor;
+  etape
+enddef;
+
+dx:=1cm;
+dy:=1cm;
+
+pair N[][];
+
+vardef Positions(expr Step)=
+  for k=0 upto (Step-1):
+    for l=0 upto k:
+      N[k][l]=(-k*dx+(l+k*.5)*dx,-k*dy);
+      label(TEX("\num{"&decimal(Stock[k][l])&"}"),N[k][l]);
+    endfor;
+    for l=0 upto k-1:
+      label(btex $\times$ etex,1/2[N[k][l],N[k][l+1]]);
+    endfor;
+  endfor;
+  for k=0 upto (Step-1):
+    for l=0 upto (k-1):
+      draw 1/5[N[k][l],N[k-1][l]]--4/5[N[k][l],N[k-1][l]];
+    endfor;
+    if k>0:
+      draw 1/5[N[k][k],N[k-1][k-1]]--4/5[N[k][k],N[k-1][k-1]];
+    fi;
+  endfor;
+  enddef;
+
+  Positions(NbEtape(#1));
+  \end{mplibcode}
+  \else
+  \begin{mpost}
+    numeric depart;
+pair Ancre[];
+numeric decalage;
+decalage=7.5mm;
+
+vardef NbEtape(expr nb)=
+  b:=2;
+  depart:=nb;
+  etape:=0;
+  Stock[0][0]=depart;
+  forever:
+    if (depart mod b)=0:
+      etape:=etape+1;
+      if etape=1:
+	Stock[etape][0]=b;
+	Stock[etape][etape]:=depart div b;
+      else:
+	for k=0 upto etape-2:
+	  Stock[etape][k]:=Stock[etape-1][k];
+	endfor;
+	Stock[etape][etape-1]:=b;
+	Stock[etape][etape]:=depart div b;
+      fi;
+      depart:=depart div b;
+    else:
+      b:=b+1;
+    fi;
+    exitif depart=1;
+  endfor;
+  etape
+enddef;
+
+dx:=1cm;
+dy:=1cm;
+
+pair N[][];
+
+vardef Positions(expr Step)=
+  for k=0 upto (Step-1):
+    for l=0 upto k:
+      N[k][l]=(-k*dx+(l+k*.5)*dx,-k*dy);
+      label(LATEX("\num{"&decimal(Stock[k][l])&"}"),N[k][l]);
+    endfor;
+    for l=0 upto k-1:
+      label(btex $\times$ etex,1/2[N[k][l],N[k][l+1]]);
+    endfor;
+  endfor;
+  for k=0 upto (Step-1):
+    for l=0 upto (k-1):
+      draw 1/5[N[k][l],N[k-1][l]]--4/5[N[k][l],N[k-1][l]];
+    endfor;
+    if k>0:
+      draw 1/5[N[k][k],N[k-1][k-1]]--4/5[N[k][k],N[k-1][k-1]];
+    fi;
+  endfor;
+  enddef;
+
+    Positions(NbEtape(#1));
+  \end{mpost}
+  \fi
+}
+
+\def\MPArbreVide#1{%
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    numeric depart;
+    pair Ancre[];
+    numeric decalage;
+    decalage=7.5mm;
+
+vardef NbEtape(expr nb)=
+  b:=2;
+  depart:=nb;
+  etape:=0;
+  Stock[0][0]=depart;
+  forever:
+    if (depart mod b)=0:
+      etape:=etape+1;
+      if etape=1:
+	Stock[etape][0]=b;
+	Stock[etape][etape]:=depart div b;
+      else:
+	for k=0 upto etape-2:
+	  Stock[etape][k]:=Stock[etape-1][k];
+	endfor;
+	Stock[etape][etape-1]:=b;
+	Stock[etape][etape]:=depart div b;
+      fi;
+      depart:=depart div b;
+    else:
+      b:=b+1;
+    fi;
+    exitif depart=1;
+  endfor;
+  etape
+enddef;
+
+dx:=1cm;
+dy:=1cm;
+
+pair N[][];
+
+vardef Positions(expr Step)=
+
+  for k=0 upto (Step-1):
+    for l=0 upto k:
+    N[k][l]=(-k*dx+(l+k*.5)*dx,-k*dy);
+    endfor;
+    for l=0 upto k-1:
+      label(btex $\times$ etex,1/2[N[k][l],N[k][l+1]]);
+    endfor;
+  endfor;
+  for k=0 upto (Step-1):
+    for l=0 upto (k-1):
+      draw 1/5[N[k][l],N[k-1][l]]--4/5[N[k][l],N[k-1][l]];
+    endfor;
+    if k>0:
+      draw 1/5[N[k][k],N[k-1][k-1]]--4/5[N[k][k],N[k-1][k-1]];
+    fi;
+    endfor;
+    label(TEX("\num{"&decimal(Stock[0][0])&"}"),N[0][0]);
+  enddef;
+
+  Positions(NbEtape(#1));
+  \end{mplibcode}
+  \else
+  \begin{mpost}
+    numeric depart;
+    pair Ancre[];
+numeric decalage;
+decalage=7.5mm;
+
+vardef NbEtape(expr nb)=
+  b:=2;
+  depart:=nb;
+  etape:=0;
+  Stock[0][0]=depart;
+  forever:
+    if (depart mod b)=0:
+      etape:=etape+1;
+      if etape=1:
+	Stock[etape][0]=b;
+	Stock[etape][etape]:=depart div b;
+      else:
+	for k=0 upto etape-2:
+	  Stock[etape][k]:=Stock[etape-1][k];
+	endfor;
+	Stock[etape][etape-1]:=b;
+	Stock[etape][etape]:=depart div b;
+      fi;
+      depart:=depart div b;
+    else:
+      b:=b+1;
+    fi;
+    exitif depart=1;
+  endfor;
+  etape
+enddef;
+
+dx:=1cm;
+dy:=1cm;
+
+pair N[][];
+
+vardef Positions(expr Step)=
+
+  for k=0 upto (Step-1):
+    for l=0 upto k:
+    N[k][l]=(-k*dx+(l+k*.5)*dx,-k*dy);
+    endfor;
+    for l=0 upto k-1:
+      label(btex $\times$ etex,1/2[N[k][l],N[k][l+1]]);
+    endfor;
+  endfor;
+  for k=0 upto (Step-1):
+    for l=0 upto (k-1):
+      draw 1/5[N[k][l],N[k-1][l]]--4/5[N[k][l],N[k-1][l]];
+    endfor;
+    if k>0:
+      draw 1/5[N[k][k],N[k-1][k-1]]--4/5[N[k][k],N[k-1][k-1]];
+    fi;
+    endfor;
+    label(LATEX("\num{"&decimal(Stock[0][0])&"}"),N[0][0]);
+  enddef;
+
+    Positions(NbEtape(#1));
+  \end{mpost}
+  \fi
+}
+
+\newcount\premier
+
+\newcommand{\NombrePremier}[1]{%écrire la décomposition complète
+  % #1 le nombre premier à tester
+  \newcount\anp\newcount\bnp\newcount\cnp%\newcount\e\newcount\f%
+  \anp=#1\relax
+  \bnp=2\relax
+  \premier=-1\relax
+  % Pour déterminer le nombre d'étapes
+  \whiledo{\anp > 1}{%
+    \modulo{\the\anp}{\the\bnp}
+    \ifnum\remainder=0\relax
+      \global\premier=\numexpr\premier+1\relax
+      \cnp=\numexpr\anp/\bnp\relax
+      \anp=\cnp\relax
+    \else%
+      \bnp=\numexpr\bnp+1\relax%
+    \fi%
+  }
+  \ifnum\premier=0
+    Le nombre \num{#1} est un nombre premier.
+  \else
+    \begin{align*}
+      \xintFor* ##1 in {\xintSeq {1}{\premier}}\do {\num{#1}&=\PremierEtape{#1}{##1}\xintifboolexpr{##1<\premier}{\\}{}}%
+    \end{align*}
+  \fi
+}
+
+\newcommand{\NombrePremierVertical}[1]{%écrire la décomposition complète
+  % #1 le nombre premier à tester
+  \newcount\anpv\newcount\bnpv\newcount\cnpv%\newcount\e\newcount\f%
+  \anpv=#1\relax
+  \bnpv=2\relax
+  \premier=-1\relax
+  % Pour déterminer le nombre d'étapes
+  \whiledo{\anpv > 1}{%
+    \modulo{\the\anpv}{\the\bnpv}
+    \ifnum\remainder=0\relax
+      \global\premier=\numexpr\premier+1\relax
+      \cnpv=\numexpr\anpv/\bnpv\relax
+      \anpv=\cnpv\relax
+    \else%
+      \bnpv=\numexpr\bnpv+1\relax%
+    \fi%
+  }
+  \ifnum\premier=0
+    Le nombre \num{#1} est un nombre premier.
+    \else
+    \begin{tabular}{c|c}
+      \xintFor* ##1 in {\xintSeq {0}{\premier}}\do
+      {\PremierMultipleVide{#1}{##1}&\xdef\Etape{\fpeval{##1+1}}\PremierDiviseurVide{#1}{\Etape}
+                                      \xintifboolexpr{##1<\premier}{\\}{\\1\\}}%
+    \end{tabular}
+  \fi
+}
+
+\newcommand{\PremierDiviseurVide}[2]{%
+  %#1 : le nombre entier à tester
+  %#2 : le nombre d'étapes à effectuer
+  \newcount\anpvv\newcount\bnpvv\newcount\cnpvv\newcount\dnpvv%
+  \ensuremath{%
+    \anpvv=#1\relax
+    \bnpvv=2\relax
+    \dnpvv=0\relax%
+    \whiledo{\anpvv > 1}{%
+      \whiledo{\dnpvv < \number#2}{%
+        \modulo{\the\anpvv}{\the\bnpvv}
+        \ifnum\remainder=0\relax
+          \dnpvv=\numexpr\dnpvv+1\relax
+          \cnpvv=\numexpr\anpvv/\bnpvv\relax
+          \anpvv=\cnpvv\relax
+          %\num{\the\bnpvv}%
+        \else%
+          \bnpvv=\numexpr\bnpvv+1\relax%
+        \fi%
+      }
+      \num{\the\bnpvv}%
+      \anpvv=1%
+    }
+  }
+}
+
+\newcommand{\PremierMultipleVide}[2]{%
+  %#1 : le nombre entier à tester
+  %#2 : le nombre d'étapes à effectuer
+  \newcount\anpmv\newcount\bnpmv\newcount\cnpmv\newcount\dnpmv%
+  \ensuremath{%
+    \anpmv=#1\relax
+    \bnpmv=2\relax
+    \dnpmv=0\relax%
+    \whiledo{\anpmv > 1}{%
+      \whiledo{\dnpmv < \number#2}{%
+        \modulo{\the\anpmv}{\the\bnpmv}
+        \ifnum\remainder=0\relax
+          \dnpmv=\numexpr\dnpmv+1\relax
+          \cnpmv=\numexpr\anpmv/\bnpmv\relax
+          \anpmv=\cnpmv\relax
+          %\num{\the\bnpmv}
+        \else%
+          \bnpmv=\numexpr\bnpmv+1\relax%
+        \fi%
+      }
+      \num{\the\anpmv}%
+      \anpmv=1%
+    }
+  }
+}
+
+\newcommand{\NombrePremierVerticalVide}[1]{%écrire la décomposition complète
+  % #1 le nombre premier à tester
+  \newcount\anpv\newcount\bnpv\newcount\cnpv%\newcount\e\newcount\f%
+  \anpv=#1\relax
+  \bnpv=2\relax
+  \premier=-1\relax
+  % Pour déterminer le nombre d'étapes
+  \whiledo{\anpv > 1}{%
+    \modulo{\the\anpv}{\the\bnpv}
+    \ifnum\remainder=0\relax
+      \global\premier=\numexpr\premier+1\relax
+      \cnpv=\numexpr\anpv/\bnpv\relax
+      \anpv=\cnpv\relax
+    \else%
+      \bnpv=\numexpr\bnpv+1\relax%
+    \fi%
+  }
+  \ifnum\premier=0
+    Le nombre \num{#1} est un nombre premier.
+    \else
+    \renewcommand{\arraystretch}{1.5}
+    \begin{tabular}{c|c}
+      \PremierMultipleVide{#1}{0}&\hbox to1cm{\dotfill}\\
+      \xintFor* ##1 in {\xintSeq {1}{\premier}}\do
+      {\hbox to1cm{\dotfill}&\hbox
+                              to1cm{\dotfill}\xintifboolexpr{##1<\premier}{\\}{\\\hbox
+      to1cm{\dotfill}\\}}%
+    \end{tabular}
+    \renewcommand{\arraystretch}{1}
+  \fi
+}
+
+\newcommand{\NombrePremierExposant}[1]{%écrire la décomposition
+  % complète
+  \newcount\anp\newcount\bnp\newcount\cnp%\newcount\e\newcount\f%
+  % #1 le nombre premier à tester
+  \anp=#1\relax%
+  \bnp=2\relax%
+  \premier=-1\relax%
+ % Pour déterminer le nombre d'étapes
+  \whiledo{\anp > 1}{%
+    \modulo{\the\anp}{\the\bnp}
+    \ifnum\remainder=0\relax%
+      \global\premier=\numexpr\premier+1\relax%
+      \cnp=\numexpr\anp/\bnp\relax%
+      \anp=\cnp\relax%
+    \else%
+      \bnp=\numexpr\bnp+1\relax%
+      \fi%
+  }
+  \ifnum\premier=0%
+    Le nombre \num{#1} est un nombre premier.%
+  \else%
+  \begin{align*}
+      \xintFor* ##1 in {\xintSeq {1}{\premier}}\do {\num{#1}&=\PremierEtape{#1}{##1}\\}%
+      \num{#1}&=\PremierExposant{#1}%
+    \end{align*}%
+  \fi%
+}%
+  
+\newcommand{\PremierEtape}[2]{%
+  %#1 : le nombre entier à tester
+  %#2 : le nombre d'étapes à effectuer
+  \newcount\anp\newcount\bnp\newcount\cnp\newcount\dnp%
+  \ensuremath{%
+    \anp=#1\relax
+    \bnp=2\relax
+    \dnp=0\relax%
+    \whiledo{\anp > 1}{%
+      \whiledo{\dnp < \number#2}{%
+        \modulo{\the\anp}{\the\bnp}
+        \ifnum\remainder=0\relax
+          \dnp=\numexpr\dnp+1\relax
+          \cnp=\numexpr\anp/\bnp\relax
+          \anp=\cnp\relax
+          \num{\the\bnp}\times%
+        \else%
+          \bnp=\numexpr\bnp+1\relax%
+        \fi%
+      }
+      \num{\the\anp}%
+      \anp=1%
+    }
+  }
+}
+
+\newcommand{\PremierExposant}[1]{%
+  %#1 : le nombre entier à tester
+  \ensuremath{%
+  \newcount\anp\newcount\bnp\newcount\cnp%
+  \newcount\pileb\newcount\exposant%
+  \exposant=0\relax%
+  \anp=#1\relax%
+  \bnp=2\relax%
+  \pileb=2\relax%
+  \whiledo{\the\anp > 1}{%
+    \modulo{\the\anp}{\the\bnp}
+    \ifnum\remainder=0\relax
+      \cnp=\numexpr\anp/\bnp\relax
+      \ifnum\pileb=\bnp
+      \exposant=\numexpr\exposant+1\relax
+      \fi
+      \anp=\cnp\relax
+    \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
+    \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
+  \anpl=#1\relax%
+  \bnpl=2\relax%
+  \pilebl=2\relax%
+  \whiledo{\the\anpl > 1}{%
+    \modulo{\the\anpl}{\the\bnpl}
+    \ifnum\remainder=0\relax
+      \cnpl=\numexpr\anpl/\bnpl\relax
+      \num{\the\bnpl}\ifnum\anpl>\bnpl\times\fi%
+      \anpl=\cnpl\relax
+    \else%
+      \bnpl=\numexpr\bnpl+1\relax%
+      \pilebl=\bnpl\relax%
+      \fi%
+    }
+  }
+}
+
+\newcommand{\ListeDiviseur}[1]{%#1 : le nombre entier à tester
+  \newcount\anp\newcount\bnp%
+  \anp=#1%
+  \bnp=2\relax%
+  1 %
+  \whiledo{\bnp<\anp}{%
+    \modulo{\the\anp}{\the\bnp}{}%
+    \ifnum\remainder=0%
+    ; $\num{\the\bnp}$ %
+    \fi%
+    \bnp=\numexpr\bnp+1%
+  }%
+  et \num{\the\anp}%
+}
+
+
+%%%%%%%%%%%%%%%%%%%
+% Simplification
+%%%%%%%%%%%%%%%%%%%
+\makeatletter%by christian Tellechea
+% Calcul du PGCD de #1 et #2
+\newcount\cnt@a\newcount\cnt@b\newcount\pgcd
+\def\PGCD#1#2{%
+  \ifnum#1>#2\cnt@a#1\cnt@b#2\else\cnt@a#2\cnt@b#1\relax\fi
+  \PGCD@i
+}
+\def\PGCD@i{\edef\PGCD@ii##1{##1{\number\cnt@a}{\number\cnt@b}}\PGCD@ii\PGCD@iii}
+\def\PGCD@iii#1#2{%
+  \cnt@b#1\relax\global\divide\cnt@b#2%
+  \global\cnt@b\numexpr#1-#2*\cnt@b%
+  \global\cnt@a#2\global\pgcd\cnt@a%
+  \ifnum\cnt@b>\z@\expandafter\PGCD@i%
+  \fi}%
+\makeatother
+
+\def\SSimplifie#1#2{%
+  % Simplification d'une écriture #1/#2
+  \ensuremath{
+    \newcount\numerateur\newcount\denominateur\newcount\valabsnum\newcount\valabsdeno
+    \numerateur=\number#1
+    \denominateur=\number#2
+    \ifnum\number#1<0\relax
+      \valabsnum=\numexpr0-\number#1
+    \else
+      \valabsnum=\number#1
+    \fi
+    \ifnum\number#2<0\relax
+      \valabsdeno=\numexpr0-\number#2
+    \else
+      \valabsdeno=\number#2
+    \fi
+    \ifnum\the\numerateur<0\relax
+      \ifnum\the\denominateur<0\relax
+        \numerateur=\valabsnum
+        \denominateur=\valabsdeno
+      \fi
+    \fi
+    \ifnum\number#2=0\relax
+      \text{\bfseries(???)}
+    \else
+      \ifnum\number#1=0\relax
+        0
+      \else
+        \PGCD{\the\valabsnum}{\the\valabsdeno}%
+        \ifnum\pgcd>1\relax
+          \ifthenelse{\pgcd=\number#2 \OR \pgcd=\the\valabsdeno}{%
+            \divide\numerateur by \denominateur\num{\the\numerateur}
+          }{\divide\numerateur by\pgcd%
+            \divide\denominateur by\pgcd%
+            \frac{\num{\the\numerateur}}{\num{\the\denominateur}}
+          }
+        \else%%%comme on est avec les négatifs, on doit regarder si la valeur absolue est égale à 1
+          \ifnum\valabsdeno=1\relax
+            \divide\numerateur by \denominateur\num{\the\numerateur}
+          \else
+            \frac{\num{\the\numerateur}}{\num{\the\denominateur}}
+          \fi
+        \fi%
+      \fi%
+    \fi%
+  }%
+}
+
+
+\newcommand{\SSimpli}[2]{%
+  % Décomposition d'une simplification de #1/#2
+  \newcount\numerateur\newcount\denominateur\newcount\valabsnum\newcount\valabsdeno%
+  \numerateur=\number#1
+  \denominateur=\number#2
+  \ifnum\number#1<0
+  \valabsnum=\numexpr0-\number#1
+  \else
+  \valabsnum=\number#1
+  \fi
+  \ifnum\number#2<0
+  \valabsdeno=\numexpr0-\number#2
+  \else
+  \valabsdeno=\number#2
+  \fi
+  \ifnum\number#2=0\relax
+    \ensuremath{\text{\bfseries(???)}}
+  \else
+      \ifnum\number#1=0\relax
+        0
+      \else
+        \PGCD{\the\valabsnum}{\the\valabsdeno}%
+        \ifnum\pgcd>1\relax
+          \ifthenelse{\pgcd=\number#2 \OR \pgcd=\the\valabsdeno}{%
+            \divide\numerateur by \denominateur\num{\the\numerateur}
+          }{%\divide\numerateur by\pgcd%
+            %\divide\denominateur by\pgcd%
+            \ensuremath{\frac{\num{\the\numerateur}_{\mbox{\tiny$\div\num{\number\pgcd}$}}}{\num{\the\denominateur}_{\mbox{\tiny$\div\num{\number\pgcd}$}}}}
+          }
+        \else
+          \ifnum\denominateur=1\relax
+            \ensuremath{\frac{\num{\the\numerateur}_{\mbox{\tiny$\div\num{\number\pgcd}$}}}{\num{\the\denominateur}_{\mbox{\tiny$\div\num{\number\pgcd}$}}}}
+          \else
+            \ensuremath{\frac{\num{\the\numerateur}}{\num{\the\denominateur}}}
+          \fi
+        \fi
+      \fi
+    \fi
+}
+
+\newcommand\DiviseurCommun[2]{%
+  % #1 : le premier nombre entier
+  % #2 : le deuxième nombre entier 
+  \newcount\anpdc\newcount\bnpdc\newcount\cnpdc%
+  \anpdc=#1%
+  \cnpdc=#2%
+  \bnpdc=2\relax%
+  \whiledo{\bnpdc<\anpdc}{%
+    \modulo{\the\anpdc}{\the\bnpdc}{}%
+    \ifnum\remainder=0%
+    \modulo{\the\cnpdc}{\the\bnpdc}{}
+    \ifnum\remainder=0%
+    \xdef\DivCom{\the\bnpdc}%
+    \bnpdc=\anpdc%
+    \else%
+    \xdef\DivCom{1}%
+    \bnpdc=\numexpr\bnpdc+1%
+    \fi%
+    \else%
+    \xdef\DivCom{1}%
+    \bnpdc=\numexpr\bnpdc+1%
+    \fi
+  }%
+}
+
+\newcommand\LongueSimplification[2]{%
+  \DiviseurCommun{#1}{#2}%
+  \xdef\NumerateurDiv{#1}%
+  \xdef\DenominateurDiv{#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}%
+      \DiviseurCommun{\NumerateurDiv}{\DenominateurDiv}%
+      \xintifboolexpr{\DivCom>1}{=}{}%
+    }
+  }
+}
+
+\setKVdefault[ClesSimplification]{Details=false,All=false,Longue=false,Fleches=false}
+
+\newcounter{NbFrac}%
+\setcounter{NbFrac}{0}%
+
+\newcommand\Simplification[3][]{%
+  \stepcounter{NbFrac}%
+  \useKVdefault[ClesSimplification]%
+  \setKV[ClesSimplification]{#1}%
+  \ifboolKV[ClesSimplification]{Fleches}{%
+    \setsepchar[*]{,*/}%\ignoreemptyitems
+    \readlist*\Listea{#2}%
+    \readlist*\Listeb{#3}%
+    \setbox1=\hbox{\Listea[1,1]{}}%
+    \setbox2=\hbox{\Listeb[1,1]}%
+    \setbox3=\hbox{\Listea[1,3]}%
+    \setbox4=\hbox{\Listeb[1,3]}%
+     \ensuremath{%
+       \frac{\tikzmarknode[anchor=north]{A-\theNbFrac}{\Listea[1,1]}{}}{\tikzmarknode[anchor=south]{B-\theNbFrac}{\Listeb[1,1]}{}}=\frac{\tikzmarknode[anchor=north]{C-\theNbFrac}{\Listea[1,3]}{}}{\tikzmarknode[anchor=south]{D-\theNbFrac}{\Listeb[1,3]}{}}%
+     }%
+     \begin{tikzpicture}[remember picture,overlay]%
+       \draw[out=45,in=135,-stealth,transform canvas={yshift=0.25em}]
+       let
+       \p1=(pic cs:A-\theNbFrac),
+       \p2=(pic cs:C-\theNbFrac)
+       in (pic cs:A-\theNbFrac) to node[midway,above]{\Listea[1,2]}(\x2,\y1);
+      \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}%
+    }{%
+      \ifboolKV[ClesSimplification]{Details}{\SSimpli{#2}{#3}}{\ifboolKV[ClesSimplification]{All}{\ensuremath{\SSimpli{#2}{#3}=\SSimplifie{#2}{#3}}}{\SSimplifie{#2}{#3}}}%
+    }%
+  }%
+}%
+
+%%%%%%%%%%%%%%%%%%%%%
+%%% Thales
+%%%%%%%%%%%%%%%%%%%%%
+\newcount\ppcm
+
+\newcommand\PPCM[2]{%
+  \PGCD{#1}{#2}
+  \ppcm=\numexpr#1*#2/\pgcd\relax
+}
+
+\setKVdefault[ClesThales]{Calcul=true,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}
+
+%On définit la figure à utiliser
+\def\MPFigThales#1#2#3#4#5{
+    % #1 Premier sommet
+    % #2 Deuxième sommet
+    % #3 Troisième sommet
+    % #4 point sur le segment #1#2
+    % #5 point sur le segment #1#3
+  \ifluatex
+  \mplibcodeinherit{enable}
+  \mplibforcehmode
+  \begin{mplibcode}
+    u:=1cm;
+    pair A,B,C,M,N,O;%
+    %On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=u*(1,1);
+    B-A=u*(4,0);
+    C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]);
+    % On définit le centre du cercle circonscrit
+    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 :)
+    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)};
+    cotes3=C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
+    M=point(0.4*length cotes1) of cotes1;
+    N=point(0.6*length cotes3) of cotes3;
+    cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)};
+    path triangle;
+    triangle=cotes1--cotes2--cotes3--cycle;
+    draw triangle;
+    draw cotes4;
+    %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 #4 etex,1.1[C,M]);
+    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{mplibcode}
+  \mplibcodeinherit{disable}
+  \else
+  \begin{mpost}
+    u:=1cm;
+    pair A,B,C,M,N,O;%
+    %On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=u*(1,1);
+    B-A=u*(4,0);
+    C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]);
+    % On définit le centre du cercle circonscrit
+    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 :)
+    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)};
+    cotes3=C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
+    M=point(0.4*length cotes1) of cotes1;
+    N=point(0.6*length cotes3) of cotes3;
+    cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)};
+    path triangle;
+    triangle=cotes1--cotes2--cotes3--cycle;
+    draw triangle;
+    draw cotes4;
+    %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 #4 etex,1.1[C,M]);
+    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 figure à utiliser
+\def\MPFigReciThales#1#2#3#4#5{
+    % #1 Premier sommet
+    % #2 Deuxième sommet
+    % #3 Troisième sommet
+    % #4 point sur le segment #1#2
+    % #5 point sur le segment #1#3
+  \ifluatex
+  \mplibcodeinherit{enable}
+  \mplibforcehmode
+  \begin{mplibcode}
+    u:=1cm;
+    pair A,B,C,M,N,O;%
+    %On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=u*(1,1);
+    B-A=u*(4,0);
+    C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]);
+    % On définit le centre du cercle circonscrit
+    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 :)
+    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)};
+    cotes3=C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
+    M=point(0.4*length cotes1) of cotes1;
+    N=point(0.6*length cotes3) of cotes3;
+    cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)};
+    path triangle;
+    triangle=cotes1--cotes2--cotes3--cycle;
+    draw triangle;
+    draw cotes4;
+    %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 #4 etex,1.1[C,M]);
+    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);
+  \end{mplibcode}
+  \mplibcodeinherit{disable}
+  \else
+  \begin{mpost}
+      u:=1cm;
+    pair A,B,C,M,N,O;%
+    %On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=u*(1,1);
+    B-A=u*(4,0);
+    C=(A--2[A,B rotatedabout(A,45)]) intersectionpoint (B--2[B,A rotatedabout(B,-60)]);
+    % On définit le centre du cercle circonscrit
+    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 :)
+    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)};
+    cotes3=C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
+    M=point(0.4*length cotes1) of cotes1;
+    N=point(0.6*length cotes3) of cotes3;
+    cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)};
+    path triangle;
+    triangle=cotes1--cotes2--cotes3--cycle;
+    draw triangle;
+    draw cotes4;
+    %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 #4 etex,1.1[C,M]);
+    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{%
+    % #1 Premier sommet
+    % #2 Deuxième sommet
+    % #3 Troisième sommet
+    % #4 point sur la droite #1#2
+    % #5 point sur la droite #1#3
+  \ifluatex
+  \mplibforcehmode
+  \mplibcodeinherit{enable}
+  \begin{mplibcode}
+    u:=1cm;
+    pair A,B,C,M,N,O;%
+    O=(2.5u,2.5u);
+    path cc;
+    cc=(fullcircle scaled 3u) shifted O;
+    %On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=point(0.1*length cc) of cc;
+    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);
+    % on dessine à main levée :)
+    M=1.4[B,A];
+    N=1.4[C,A];
+    path cotes[];
+    cotes1=A{dir(angle(B-A)+5)}..1.15[A,B]{dir(angle(B-A)+5)};
+    cotes2=1.15[C,B]{dir(angle(C-B)+5)}..1.15[B,C]{dir(angle(C-B)+5)};
+    cotes3=1.15[A,C]{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
+    cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)};
+    cotes5=A{dir(angle(M-A)+5)}..1.15[A,M]{dir(angle(M-A)+5)};
+    cotes6=A{dir(angle(N-A)+5)}..1.15[A,N]{dir(angle(N-A)+5)};
+    for k=1 upto 6:
+    draw cotes[k];
+    endfor;
+    pair I;
+    % On définit le centre du cercle inscrit à AMC
+    (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]);
+    label(btex #4 etex,1.1[B,M]);
+    label(btex #5 etex,1.1[C,N]);
+    fill (fullcircle scaled 0.75mm) shifted (cotes5 intersectionpoint cotes4);
+    fill (fullcircle scaled 0.75mm) shifted (cotes6 intersectionpoint cotes4);
+    pair I,J,K;
+    I=1.1[N,M];
+    J=1.1[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{mplibcode}
+  \mplibcodeinherit{disable}
+  \else
+  \begin{mpost}
+    u:=1cm;
+    pair A,B,C,M,N,O;%
+    O=(2.5u,2.5u);
+    path cc;
+    cc=(fullcircle scaled 3u) shifted O;
+    %On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=point(0.1*length cc) of cc;
+    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);
+    % on dessine à main levée :)
+    M=1.4[B,A];
+    N=1.4[C,A];
+    path cotes[];
+    cotes1=A{dir(angle(B-A)+5)}..1.15[A,B]{dir(angle(B-A)+5)};
+    cotes2=1.15[C,B]{dir(angle(C-B)+5)}..1.15[B,C]{dir(angle(C-B)+5)};
+    cotes3=1.15[A,C]{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
+    cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)};
+    cotes5=A{dir(angle(M-A)+5)}..1.15[A,M]{dir(angle(M-A)+5)};
+    cotes6=A{dir(angle(N-A)+5)}..1.15[A,N]{dir(angle(N-A)+5)};
+    for k=1 upto 6:
+    draw cotes[k];
+    endfor;
+    pair I;
+    % On définit le centre du cercle inscrit à AMC
+    (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]);
+    label(btex #4 etex,1.1[B,M]);
+    label(btex #5 etex,1.1[C,N]);
+    fill (fullcircle scaled 0.75mm) shifted (cotes5 intersectionpoint cotes4);
+    fill (fullcircle scaled 0.75mm) shifted (cotes6 intersectionpoint cotes4);
+    pair I,J,K;
+    I=1.1[N,M];
+    J=1.1[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\MPFigReciThalesCroisee#1#2#3#4#5{%
+  % #1 Premier sommet
+    % #2 Deuxième sommet
+    % #3 Troisième sommet
+    % #4 point sur la droite #1#2
+    % #5 point sur la droite #1#3
+  \ifluatex
+  \mplibforcehmode
+  \mplibcodeinherit{enable}
+  \begin{mplibcode}
+    u:=1cm;
+    pair A,B,C,M,N,O;%
+    O=(2.5u,2.5u);
+    path cc;
+    cc=(fullcircle scaled 3u) shifted O;
+    %On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=point(0.1*length cc) of cc;
+    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);
+    % on dessine à main levée :)
+    M=1.4[B,A];
+    N=1.4[C,A];
+    path cotes[];
+    cotes1=A{dir(angle(B-A)+5)}..1.15[A,B]{dir(angle(B-A)+5)};
+    cotes2=1.15[C,B]{dir(angle(C-B)+5)}..1.15[B,C]{dir(angle(C-B)+5)};
+    cotes3=1.15[A,C]{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
+    cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)};
+    cotes5=A{dir(angle(M-A)+5)}..1.15[A,M]{dir(angle(M-A)+5)};
+    cotes6=A{dir(angle(N-A)+5)}..1.15[A,N]{dir(angle(N-A)+5)};
+    for k=1 upto 6:
+    draw cotes[k];
+    endfor;
+    pair I;
+    % On définit le centre du cercle inscrit à AMC
+    (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]);
+    label(btex #4 etex,1.1[B,M]);
+    label(btex #5 etex,1.1[C,N]);
+    fill (fullcircle scaled 0.75mm) shifted (cotes5 intersectionpoint cotes4);
+    fill (fullcircle scaled 0.75mm) shifted (cotes6 intersectionpoint cotes4);
+    fill (fullcircle scaled 0.75mm) shifted (cotes1 intersectionpoint cotes2);
+    fill (fullcircle scaled 0.75mm) shifted (cotes3 intersectionpoint cotes2);
+  \end{mplibcode}
+  \mplibcodeinherit{disable}
+  \else
+  \begin{mpost}
+    u:=1cm;
+    pair A,B,C,M,N,O;%
+    O=(2.5u,2.5u);
+    path cc;
+    cc=(fullcircle scaled 3u) shifted O;
+    %On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=point(0.1*length cc) of cc;
+    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);
+    % on dessine à main levée :)
+    M=1.4[B,A];
+    N=1.4[C,A];
+    path cotes[];
+    cotes1=A{dir(angle(B-A)+5)}..1.15[A,B]{dir(angle(B-A)+5)};
+    cotes2=1.15[C,B]{dir(angle(C-B)+5)}..1.15[B,C]{dir(angle(C-B)+5)};
+    cotes3=1.15[A,C]{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)};
+    cotes4=1.5[N,M]{dir(angle(N-M)+5)}..1.5[M,N]{dir(angle(N-M)+5)};
+    cotes5=A{dir(angle(M-A)+5)}..1.15[A,M]{dir(angle(M-A)+5)};
+    cotes6=A{dir(angle(N-A)+5)}..1.15[A,N]{dir(angle(N-A)+5)};
+    for k=1 upto 6:
+    draw cotes[k];
+    endfor;
+    pair I;
+    % On définit le centre du cercle inscrit à AMC
+    (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]);
+    label(btex #4 etex,1.1[B,M]);
+    label(btex #5 etex,1.1[C,N]);
+    fill (fullcircle scaled 0.75mm) shifted (cotes5 intersectionpoint cotes4);
+    fill (fullcircle scaled 0.75mm) shifted (cotes6 intersectionpoint cotes4);
+    fill (fullcircle scaled 0.75mm) shifted (cotes1 intersectionpoint cotes2);
+    fill (fullcircle scaled 0.75mm) shifted (cotes3 intersectionpoint cotes2);
+  \end{mpost}
+  \fi
+}
+
+%%%
+\newcommand{\TTThales}[6][]{%
+  \useKVdefault[ClesThales]%
+  \setKV[ClesThales]{#1}%
+  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} \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$(#2#3)$}, \ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{$#6$} est un point \ifboolKV[ClesThales]{Segment}{du segment}{de la droite} \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$(#2#4)$}.%
+  \\Comme les droites \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$(#5#6)$} et \ifboolKV[ClesThales]{Remediation}{\pointilles[2cm]}{$(#3#4)$} sont parallèles, alors \ifboolKV[ClesThales]{Propor}{le tableau%
+    \[\begin{array}{c|c|c}
+        \ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#5}&\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#6}&\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#5#6}\\
+        \hline
+        \ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#3}&\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#4}&\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#3#4}\\
+      \end{array}
+    \]
+    est un tableau de proportionnalité d'après le théorème de Thalès.%
+  }{%
+    le théorème de Thalès permet d'écrire :%
+    \[\frac{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#5}}{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#3}}=\frac{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#6}}{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#2#4}}=\frac{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#5#6}}{\ifboolKV[ClesThales]{Remediation}{\pointilles[1cm]}{#3#4}}\]%
+  }
+}
+
+\newcommand{\TThalesCalculsD}[8][]{%
+  \setKV[ClesThales]{#1}%
+  \newcount\zzz\newcount\yyy\newcount\xxx%Pour se rappeller des calculs à faire et combien en faire%
+  \def\Nomx{}%
+  \def\Nomy{}%
+  \def\Nomz{}%
+  \zzz=0\yyy=0\xxx=0%
+  \TTThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par
+\IfDecimal{#3}{%
+  \IfDecimal{#6}{}{%
+    \IfDecimal{#4}{%
+        \IfDecimal{#7}{%
+          \xxx=5263%#6&=\frac{#3\times#7}{#4}\\
+          \edef\Nomx{#6}\opcopy{#3}{valx}\opcopy{#7}{Valx}\opcopy{#4}{denox}%
+          \xdef\ResultatThalesx{\fpeval{round(#3*#7/#4,\useKV[ClesThales]{Precision})}}%
+        }{%
+          \IfDecimal{#8}{\IfDecimal{#5}{\xxx=5274%\[#6=\frac{#3\times#8}{#5}\]
+              \edef\Nomx{#6}\opcopy{#3}{valx}\opcopy{#8}{Valx}\opcopy{#5}{denox}%
+              \xdef\ResultatThalesx{\fpeval{round(#3*#8/#5,\useKV[ClesThales]{Precision})}}%
+          }{}}{}
+        }
+      }{\IfDecimal{#8}{\IfDecimal{#5}{\xxx=5274%\[#6=\frac{#3\times#8}{#5}\]
+            \edef\Nomx{#6}\opcopy{#3}{valx}\opcopy{#8}{Valx}\opcopy{#5}{denox}%
+            \xdef\ResultatThalesx{\fpeval{round(#3*#8/#5,\useKV[ClesThales]{Precision})}}%
+          }{}}{}
+      }
+    }
+  }{%
+    \IfDecimal{#6}{%
+      \IfDecimal{#4}{%
+        \IfDecimal{#7}{%
+          \xxx=2536%\[#3=\frac{#6\times#4}{#7}\]%
+          \edef\Nomx{#3}\opcopy{#6}{valx}\opcopy{#4}{Valx}\opcopy{#7}{denox}%
+          \xdef\ResultatThalesx{\fpeval{round(#6*#4/#7,\useKV[ClesThales]{Precision})}}%
+        }{%
+          \IfDecimal{#5}{\IfDecimal{#8}{\xxx=2547
+              \edef\Nomx{#3}\opcopy{#6}{valx}\opcopy{#5}{Valx}\opcopy{#8}{denox}%\[#3=\frac{#6\times#5}{#8}\]
+              \xdef\ResultatThalesx{\fpeval{round(#6*#5/#8,\useKV[ClesThales]{Precision})}}%
+            }{}}{}
+        }
+      }{\IfDecimal{#5}{\IfDecimal{#8}{\xxx=2547
+            \edef\Nomx{#3}\opcopy{#6}{valx}\opcopy{#5}{Valx}\opcopy{#8}{denox}%\[#3=\frac{#6\times#5}{#8}\]
+            \xdef\ResultatThalesx{\fpeval{round(#6*#5/#8,\useKV[ClesThales]{Precision})}}%
+          }{}}{}
+      }
+    }{}
+  }%
+  % 
+  \IfDecimal{#4}{%
+    \IfDecimal{#7}{}{%
+      \IfDecimal{#5}{%
+        \IfDecimal{#8}{%
+          \yyy=6374%\[#7=\frac{#4\times#8}{#5}\]%
+          \edef\Nomy{#7}\opcopy{#4}{valy}\opcopy{#8}{Valy}\opcopy{#5}{denoy}%
+          \xdef\ResultatThalesy{\fpeval{round(#4*#8/#5,\useKV[ClesThales]{Precision})}}%
+        }{%
+          \IfDecimal{#6}{\IfDecimal{#3}{\yyy=6352%\[#7=\frac{#4\times#6}{#3}\]
+              \edef\Nomy{#7}\opcopy{#4}{valy}\opcopy{#6}{Valy}\opcopy{#3}{denoy}%
+              \xdef\ResultatThalesy{\fpeval{round(#4*#6/#3,\useKV[ClesThales]{Precision})}}%
+            }{}}{}
+        }
+      }{\IfDecimal{#6}{\IfDecimal{#3}{\yyy=6352%\[#7=\frac{#4\times#6}{#3}\]
+            \edef\Nomy{#7}\opcopy{#4}{valy}\opcopy{#6}{Valy}\opcopy{#3}{denoy}%
+            \xdef\ResultatThalesy{\fpeval{round(#4*#6/#3,\useKV[ClesThales]{Precision})}}%
+            }{}}{}
+      }
+    }
+  }{%
+    \IfDecimal{#7}{%
+      \IfDecimal{#5}{%
+        \IfDecimal{#8}{%
+          \yyy=3647%\[#4=\frac{#7\times#5}{#8}\]%
+          \edef\Nomy{#4}\opcopy{#7}{valy}\opcopy{#5}{Valy}\opcopy{#8}{denoy}%
+          \xdef\ResultatThalesy{\fpeval{round(#7*#5/#8,\useKV[ClesThales]{Precision})}}%
+        }{%
+          \IfDecimal{#3}{\IfDecimal{#6}{\yyy=3625%\[#4=\frac{#7\times#3}{#6}\]
+              \edef\Nomy{#4}\opcopy{#7}{valy}\opcopy{#3}{Valy}\opcopy{#6}{denoy}%
+              \xdef\ResultatThalesy{\fpeval{round(#7*#3/#6,\useKV[ClesThales]{Precision})}}%
+            }{}}{}
+        }
+      }{\IfDecimal{#3}{\IfDecimal{#6}{\yyy=3625%\[#4=\frac{#7\times#3}{#6}\]
+            \edef\Nomy{#4}\opcopy{#7}{valy}\opcopy{#3}{Valy}\opcopy{#6}{denoy}%
+            \xdef\ResultatThalesy{\fpeval{round(#7*#3/#6,\useKV[ClesThales]{Precision})}}%
+            }{}}{}
+      }}{}}%
+  % 
+  \IfDecimal{#5}{%
+    \IfDecimal{#8}{}{%
+      \IfDecimal{#4}{
+        \IfDecimal{#7}{
+          \zzz=7463%\[#8=\frac{#5\times#7}{#4}\]%
+          \edef\Nomz{#8}\opcopy{#5}{valz}\opcopy{#7}{Valz}\opcopy{#4}{denoz}%
+          \xdef\ResultatThalesz{\fpeval{round(#5*#7/#4,\useKV[ClesThales]{Precision})}}%
+        }{%
+          \IfDecimal{#3}{\IfDecimal{#6}{\zzz=7452%\[#8=\frac{#5\times#6}{#3}\]
+              \edef\Nomz{#8}\opcopy{#5}{valz}\opcopy{#6}{Valz}\opcopy{#3}{denoz}%
+              \xdef\ResultatThalesz{\fpeval{round(#5*#6/#3,\useKV[ClesThales]{Precision})}}%
+            }{}}{}
+        }
+      }{\IfDecimal{#3}{\IfDecimal{#6}{\zzz=7452%\[#8=\frac{#5\times#6}{#3}\]
+            \edef\Nomz{#8}\opcopy{#5}{valz}\opcopy{#6}{Valz}\opcopy{#3}{denoz}%
+            \xdef\ResultatThalesz{\fpeval{round(#5*#6/#3,\useKV[ClesThales]{Precision})}}%
+            }{}}{}
+      }
+    }
+  }{%
+    \IfDecimal{#8}{%
+      \IfDecimal{#4}{%
+        \IfDecimal{#7}{%
+          \zzz=4736% \[#5=\frac{#8\times#4}{#7}\]%
+          \edef\Nomz{#5}\opcopy{#8}{valz}\opcopy{#4}{Valz}\opcopy{#7}{denoz}%
+          \xdef\ResultatThalesz{\fpeval{round(#8*#4/#7,\useKV[ClesThales]{Precision})}}%
+        }{%
+          \IfDecimal{#3}{\IfDecimal{#6}{\zzz=4725%\[#5=\frac{#8\times#3}{#6}\]
+              \edef\Nomz{#5}\opcopy{#8}{valz}\opcopy{#3}{Valz}\opcopy{#6}{denoz}%
+              \xdef\ResultatThalesz{\fpeval{round(#8*#3/#6,\useKV[ClesThales]{Precision})}}%
+            }{}}{}
+        }
+      }{\IfDecimal{#3}{\IfDecimal{#6}{\zzz=4725%\[#5=\frac{#8\times#3}{#6}\]
+            \edef\Nomz{#5}\opcopy{#8}{valz}\opcopy{#3}{Valz}\opcopy{#6}{denoz}%
+            \xdef\ResultatThalesz{\fpeval{round(#8*#3/#6,\useKV[ClesThales]{Precision})}}%
+            }{}}{}
+      }}{}
+  }%  
+  %%
+\StrMid{\the\zzz}{1}{1}[\cmza]%
+\StrMid{\the\yyy}{1}{1}[\cmya]%
+\StrMid{\the\xxx}{1}{1}[\cmxa]%
+\ifboolKV[ClesThales]{Calcul}{%
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%
+  On remplace par les longueurs connues :%
+  \ifboolKV[ClesThales]{Propor}{%
+    \[\begin{array}{c|c|c}
+        \IfDecimal{#3}{\num{#3}}{#3}&\IfDecimal{#4}{\num{#4}}{#4}&\IfDecimal{#5}{\num{#5}}{#5}\\
+        \hline
+        \IfDecimal{#6}{\num{#6}}{#6}&\IfDecimal{#7}{\num{#7}}{#7}&\IfDecimal{#8}{\num{#8}}{#8}
+      \end{array}
+    \]
+  }{%
+    \[\frac{\IfDecimal{#3}{\num{#3}}{#3}}{\IfDecimal{#6}{\num{#6}}{#6}}=\frac{\IfDecimal{#4}{\num{#4}}{#4}}{\IfDecimal{#7}{\num{#7}}{#7}}=\frac{\IfDecimal{#5}{\num{#5}}{#5}}{\IfDecimal{#8}{\num{#8}}{#8}}\]
+  }%
+  % On choisit éventuellement le calcul à faire s'il y en a plusieurs.
+  \xdef\CompteurCalcul{\useKV[ClesThales]{ChoixCalcul}}%
+  \xintifboolexpr{\CompteurCalcul>0}{\xintifboolexpr{\CompteurCalcul=1}{\xdef\cmya{0}\xdef\cmza{0}}{\xintifboolexpr{\CompteurCalcul=2}{\xdef\cmxa{0}\xdef\cmza{0}}{\xdef\cmxa{0}\xdef\cmya{0}}}}{}%
+  %%on fait les calculs
+\begin{align*}
+    %Premier compteur \xxx
+    \ifnum\cmxa>0
+      \Nomx\uppercase{&}=\frac{\opexport{valx}{\valx}\num{\valx}\times\opexport{Valx}{\Valx}\num{\Valx}}{\opexport{denox}{\denox}\num{\denox}}\relax%\global\numx=\numexpr\opprint{valx}*\opprint{Valx}\relax
+    \fi
+    %    % Deuxième compteur \yyy
+    \ifnum\cmya>0
+      \ifnum\cmxa=0
+      \else
+        \uppercase{&}
+      \fi%
+      \Nomy\uppercase{&}=\frac{\opexport{valy}{\valy}\num{\valy}\times\opexport{Valy}{\Valy}\num{\Valy}}{\opexport{denoy}{\denoy}\num{\denoy}}\relax%\global\numy=\numexpr\opprint{valy}*\opprint{Valy}\relax
+    \fi
+    % Troisième compteur \zzz
+    \ifnum\cmza>0
+      \ifnum\cmxa=0
+        \ifnum\cmya=0                           
+          %
+        \else
+          \uppercase{&}
+        \fi
+        \Nomz\uppercase{&}=\frac{\opexport{valz}{\valz}\num{\valz}\times\opexport{Valz}{\Valz}\num{\Valz}}{\opexport{denoz}{\denoz}\num{\denoz}}\relax%\global\numz=\numexpr\opprint{valz}*\opprint{Valz}\relax
+      \else
+        \uppercase{&}\Nomz\uppercase{&}=\frac{\opexport{valz}{\valz}\num{\valz}\times\opexport{Valz}{\Valz}\num{\Valz}}{\opexport{denoz}{\denoz}\num{\denoz}}\relax%\global\numz=\numexpr\opprint{valz}*\opprint{Valz}\relax
+      \fi
+    \fi
+    \\
+%    % 2eme ligne du tableau : calcul des numérateurs
+%        %Premier compteur \xxx
+    \ifnum\cmxa>0
+      \Nomx\uppercase{&}=\frac{\opmul*{valx}{Valx}{numx}\opexport{numx}{\numx}\num{\numx}}{\opprint{denox}}
+    \fi
+    %    % Deuxième compteur \yyy
+    \ifnum\cmya>0
+      \ifnum\cmxa=0
+        %
+      \else
+        \uppercase{&}
+      \fi
+      \Nomy\uppercase{&}=\frac{\opmul*{valy}{Valy}{numy}\opexport{numy}{\numy}\num{\numy}}{\opprint{denoy}}%
+    \fi
+%    %Troisième compteur \zzz
+    \ifnum\cmza>0
+      \ifnum\cmxa=0
+        \ifnum\cmya=0                           
+          %
+        \else
+          \uppercase{&}
+        \fi
+        \Nomz\uppercase{&}=\frac{\opmul*{valz}{Valz}{numz}\opexport{numz}{\numz}\num{\numz}}{\opprint{denoz}}
+      \else
+        \uppercase{&}\Nomz\uppercase{&}=\frac{\opmul*{valz}{Valz}{numz}\opexport{numz}{\numz}\num{\numz}}{\opprint{denoz}}
+      \fi
+    \fi
+    \\
+%    % 3eme ligne : Calculs
+    \ifnum\cmxa>0
+      \Nomx\uppercase{&}\opdiv*{numx}{denox}{resultatx}{restex}\opcmp{restex}{0}\ifopeq=\opprint{resultatx}~\text{\useKV[ClesThales]{Unite}}\else\approx\opround{resultatx}{\useKV[ClesThales]{Precision}}{resultatx}\opprint{resultatx}~\text{\useKV[ClesThales]{Unite}}\fi\opexport{resultatx}{\resultatx}%\xdef\ResultatThalesx{\num{\resultatx}}%
+    \fi
+    %    % Deuxième compteur \yyy
+    \ifnum\cmya>0
+      \ifnum\cmxa=0
+        %
+      \else
+        \uppercase{&}
+      \fi
+      \Nomy\uppercase{&}\opdiv*{numy}{denoy}{resultaty}{restey}\opcmp{restey}{0}\ifopeq=\opprint{resultaty}~\text{\useKV[ClesThales]{Unite}}\else\approx\opround{resultaty}{\useKV[ClesThales]{Precision}}{resultaty}\opprint{resultaty}~\text{\useKV[ClesThales]{Unite}}\fi\opexport{resultaty}{\resultaty}%\xdef\ResultatThalesy{\num{\resultaty}}
+    \fi
+%    %Troisième compteur \zzz
+    \ifnum\cmza>0
+      \ifnum\cmxa=0
+        \ifnum\cmya=0                           
+          %
+        \else
+          \uppercase{&}
+        \fi
+        \Nomz\uppercase{&}\opdiv*{numz}{denoz}{resultatz}{restez}\opcmp{restez}{0}\ifopeq=\opprint{resultatz}~\text{\useKV[ClesThales]{Unite}}\else\approx\opround{resultatz}{\useKV[ClesThales]{Precision}}{resultatz}\opprint{resultatz}~\text{\useKV[ClesThales]{Unite}}\fi\opexport{resultatz}{\resultatz}%\xdef\ResultatThalesz{\num{\resultatz}}
+      \else
+        \uppercase{&}\Nomz\uppercase{&}\opdiv*{numz}{denoz}{resultatz}{restez}\opcmp{restez}{0}\ifopeq=\opprint{resultatz}~\text{\useKV[ClesThales]{Unite}}\else\approx\opround{resultatz}{\useKV[ClesThales]{Precision}}{resultatz}\opprint{resultatz}~\text{\useKV[ClesThales]{Unite}}\fi\opexport{resultatz}{\resultatz}%\xdef\ResultatThalesz{\num{\resultatz}}
+      \fi
+    \fi
+\end{align*}
+}{}
+}
+
+\newcommand{\TThalesCalculsE}[8][]{%
+  \setKV[ClesThales]{#1}%
+  \newcount\zzz\newcount\yyy\newcount\xxx%Pour se rappeller des calculs à faire et combien en faire%
+  \newcount\valx\newcount\Valx%
+  \newcount\valy\newcount\Valy%
+  \newcount\valz\newcount\Valz%
+  \newcount\numx\newcount\numy\newcount\numz%
+  \newcount\denox\newcount\denoy\newcount\denoz%
+  \def\Nomx{}%
+  \def\Nomy{}%
+  \def\Nomz{}%
+  \zzz=0\yyy=0\xxx=0%
+  \TTThales[#1]{\StrMid{#2}{1}{1}}{\StrMid{#2}{2}{2}}{\StrMid{#2}{3}{3}}{\StrMid{#2}{4}{4}}{\StrMid{#2}{5}{5}}\par%
+\IfDecimal{#3}{%
+  \IfDecimal{#6}{}{%
+    \IfDecimal{#4}{%
+        \IfDecimal{#7}{%
+          \xxx=5263%#6&=\frac{#3\times#7}{#4}\\
+          \edef\Nomx{#6}\valx=#3\Valx=#7\denox=#4%
+        }{%
+          \IfDecimal{#8}{\IfDecimal{#5}{\xxx=5274%\[#6=\frac{#3\times#8}{#5}\]
+            \edef\Nomx{#6}\valx=#3\Valx=#8\denox=#5%
+          }{}}{}
+        }
+      }{\IfDecimal{#8}{\IfDecimal{#5}{\xxx=5274%\[#6=\frac{#3\times#8}{#5}\]
+            \edef\Nomx{#6}\valx=#3\Valx=#8\denox=#5%
+          }{}}{}
+      }
+    }
+  }{%
+    \IfDecimal{#6}{%
+      \IfDecimal{#4}{%
+        \IfDecimal{#7}{%
+          \xxx=2536%\[#3=\frac{#6\times#4}{#7}\]%
+          \edef\Nomx{#3}\valx=#6\Valx=#4\denox=#7%
+        }{%
+          \IfDecimal{#5}{\IfDecimal{#8}{\xxx=2547
+            \edef\Nomx{#3}\valx=#6\Valx=#5\denox=#8%\[#3=\frac{#6\times#5}{#8}\]
+            }{}}{}
+        }
+      }{\IfDecimal{#5}{\IfDecimal{#8}{\xxx=2547
+            \edef\Nomx{#3}\valx=#6\Valx=#5\denox=#8%\[#3=\frac{#6\times#5}{#8}\]
+            }{}}{}
+      }
+    }{}
+  }%
+  % 
+  \IfDecimal{#4}{%
+    \IfDecimal{#7}{}{%
+      \IfDecimal{#5}{%
+        \IfDecimal{#8}{%
+          \yyy=6374%\[#7=\frac{#4\times#8}{#5}\]%
+          \edef\Nomy{#7}\valy=#4\Valy=#8\denoy=#5%
+        }{%
+          \IfDecimal{#6}{\IfDecimal{#3}{\yyy=6352%\[#7=\frac{#4\times#6}{#3}\]
+            \edef\Nomy{#7}\valy=#4\Valy=#6\denoy=#3%
+            }{}}{}
+        }
+      }{\IfDecimal{#6}{\IfDecimal{#3}{\yyy=6352%\[#7=\frac{#4\times#6}{#3}\]
+            \edef\Nomy{#7}\valy=#4\Valy=#6\denoy=#3%
+            }{}}{}
+      }
+    }
+  }{%
+    \IfDecimal{#7}{%
+      \IfDecimal{#5}{%
+        \IfDecimal{#8}{%
+          \yyy=3647%\[#4=\frac{#7\times#5}{#8}\]%
+          \edef\Nomy{#4}\valy=#7\Valy=#5\denoy=#8%
+        }{%
+          \IfDecimal{#3}{\IfDecimal{#6}{\yyy=3625%\[#4=\frac{#7\times#3}{#6}\]
+            \edef\Nomy{#4}\valy=#7\Valy=#3\denoy=#6%
+            }{}}{}
+        }
+      }{\IfDecimal{#3}{\IfDecimal{#6}{\yyy=3625%\[#4=\frac{#7\times#3}{#6}\]
+            \edef\Nomy{#4}\valy=#7\Valy=#3\denoy=#6%
+            }{}}{}
+      }}{}}%
+  % 
+  \IfDecimal{#5}{%
+    \IfDecimal{#8}{}{%
+      \IfDecimal{#4}{
+        \IfDecimal{#7}{
+          \zzz=7463%\[#8=\frac{#5\times#7}{#4}\]%
+          \edef\Nomz{#8}\valz=#5\Valz=#7\denoz=#4%
+        }{%
+          \IfDecimal{#3}{\IfDecimal{#6}{\zzz=7452%\[#8=\frac{#5\times#6}{#3}\]
+            \edef\Nomz{#8}\valz=#5\Valz=#6\denoz=#3%
+            }{}}{}
+        }
+      }{\IfDecimal{#3}{\IfDecimal{#6}{\zzz=7452%\[#8=\frac{#5\times#6}{#3}\]
+            \edef\Nomz{#8}\valz=#5\Valz=#6\denoz=#3%
+            }{}}{}
+      }
+    }
+  }{%
+    \IfDecimal{#8}{%
+      \IfDecimal{#4}{%
+        \IfDecimal{#7}{%
+          \zzz=4736% \[#5=\frac{#8\times#4}{#7}\]%
+          \edef\Nomz{#5}\valz=#8\Valz=#4\denoz=#7%
+        }{%
+          \IfDecimal{#3}{\IfDecimal{#6}{\zzz=4725%\[#5=\frac{#8\times#3}{#6}\]
+            \edef\Nomz{#5}\valz=#8\Valz=#3\denoz=#6%
+            }{}}{}
+        }
+      }{\IfDecimal{#3}{\IfDecimal{#6}{\zzz=4725%\[#5=\frac{#8\times#3}{#6}\]
+            \edef\Nomz{#5}\valz=#8\Valz=#3\denoz=#6%
+            }{}}{}
+      }}{}
+  }%  
+  %%
+\StrMid{\the\zzz}{1}{1}[\cmza]%
+\StrMid{\the\yyy}{1}{1}[\cmya]%
+\StrMid{\the\xxx}{1}{1}[\cmxa]%
+\ifboolKV[ClesThales]{Calcul}{%
+  %%%%%%%%%%%%%%%%%%%%%%%%%%%
+    On remplace par les longueurs connues :
+  \ifboolKV[ClesThales]{Propor}{%
+    \[\begin{array}{c|c|c}
+        \IfDecimal{#3}{\num{#3}}{#3}&\IfDecimal{#4}{\num{#4}}{#4}&\IfDecimal{#5}{\num{#5}}{#5}\\
+        \hline
+        \IfDecimal{#6}{\num{#6}}{#6}&\IfDecimal{#7}{\num{#7}}{#7}&\IfDecimal{#8}{\num{#8}}{#8}\\
+      \end{array}
+    \]
+  }{%
+    \[\frac{\IfDecimal{#3}{\num{#3}}{#3}}{\IfDecimal{#6}{\num{#6}}{#6}}=\frac{\IfDecimal{#4}{\num{#4}}{#4}}{\IfDecimal{#7}{\num{#7}}{#7}}=\frac{\IfDecimal{#5}{\num{#5}}{#5}}{\IfDecimal{#8}{\num{#8}}{#8}}\]
+  }%
+  % On choisit éventuellement le calcul à faire s'il y en a plusieurs.
+  \xdef\CompteurCalcul{\useKV[ClesThales]{ChoixCalcul}}%
+  \xintifboolexpr{\CompteurCalcul>0}{\xintifboolexpr{\CompteurCalcul=1}{\xdef\cmya{0}\xdef\cmza{0}}{\xintifboolexpr{\CompteurCalcul=2}{\xdef\cmxa{0}\xdef\cmza{0}}{\xdef\cmxa{0}\xdef\cmya{0}}}}%
+  %%on fait les calculs
+\begin{align*}
+    %Premier compteur \xxx
+    \ifnum\cmxa>0
+      \Nomx\uppercase{&}=\frac{\the\valx\times\the\Valx}{\the\denox}\global\numx=\numexpr\the\valx*\the\Valx\relax
+    \fi
+    %    % Deuxième compteur \yyy
+    \ifnum\cmya>0
+      \ifnum\cmxa=0
+      \else
+        \uppercase{&}
+      \fi%
+      \Nomy\uppercase{&}=\frac{\the\valy\times\the\Valy}{\the\denoy}\global\numy=\numexpr\the\valy*\the\Valy\relax
+     % \else
+     %   \uppercase{&}\Nomy\uppercase{&}=\frac{\the\valy\times\the\Valy}{\the\denoy}\global\numy=\numexpr\the\valy*\the\Valy\relax
+     % \fi
+    \fi
+    % Troisième compteur \zzz
+    \ifnum\cmza>0
+      \ifnum\cmxa=0
+        \ifnum\cmya=0                           
+          %\Nomz\uppercase{&}=\frac{\the\valz\times\the\Valz}{\the\denoz}\global\numz=\numexpr\the\valz*\the\Valz\relax
+        \else
+          \uppercase{&}%\Nomz\uppercase{&}=\frac{\the\valz\times\the\Valz}{\the\denoz}\global\numz=\numexpr\the\valz*\the\Valz\relax
+        \fi
+        \Nomz\uppercase{&}=\frac{\the\valz\times\the\Valz}{\the\denoz}\global\numz=\numexpr\the\valz*\the\Valz\relax
+      \else
+        \uppercase{&}\Nomz\uppercase{&}=\frac{\the\valz\times\the\Valz}{\the\denoz}\global\numz=\numexpr\the\valz*\the\Valz\relax
+      \fi
+    \fi
+    \\
+    % 2eme ligne du tableau : calcul des numérateurs
+        %Premier compteur \xxx
+    \ifnum\cmxa>0
+      \Nomx\uppercase{&}=\frac{\num{\the\numx}}{\num{\the\denox}}
+    \fi
+    %    % Deuxième compteur \yyy
+    \ifnum\cmya>0
+      \ifnum\cmxa=0
+        %\Nomy\uppercase{&}=\frac{\num{\the\numy}}{\num{\the\denoy}}
+      \else
+        \uppercase{&}%\Nomy\uppercase{&}=\frac{\num{\the\numy}}{\num{\the\denoy}}
+      \fi
+      \Nomy\uppercase{&}=\frac{\num{\the\numy}}{\num{\the\denoy}}%
+    \fi
+    %Troisième compteur \zzz
+    \ifnum\cmza>0
+      \ifnum\cmxa=0
+        \ifnum\cmya=0                           
+          %\Nomz\uppercase{&}=\frac{\num{\the\numz}}{\num{\the\denoz}}
+        \else
+          \uppercase{&}%\Nomz\uppercase{&}=\frac{\num{\the\numz}}{\num{\the\denoz}}
+        \fi
+        \Nomz\uppercase{&}=\frac{\num{\the\numz}}{\num{\the\denoz}}
+      \else
+        \uppercase{&}\Nomz\uppercase{&}=\frac{\num{\the\numz}}{\num{\the\denoz}}
+      \fi
+    \fi
+    \\
+    % 3eme ligne : faire les simplifications ou pas ?
+    %Premier compteur \xxx
+    \ifnum\cmxa>0
+      \PGCD{\the\numx}{\the\denox}
+      \ifnum\pgcd>1
+        \Nomx\uppercase{&}=\SSimpli{\the\numx}{\the\denox}
+      \else
+        \uppercase{&}
+      \fi
+    \fi                    
+    %    % Deuxième compteur \yyy
+    \ifnum\cmya>0
+      \PGCD{\the\numy}{\the\denoy}
+      \ifnum\cmxa=0
+         \ifnum\pgcd>1
+           \Nomy\uppercase{&}=\SSimpli{\the\numy}{\the\denoy}
+         \else
+           \uppercase{&}
+         \fi
+      \else
+        \ifnum\pgcd>1
+          \uppercase{&}\Nomy\uppercase{&}=\SSimpli{\the\numy}{\the\denoy}
+        \else
+          \uppercase{&&}
+        \fi
+      \fi
+    \fi
+    %Troisième compteur \zzz
+    \ifnum\cmza>0
+      \PGCD{\the\numz}{\the\denoz}
+      \ifnum\cmxa=0
+        \ifnum\cmya=0
+          \ifnum\pgcd>1
+            \Nomz\uppercase{&}=\SSimpli{\the\numz}{\the\denoz}
+          \else
+            \uppercase{&}
+          \fi
+        \else
+          \ifnum\pgcd>1
+            \uppercase{&}\Nomz\uppercase{&}=\SSimpli{\the\numz}{\the\denoz}
+          \else
+            \uppercase{&&}
+          \fi
+        \fi
+      \else
+        \ifnum\pgcd>1
+          \uppercase{&}\Nomz\uppercase{&}=\SSimpli{\the\numz}{\the\denoz}
+        \else
+          \uppercase{&&}
+        \fi
+      \fi
+    \fi
+    \\
+    % 4eme ligne : Terminer les simplifications ?
+    %Premier compteur \xxx
+    \ifnum\cmxa>0
+      \PGCD{\the\numx}{\the\denox}
+      \ifnum\pgcd>1
+        \ifnum\pgcd<\the\denox
+          \Nomx\uppercase{&}=\SSimplifie{\the\numx}{\the\denox}
+        \else
+          \uppercase{&}
+        \fi
+      \else
+        \uppercase{&}
+      \fi
+    \fi                    
+    %    % Deuxième compteur \yyy
+    \ifnum\cmya>0
+      \PGCD{\the\numy}{\the\denoy}
+      \ifnum\cmxa=0
+        \ifnum\pgcd>1
+          \ifnum\pgcd<\the\denoy
+            \Nomy\uppercase{&}=\SSimplifie{\the\numy}{\the\denoy}
+          \else
+            \uppercase{&}
+          \fi
+         \else
+           \uppercase{&}
+         \fi
+      \else
+        \ifnum\pgcd>1
+          \ifnum\pgcd<\the\denoy
+            \uppercase{&}\Nomy\uppercase{&}=\SSimplifie{\the\numy}{\the\denoy}
+          \else
+            \uppercase{&&}
+          \fi
+        \else
+          \uppercase{&&}
+        \fi
+      \fi
+    \fi
+    %Troisième compteur \zzz
+    \ifnum\cmza>0
+      \PGCD{\the\numz}{\the\denoz}
+      \ifnum\cmxa=0
+        \ifnum\cmya=0
+          \ifnum\pgcd>1
+            \ifnum\pgcd<\the\denoz
+              \Nomz\uppercase{&}=\SSimplifie{\the\numz}{\the\denoz}
+            \else
+              \uppercase{&}
+            \fi
+          \else
+            \uppercase{&}
+          \fi
+        \else
+          \ifnum\pgcd>1
+            \ifnum\pgcd<\the\denoz
+              \uppercase{&}\Nomz\uppercase{&}=\SSimplifie{\the\numz}{\the\denoz}
+            \else
+              \uppercase{&&}
+            \fi
+          \else
+            \uppercase{&&}
+          \fi
+        \fi
+      \else
+        \ifnum\pgcd>1
+          \ifnum\pgcd<\the\denoz
+            \uppercase{&}\Nomz\uppercase{&}=\SSimplifie{\the\numz}{\the\denoz}
+          \else
+            \uppercase{&&}
+          \fi
+        \else
+          \uppercase{&&}
+        \fi
+      \fi
+    \fi%\\
+\end{align*}
+}{}%
+}
+
+\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}}}%
+  }%
+}%
+%%%%
+
+\newcommand{\ReciThales}[6][]{%
+  Dans le triangle $#2#3#4$, $#5$ est un point \ifboolKV[ClesThales]{Segment}{du segment $[#2#3]$}{de la
+    droite $(#2#3)$}, $#6$ est un point \ifboolKV[ClesThales]{Segment}{du segment $[#2#4]$}{de la droite $(#2#4)$}.
+  \ifboolKV[ClesThales]{Propor}{Le tableau $\begin{array}{c|c}
+        #2#5&#2#6\\
+        \hline
+        #2#3&#2#4\\
+      \end{array}
+    $ est-il un tableau de proportionnalité ?
+  }{%
+  }
+}
+
+\newcommand{\ReciThalesCalculs}[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]{Produit}{%
+    \begin{align*}
+      \dfrac{\NomA\NomM}{\NomA\NomB}=\dfrac{\num{#3}}{\num{#4}}&&\dfrac{\NomA\NomN}{\NomA\NomC}=\dfrac{\num{#5}}{\num{#6}}
+    \end{align*}
+    Effectuons les produits en croix :\xdef\NumA{\fpeval{#3*#6}}\xdef\NumB{\fpeval{#4*#5}}
+    \begin{align*}
+      \num{#3}\times\num{#6}&=\num{\fpeval{#3*#6}}&&&\num{#4}\times\num{#5}&=\num{\fpeval{#4*#5}}
+    \end{align*}
+    \xintifboolexpr{\NumA = \NumB}{Comme les produits en croix sont
+      égaux alors
+      $\dfrac{\NomA\NomM}{\NomA\NomB}=\dfrac{\NomA\NomN}{\NomA\NomC}$.\\[0.5em]%
+    }{%
+      Comme les produits en croix sont différents alors
+      $\dfrac{\NomA\NomM}{\NomA\NomB}\not=\dfrac{\NomA\NomN}{\NomA\NomC}$.\\%
+    }%
+  }{%
+    \[\left.
+        \begin{array}{l}
+          \dfrac{\NomA\NomM}{\NomA\NomB}=\dfrac{\num{#3}}{\num{#4}}\ifx\bla#7\bla\ifboolKV[ClesThales]{Simplification}{\PGCD{#3}{#4}\xintifboolexpr{\pgcd=1}{%il faut regarder si on doit continuer avec le PPCM...
+          \PGCD{#5}{#6}\xintifboolexpr{\pgcd>1}{\xdef\DenomSimpaa{\fpeval{#6/\pgcd}}\PPCM{#4}{\DenomSimpaa}\xintifboolexpr{\ppcm=#4}{}{=\dfrac{#3\times\num{\fpeval{\ppcm/#4}}}{#4\times\num{\fpeval{\ppcm/#4}}}=\dfrac{\num{\fpeval{#3*\ppcm/#4}}}{\num{\fpeval{\ppcm}}}}}{}%
+          }{=\displaystyle\Simplification[All]{#3}{#4}\PGCD{#3}{#4}\xdef\NumSimp{\fpeval{#3/\pgcd}}\xdef\DenomSimp{\fpeval{#4/\pgcd}}\PGCD{#5}{#6}\xdef\NumSimpa{\fpeval{#5/\pgcd}}\xdef\DenomSimpa{\fpeval{#6/\pgcd}}\PPCM{\DenomSimp}{\DenomSimpa}\xintifboolexpr{\fpeval{\the\ppcm/\DenomSimp}=1}{}{=\dfrac{\num{\NumSimp}\times\num{\fpeval{\the\ppcm/\DenomSimp}}}{\num{\DenomSimp}\times\PPCM{\DenomSimp}{\DenomSimpa}\num{\fpeval{\the\ppcm/\DenomSimp}}}=\dfrac{\PPCM{\DenomSimp}{\DenomSimpa}\num{\fpeval{\NumSimp*\the\ppcm/\DenomSimp}}}{\PPCM{\DenomSimp}{\DenomSimpa}\num{\the\ppcm}}}}}{\PPCM{#4}{#6}\xintifboolexpr{\fpeval{\the\ppcm/#4}=1}{}{=\dfrac{\num{#3}\times\num{\fpeval{\the\ppcm/#4}}}{\num{#4}\times\PPCM{#4}{#6}\num{\fpeval{\the\ppcm/#4}}}=\dfrac{\PPCM{#4}{#6}\num{\fpeval{#3*\the\ppcm/#4}}}{\PPCM{#4}{#6}\num{\the\ppcm}}}}\xdef\NumA{\fpeval{#3*#6}}\else%
+         \xintifboolexpr{#7=1}{}{=\dfrac{\num{#3}\times\num{#7}}{\num{#4}\times\num{#7}}=\dfrac{\num{\fpeval{#3*#7}}}{\num{\fpeval{#4*#7}}}}\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\xintifboolexpr{\the\ppcm=\fpeval{#4*#7}}{}{=\dfrac{\num{\fpeval{#3*#7}}\times\num{\fpeval{\the\ppcm/(#4*#7)}}}{\num{\fpeval{#4*#7}}\times\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{\the\ppcm/(#4*#7)}}}=\dfrac{\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{#3*\the\ppcm/#4}}}{\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{\the\ppcm}}}}\xdef\NumA{\fpeval{#3*#7*#6*#8}}
+          \fi
+          \\
+          \\
+          \dfrac{\NomA\NomN}{\NomA\NomC}=\dfrac{\num{#5}}{\num{#6}}%
+          \ifx\bla#8\bla%
+          \ifboolKV[ClesThales]{Simplification}{\PGCD{#5}{#6}\xintifboolexpr{\pgcd=1}{%il faut regarder si on doit continuer avec le PPCM...
+          \PGCD{#3}{#4}\xintifboolexpr{\pgcd>1}{\xdef\DenomSimpaa{\fpeval{#4/\pgcd}}\PPCM{#6}{\DenomSimpaa}\xintifboolexpr{\ppcm=#6}{}{=\dfrac{#5\times\num{\fpeval{\ppcm/#6}}}{#6\times\num{\fpeval{\ppcm/#6}}}=\dfrac{\num{\fpeval{#5*\ppcm/#6}}}{\num{\fpeval{\ppcm}}}}}{}%
+          }{=\displaystyle\Simplification[All]{#5}{#6}\PGCD{#5}{#6}\xdef\NumSimp{\fpeval{#5/\pgcd}}\xdef\DenomSimp{\fpeval{#6/\pgcd}}\PGCD{#3}{#4}\xdef\NumSimpa{\fpeval{#3/\pgcd}}\xdef\DenomSimpa{\fpeval{#4/\pgcd}}\PPCM{\DenomSimp}{\DenomSimpa}\xintifboolexpr{\fpeval{\the\ppcm/\DenomSimp}=1}{}{=\dfrac{\num{\NumSimp}\times\num{\fpeval{\the\ppcm/\DenomSimp}}}{\num{\DenomSimp}\times\PPCM{\DenomSimp}{\DenomSimpa}\num{\fpeval{\the\ppcm/\DenomSimp}}}=\dfrac{\PPCM{\DenomSimp}{\DenomSimpa}\num{\fpeval{\NumSimp*\the\ppcm/\DenomSimp}}}{\PPCM{\DenomSimp}{\DenomSimpa}\num{\the\ppcm}}}}}{\PPCM{#4}{#6}\xintifboolexpr{\fpeval{\the\ppcm/#6}=1}{}{=\dfrac{\num{#5}\times\num{\fpeval{\the\ppcm/#6}}}{\num{#6}\times\PPCM{#4}{#6}\num{\fpeval{\the\ppcm/#6}}}=\dfrac{\PPCM{#4}{#6}\num{\fpeval{#5*\the\ppcm/#6}}}{\PPCM{#4}{#6}\num{\the\ppcm}}}}\xdef\NumB{\fpeval{#5*#4}}%
+          \else%
+          \xintifboolexpr{#8=1}{}{=\dfrac{\num{#5}\times\num{#8}}{\num{#6}\times\num{#8}}=\dfrac{\num{\fpeval{#5*#8}}}{\num{\fpeval{#6*#8}}}}\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\xintifboolexpr{\the\ppcm=\fpeval{#6*#8}}{}{=\dfrac{\num{\fpeval{#5*#8}}\times\num{\fpeval{\the\ppcm/(#6*#8)}}}{\num{\fpeval{#6*#8}}\times\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{\the\ppcm/(#6*#8)}}}=\dfrac{\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{#5*\the\ppcm/#6}}}{\xdef\NumC{\fpeval{#4*#7}}\xdef\NumD{\fpeval{#6*#8}}\PPCM{\NumC}{\NumD}\num{\fpeval{\the\ppcm}}}
+          }\xdef\NumB{\fpeval{#5*#8*#4*#7}}
+          \fi\\
+        \end{array}
+      \right\}\ifnum\NumA=\NumB \dfrac{\NomA\NomM}{\NomA\NomB}=\dfrac{\NomA\NomN}{\NomA\NomC}\else\dfrac{\NomA\NomM}{\NomA\NomB}\not=\dfrac{\NomA\NomN}{\NomA\NomC}\fi
+    \]
+  }
+  \ifboolKV[ClesThales]{Propor}{%
+    \ifnum\NumA=\NumB Donc le tableau $\begin{array}{c|c}
+        \NomA\NomM&\NomA\NomN\\
+        \hline
+        \NomA\NomB&\NomA\NomC\\
+      \end{array}
+    $ est bien un tableau de proportionnalité.\\De plus, les points
+    $\NomA$, $\NomM$, $\NomB$ sont alignés dans le même ordre que les
+    points $\NomA$, $\NomN$, $\NomC$. Donc les droites $(\NomM\NomN)$
+    et $(\NomB\NomC)$ sont parallèles d'après la réciproque du
+    théorème de Thalès.\else%
+    Donc les droites $(\NomM\NomN)$ et $(\NomB\NomC)$ ne sont pas parallèles.\fi
+  }{%
+    \xintifboolexpr{\NumA=\NumB}{%
+      De plus, les points $\NomA$, $\NomM$, $\NomB$ sont alignés dans
+      le même ordre que les points $\NomA$, $\NomN$, $\NomC$. Donc les
+      droites $(\NomM\NomN)$ et $(\NomB\NomC)$ sont parallèles d'après
+      la réciproque du théorème de Thalès.}{%
+      Donc les droites $(\NomM\NomN)$ et $(\NomB\NomC)$ ne sont pas
+      parallèles.}
+  }
+}
+
+\newcommand\ReciproqueThales[8][]{%
+  % #1 Clés
+  % #2 NomTriangle + Points ABCEF pour droite (BC)//(EF)
+  % #3 longueur AE
+  % #4 longueur AB
+  % #5 longueur AF
+  % #6 longueur AC
+  \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.}
+      \[\MPFigReciThales{\NomA}{\NomB}{\NomC}{\NomM}{\NomN}\]
+      \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}
+    }
+  }
+}
+
+\newcommand{\Thales}[8][]{%
+  \useKVdefault[ClesThales]%
+  \setKV[ClesThales]{#1}%
+  \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}}%
+    }{%
+      \TThales[#1]{#2}{#3}{#4}{#5}{#6}{#7}{#8}%
+    }
+  }%
+}%
+
+%%%%%%%%%%%%%%%%
+%% Trigonométrie
+%%%%%%%%%%%%%%%%
+\def\MPFigTrigo#1#2#3#4#5#6#7{%
+  \ifluatex
+    \mplibcodeinherit{enable}
+   \mplibforcehmode
+  \begin{mplibcode}
+    u:=1cm;
+    pair A,B,C,O,I,D,E,F;%
+    % On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=u*(1,1);
+    B-A=u*(3,0);
+    C=(A--2[A,B rotatedabout(A,50)]) intersectionpoint (B--2[B,A rotatedabout(B,-90)]);
+    % On définit le centre du cercle circonscrit
+    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 :)
+    path triangle;
+    triangle=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}--B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}--C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}--cycle;
+    % on définit l'angle droit
+    D-B=7*unitvector(C-B);
+    F-B=7*unitvector(A-B);
+    E-D=F-B;
+    draw D{dir(angle(E-D)+5)}..E{dir(angle(E-D)+5)}--E{dir(angle(F-E)+5)}..F{dir(angle(F-E)+5)};
+    % L'angle :)
+    path cc;
+    cc=fullcircle scaled 1u;
+    % on marque les angles
+    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
+    picture z;
+    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 \ang{#7} etex,A+0.95u*unitvector(I-A));
+    decalage:=3mm;
+    if #6<0:
+    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]]);
+      else:
+        label(btex \num{#6} etex rotated angle(C-A),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]]);
+      else:
+        label(btex \num{#6} etex rotated angle(A-C),1.1[B,1/2[A,C]]);
+      fi;
+    fi;
+  fi;   
+  if #4<0:
+  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)));
+      else:
+        label(btex \num{#4} etex rotated(angle(B-C)),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)));
+      else:
+        label(btex \num{#4} etex rotated(angle(C-B)),1/2[B,C]-decalage*(unitvector(A-B)));
+      fi;
+    fi;
+  fi;
+  if #5<0:
+  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)));
+      else:
+        label(btex \num{#5} etex rotated angle(A-B),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)));
+      else:
+        label(btex \num{#5} etex rotated angle(B-A),1/2[A,B]-decalage*(unitvector(C-B)));
+      fi;
+    fi;
+    fi;
+  \end{mplibcode}
+  \mplibcodeinherit{disable}
+  \else
+  \begin{mpost}
+    u:=1cm;
+    pair A,B,C,O,I,D,E,F;%
+    % On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+    A=u*(1,1);
+    B-A=u*(3,0);
+    C=(A--2[A,B rotatedabout(A,50)]) intersectionpoint (B--2[B,A rotatedabout(B,-90)]);
+    % On définit le centre du cercle circonscrit
+    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 :)
+    path triangle;
+    triangle=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}--B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}--C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}--cycle;
+    % on définit l'angle droit
+    D-B=7*unitvector(C-B);
+    F-B=7*unitvector(A-B);
+    E-D=F-B;
+    draw D{dir(angle(E-D)+5)}..E{dir(angle(E-D)+5)}--E{dir(angle(F-E)+5)}..F{dir(angle(F-E)+5)};
+    % L'angle :)
+    path cc;
+    cc=fullcircle scaled 1u;
+    % on marque les angles
+    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
+    picture z;
+    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 \ang{#7} etex,A+0.95u*unitvector(I-A));
+    decalage:=3mm;
+    if #6<0:
+    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]]);
+      else:
+        label(btex \num{#6} etex rotated angle(C-A),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]]);
+      else:
+        label(btex \num{#6} etex rotated angle(A-C),1.1[B,1/2[A,C]]);
+      fi;
+    fi;
+  fi;   
+  if #4<0:
+  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)));
+      else:
+        label(btex \num{#4} etex rotated(angle(B-C)),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)));
+      else:
+        label(btex \num{#4} etex rotated(angle(C-B)),1/2[B,C]-decalage*(unitvector(A-B)));
+      fi;
+    fi;
+  fi;
+  if #5<0:
+  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)));
+      else:
+        label(btex \num{#5} etex rotated angle(A-B),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)));
+      else:
+        label(btex \num{#5} etex rotated angle(B-A),1/2[A,B]-decalage*(unitvector(C-B)));
+      fi;
+    fi;
+  fi;
+\end{mpost}
+\fi
+}
+
+\def\MPFigTrigoAngle#1#2#3#4#5#6{%
+  % #1 A
+  % #2 B
+  % #3 C
+  % #4 opp
+  % #5 adj
+  % #6 hyp
+  \ifluatex
+    \mplibcodeinherit{enable}
+   \mplibforcehmode
+  \begin{mplibcode}
+    u:=1cm;
+  pair A,B,C,O,I,D,E,F;%
+  % On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+  A=u*(1,1);
+  B-A=u*(3,0);
+  C=(A--2[A,B rotatedabout(A,50)]) intersectionpoint (B--2[B,A rotatedabout(B,-90)]);
+    % On définit le centre du cercle circonscrit
+  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
+  (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 :)
+  path triangle;
+  triangle=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}--B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}--C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}--cycle;
+  %on définit l'angle droit
+  D-B=7*unitvector(C-B);
+  F-B=7*unitvector(A-B);
+  E-D=F-B;
+  draw D{dir(angle(E-D)+5)}..E{dir(angle(E-D)+5)}--E{dir(angle(F-E)+5)}..F{dir(angle(F-E)+5)};
+  %L'angle :)
+  path cc;
+  cc=fullcircle scaled 1u;
+  % on marque les angles
+  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
+  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]]);
+  else:
+  label(btex \num{#6} etex rotated angle(A-C),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)));
+  else:
+    label(btex \num{#4} etex rotated(angle(C-B)),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)));
+  else:
+  label(btex \num{#5} etex rotated angle(B-A),1/2[A,B]-decalage*(unitvector(C-B)));
+  fi;
+\end{mplibcode}
+\mplibcodeinherit{disable}
+  \else
+  \begin{mpost}
+      u:=1cm;
+  pair A,B,C,O,I,D,E,F;%
+    %On place les points A,B,C sur le cercle de manière à faciliter la rotation de la figure
+  A=u*(1,1);
+  B-A=u*(3,0);
+  C=(A--2[A,B rotatedabout(A,50)]) intersectionpoint (B--2[B,A rotatedabout(B,-90)]);
+    % On définit le centre du cercle circonscrit
+  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 :)
+  path triangle;
+  triangle=A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}--B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}--C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}--cycle;
+  %on définit l'angle droit
+  D-B=7*unitvector(C-B);
+  F-B=7*unitvector(A-B);
+  E-D=F-B;
+  draw D{dir(angle(E-D)+5)}..E{dir(angle(E-D)+5)}--E{dir(angle(F-E)+5)}..F{dir(angle(F-E)+5)};
+  %L'angle :)
+  path cc;
+  cc=fullcircle scaled 1u;
+    % on marque les angles
+  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
+  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]]);
+  else:
+  label(btex \num{#6} etex rotated angle(A-C),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)));
+  else:
+    label(btex \num{#4} etex rotated(angle(C-B)),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)));
+  else:
+  label(btex \num{#5} etex rotated angle(B-A),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}%
+
+\newcommand\TrigoCalculs[5][]{%
+  \setKV[ClesTrigo]{#1}%
+  % #1 Clés
+  % #2 Nom du triangle ABC, rectangle en B, angle connu ou pas : BAC
+  % #3 Longueur
+  % #4 Longueur
+   %#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 :
+  \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\\
+        \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*}%
+    }{%
+      \begin{align*}
+        \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*}%
+    }%
+    \xdef\ResultatTrigo{\fpeval{round(\fpeval{#4*cosd(#5)},\useKV[ClesTrigo]{Precision})}}%
+    \else
+    \ifx\bla#4\bla%on calcule l'hypothénuse
+    \ifboolKV[ClesTrigo]{Propor}{%
+      \begin{align*}
+        \NomA\NomC\times\cos(\widehat{\NomB\NomA\NomC})&=\NomA\NomB\\
+        \NomA\NomC\times\cos(\ang{#5})&=\num{#3}\\
+        \NomA\NomC&=\frac{\num{#3}}{\cos(\ang{#5})}\\
+        \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*}
+    }{%
+      \begin{align*}
+        \cos(\widehat{\NomB\NomA\NomC})&=\frac{\NomA\NomB}{\NomA\NomC}\\
+        \cos(\ang{#5})&=\frac{\num{#3}}{\NomA\NomC}\\
+        \NomA\NomC&=\frac{\num{#3}}{\cos(\ang{#5})}\\
+        \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
+    \ifboolKV[ClesTrigo]{Propor}{%
+      \begin{align*}
+        \NomA\NomC\times\cos(\widehat{\NomB\NomA\NomC})&=\NomA\NomB\\
+        \num{#4}\times\cos(\widehat{\NomB\NomA\NomC})&=\num{#3}\\
+        \cos(\widehat{\NomB\NomA\NomC})&=\frac{\num{#3}}{\num{#4}}\\
+        \widehat{\NomB\NomA\NomC}&\IfInteger{\fpeval{round(\fpeval{acosd(#3/#4)},2)}}{=}{\approx}\ang{\fpeval{round(\fpeval{acosd(#3/#4)})}}%
+      \end{align*}%
+    }{%
+      \begin{align*}
+        \cos(\widehat{\NomB\NomA\NomC})&=\frac{\NomA\NomB}{\NomA\NomC}\\
+        \cos(\widehat{\NomB\NomA\NomC})&=\frac{\num{#3}}{\num{#4}}\\
+        \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
+  }{}
+  \ifboolKV[ClesTrigo]{Sinus}{%
+    \ifx\bla#3\bla%on calcule le côté opposé
+    \ifboolKV[ClesTrigo]{Propor}{%
+      \begin{align*}
+        \NomA\NomC\times\sin(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\
+        \num{#4}\times\sin(\ang{#5})&=\NomB\NomC\\
+        \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*}%
+    }{%
+      \begin{align*}
+        \sin(\widehat{\NomB\NomA\NomC})&=\frac{\NomB\NomC}{\NomA\NomC}\\
+        \sin(\ang{#5})&=\frac{\NomB\NomC}{\num{#4}}\\
+        \num{#4}\times\sin(\ang{#5})&=\NomB\NomC\\
+        \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
+    \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
+    \ifboolKV[ClesTrigo]{Propor}{%
+      \begin{align*}
+        \NomA\NomC\times\sin(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\
+        \num{#4}\times\sin(\widehat{\NomB\NomA\NomC})&=\num{#3}\\
+        \sin(\widehat{\NomB\NomA\NomC})&=\frac{\num{#3}}{\num{#4}}\\
+        \widehat{\NomB\NomA\NomC}&\IfInteger{\fpeval{round(\fpeval{asind(#3/#4)},2)}}{=}{\approx}\ang{\fpeval{round(\fpeval{asind(#3/#4)})}}%
+      \end{align*}%
+    }{
+      \begin{align*}
+        \sin(\widehat{\NomB\NomA\NomC})&=\frac{\NomB\NomC}{\NomA\NomC}\\
+        \sin(\widehat{\NomB\NomA\NomC})&=\frac{\num{#3}}{\num{#4}}\\
+        \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
+  }{}
+  \ifboolKV[ClesTrigo]{Tangente}{%
+    \ifx\bla#3\bla%on calcule le côté opposé
+    \ifboolKV[ClesTrigo]{Propor}{%
+      \begin{align*}
+        \NomA\NomB\times\tan(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\%
+        \num{#4}\times\tan(\ang{#5})&=\NomB\NomC\\%
+        \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*}%
+    }{%
+      \begin{align*}
+        \tan(\widehat{\NomB\NomA\NomC})&=\frac{\NomB\NomC}{\NomA\NomB}\\
+        \tan(\ang{#5})&=\frac{\NomB\NomC}{\num{#4}}\\
+        \num{#4}\times\tan(\ang{#5})&=\NomB\NomC\\
+        \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
+    \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})}}%
+    \else%on calcule l'angle
+    \ifboolKV[ClesTrigo]{Propor}{%
+      \begin{align*}
+        \NomA\NomB\times\tan(\widehat{\NomB\NomA\NomC})&=\NomB\NomC\\
+        \num{#4}\times\tan(\widehat{\NomB\NomA\NomC})&=\num{#3}\\
+        \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
+  }{}
+}
+
+\newcommand\Trigo[5][]{%
+  \useKVdefault[ClesTrigo]%
+  \setKV[ClesTrigo]{#1}%
+  % #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
+  % 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}
+          \end{center}
+          \else
+          \begin{center}
+            \MPFigTrigo{\NomA}{\NomB}{\NomC}{-1}{#3}{0}{#5}
+          \end{center}
+          \fi
+        }{}%
+        \ifboolKV[ClesTrigo]{Sinus}{%
+          \ifx#3\bla\bla%adjacent inconnu
+          \begin{center}
+            \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{-1}{#4}{#5}
+          \end{center}
+          \else
+          \begin{center}
+            \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{-1}{0}{#5}
+          \end{center}
+          \fi
+        }{}%
+        \ifboolKV[ClesTrigo]{Tangente}{%
+          \ifx#3\bla\bla%adjacent inconnu
+          \begin{center}
+            \MPFigTrigo{\NomA}{\NomB}{\NomC}{0}{#4}{-1}{#5}
+          \end{center}
+          \else%
+          \begin{center}
+            \MPFigTrigo{\NomA}{\NomB}{\NomC}{#3}{0}{-1}{#5}
+          \end{center}
+          \fi%
+        }{}%
+      }%
+      \par\columnbreak\par
+      \TrigoCalculs{#2}{#3}{#4}{#5}%
+    \end{multicols}
+  }{%
+    \TrigoCalculs{#2}{#3}{#4}{#5}%
+  }%
+}%
+
+%%%%%%%%%%%%%%%
+%% Statistiques
+%%%%%%%%%%%%%%%
+\newcommand\NbDonnees{}
+\newcommand\SommeDonnees{}%
+\newcommand\EffectifTotal{}%
+\newcommand\Moyenne{}%
+\newcommand\Etendue{}%
+\newcommand\Mediane{}%
+\newcommand\DonneeMax{}%
+\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}
+
+% 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{%
+  \tabtoksa{\useKV[ClesStat]{Donnee}}\tabtoksb{\useKV[ClesStat]{Effectif}}%
+  \foreachitem\compteur\in\ListeComplete{\expandafter\updatetoks\compteur\nil}%
+  \[%
+    \begin{tabular}{|>{\columncolor{gray!15}}c|*{\number\numexpr\ListeCompletelen}{>{\centering\arraybackslash}p{\useKV[ClesStat]{Largeur}}|}}%
+    \hline%
+    \rowcolor{gray!15}\the\tabtoksa\\\hline%
+    \the\tabtoksb\\\hline%
+      \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculFrequence{##1}}}\\\hline}{}%
+      \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculAngle{##1}}}\\\hline}{}%
+      \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\CalculSemiAngle{##1}}\\\hline}{}%
+      \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculECC{##1}}}\\\hline}{}%
+    \end{tabular}
+  \]
+}
+
+\def\buildtabt{%
+  \tabtoksa{\useKV[ClesStat]{Donnee}}\tabtoksb{\useKV[ClesStat]{Effectif}}%
+  \foreachitem\compteur\in\ListeComplete{\expandafter\updatetoks\compteur\nil}%
+  \[%
+    \begin{tabular}{|>{\columncolor{gray!15}}c|*{\number\numexpr\ListeCompletelen+1}{>{\centering\arraybackslash}p{\useKV[ClesStat]{Largeur}}|}}%
+    \hline%
+    \rowcolor{gray!15}\the\tabtoksa&Total\\\hline%
+      \the\tabtoksb&\ifboolKV[ClesStat]{TableauVide}{}{\num{\EffectifTotal}}%
+      \\\hline%
+      \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculFrequence{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{100}\\\hline}{}%
+      \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculAngle{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{360}\\\hline}{}%
+      \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculSemiAngle{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{180}\\\hline}{}%
+      \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculECC{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{\num{\EffectifTotal}}\\\hline}{}%
+    \end{tabular}
+  \]
+}
+
+\def\updatetoksq#1/#2\nil{\addtotok\tabtoksa{&#1}\addtotok\tabtoksb{&\num{#2}}}
+\def\buildtabq{%
+  \tabtoksa{\useKV[ClesStat]{Donnee}}\tabtoksb{\useKV[ClesStat]{Effectif}}%
+  \foreachitem\compteur\in\ListeComplete{\expandafter\updatetoksq\compteur\nil}%
+  \[%
+    \begin{tabular}{|>{\columncolor{gray!15}}c|*{\number\numexpr\ListeCompletelen}{>{\centering\arraybackslash}p{\useKV[ClesStat]{Largeur}}|}}%
+    \hline%
+    \rowcolor{gray!15}\the\tabtoksa\\\hline%
+    \the\tabtoksb\\\hline%
+      \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculFrequence{##1}}}\\\hline}{}%
+      \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculAngle{##1}}}\\\hline}{}%
+      \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculSemiAngle{##1}}}\\\hline}{}%
+      \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculECC{##1}}}\\\hline}{}%
+    \end{tabular}
+  \]
+}
+
+\def\buildtabqt{%
+  \tabtoksa{\useKV[ClesStat]{Donnee}}\tabtoksb{\useKV[ClesStat]{Effectif}}%
+  \foreachitem\compteur\in\ListeComplete{\expandafter\updatetoksq\compteur\nil}%
+  \[%
+    \begin{tabular}{|>{\columncolor{gray!15}}c|*{\number\numexpr\ListeCompletelen+1}{>{\centering\arraybackslash}p{\useKV[ClesStat]{Largeur}}|}}%
+    \hline%
+    \rowcolor{gray!15}\the\tabtoksa&Total\\\hline%
+    \the\tabtoksb&\num{\EffectifTotal}\\\hline%
+      \ifboolKV[ClesStat]{Frequence}{Fréquence (\%)\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculFrequence{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{100}\\\hline}{}%
+      \ifboolKV[ClesStat]{Angle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculAngle{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{360}\\\hline}{}%
+      \ifboolKV[ClesStat]{SemiAngle}{Angle (\si{\degree})\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculSemiAngle{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{180}\\\hline}{}%
+      \ifboolKV[ClesStat]{ECC}{E.C.C.\xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{&\ifboolKV[ClesStat]{TableauVide}{}{\CalculECC{##1}}}&\ifboolKV[ClesStat]{TableauVide}{}{\num{\EffectifTotal}}\\\hline}{}%
+    \end{tabular}
+  \]
+}
+
+% Pour construire le diagramme en bâtons
+\def\Updatetoks#1/#2\nil{\addtotok\toklistepoint{(#1,#2),}}
+\def\buildgraph{%
+  \newtoks\toklistepoint
+  \foreachitem\compteur\in\ListeComplete{\expandafter\Updatetoks\compteur\nil}%
+  \[\MPStat{\useKV[ClesStat]{Unitex}}{\useKV[ClesStat]{Unitey}}{\the\toklistepoint}{\useKV[ClesStat]{Donnee}}{\useKV[ClesStat]{Effectif}}{\useKV[ClesStat]{Origine}}\]%
+}%
+
+% Pour construire le diagramme en bâtons qualitatif
+\def\Updatetoksq#1/#2\nil{\addtotok\toklistepointq{"#1",#2,}}
+\def\buildgraphq{%
+  \newtoks\toklistepointq
+  \toklistepointq{}
+  \foreachitem\compteur\in\ListeComplete{\expandafter\Updatetoksq\compteur\nil}  
+  \[\MPStatQ{2*\useKV[ClesStat]{Unitex}}{0.5*\useKV[ClesStat]{Unitey}}{\the\toklistepointq}{\useKV[ClesStat]{Donnee}}{\useKV[ClesStat]{Effectif}}{\useKV[ClesStat]{Origine}}\]
+}
+
+% Pour construire le diagramme circulaire qualitatif
+\def\buildgraphcq#1{%
+  \newtoks\toklistepointq%
+  \toklistepointq{}%
+  \foreachitem\compteur\in\ListeComplete{\expandafter\Updatetoksq\compteur\nil}%
+  \ifboolKV[ClesStat]{AffichageAngle}{%
+    \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{1}\]%
+  }{%
+    \[\MPStatCirculaireQ{\useKV[ClesStat]{Rayon}}{\the\toklistepointq}{#1}{0}\]%
+  }%
+}%
+
+%% calcul des fréquences
+\newcommand\CalculFrequence[1]{%
+  \fpeval{round(\ListeComplete[#1,2]*100/\EffectifTotal,0)}
+}
+
+%% calcul des angles
+\newcommand\CalculAngle[1]{%
+  \fpeval{round(\ListeComplete[#1,2]*360/\EffectifTotal,0)}
+}
+\newcommand\CalculSemiAngle[1]{%
+  \fpeval{round(\ListeComplete[#1,2]*180/\EffectifTotal,0)}
+}
+
+%% calcul des ECC
+\newcount\CompteurECC%
+\newcount\CompteurECCTotal%
+
+\newcommand\CalculECC[1]{%
+  \xdef\TotalECC{0}%
+  \CompteurECC=1%
+  \CompteurECCTotal=\numexpr#1+1%
+  \whiledo{\CompteurECC < \CompteurECCTotal}{
+    \xdef\TotalECC{\fpeval{\TotalECC+\ListeComplete[\the\CompteurECC,2]}}%
+    \CompteurECC=\numexpr\CompteurECC+1%
+  }%
+  \num{\TotalECC}%
+}
+
+% la construction du graphique
+\def\MPStat#1#2#3#4#5#6{%
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    maxx:=0;
+    maxy:=0;
+    unitex:=#1*cm;
+    unitey:=#2*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);
+    if xpart(p_)>maxx:
+    maxx:=xpart(p_)-(#6);
+    fi;
+    if ypart(p_)>maxy:
+    maxy:=ypart(p_);
+    fi;
+    A[n]=unitex*(xpart(p_)-(#6),0);
+    B[n]=unitey*(0,ypart(p_));
+    label.bot(TEX("\num{"&decimal(xpart(p_))&"}"),A[n]);
+    label.lft(TEX("\num{"&decimal(ypart(p_))&"}"),B[n]);
+    fi;
+    endfor;
+    enddef;
+    toto(#3);
+    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));
+  \end{mplibcode}
+  \else
+  \begin{mpost}
+    maxx:=0;
+    maxy:=0;
+    unitex:=#1*cm;
+    unitey:=#2*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);
+    if xpart(p_)>maxx:
+    maxx:=xpart(p_)-(#6);
+    fi;
+    if ypart(p_)>maxy:
+    maxy:=ypart(p_);
+    fi;
+    A[n]=unitex*(xpart(p_)-(#6),0);
+    B[n]=unitey*(0,ypart(p_));
+    label.bot(LATEX("\num{"&decimal(xpart(p_))&"}"),A[n]);
+    label.lft(LATEX("\num{"&decimal(ypart(p_))&"}"),B[n]);
+    fi;
+    endfor;
+    enddef;
+    toto(#3);
+    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));
+  \end{mpost}
+  \fi
+}
+
+% la construction du graphique qualitatif
+\def\MPStatQ#1#2#3#4#5#6{%
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    maxy:=0;
+    unitex:=#1*cm;
+    unitey:=#2*cm;
+    pair A[],B[],P[];
+    n:=0;
+    vardef toto(text t)=
+    for p_=t:
+    if numeric p_:
+    P[n]=((n+1)*unitex,unitey*p_);
+    B[n]=(0,unitey*p_);
+    label.lft(TEX("\num{"&decimal(p_)&"}"),B[n]);
+    if p_>maxy:
+    maxy:=p_;
+    fi;
+    n:=n+1;
+    else:
+    A[n]=unitex*(n+1,0);
+    label.bot(TEX(p_) rotated 90,A[n]);
+    fi;
+    endfor;
+    enddef;
+    toto(#3);
+    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));
+    \end{mplibcode}
+  \else
+  \begin{mpost}
+    maxy:=0;
+    unitex:=#1*cm;
+    unitey:=#2*cm;
+    pair A[],B[],P[];
+    n:=0;
+    vardef toto(text t)=
+    for p_=t:
+    if numeric p_:
+    P[n]=((n+1)*unitex,unitey*p_);
+    B[n]=(0,unitey*p_);
+    label.lft(LATEX("\num{"&decimal(p_)&"}"),B[n]);
+    if p_>maxy:
+    maxy:=p_;
+    fi;
+    n:=n+1;
+    else:
+    A[n]=unitex*(n+1,0);
+    label.bot(LATEX(p_) rotated 90,A[n]);
+    fi;
+    endfor;
+    enddef;
+    toto(#3);
+    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));
+  \end{mpost}
+  \fi
+}
+
+% la construction du graphique qualitatif
+\def\MPStatCirculaireQ#1#2#3#4{%
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    pair A[],O,B[],C[],D[];
+    O=(0,0);
+    n:=0;
+    numeric total[],ang[];
+    total[0]=0;
+    ang[0]:=0;
+    path cc;
+    cc=(fullcircle scaled (2*#1));
+    if #3=360:
+    draw cc;
+    else:
+    draw (subpath(0,length cc/2) of cc)--cycle;
+    fi;
+    A[0]=point(0) of cc;
+    vardef toto(text t)=
+    for p_=t:
+    if numeric p_:
+    n:=n+1;
+    total[n]:=total[n-1]+p_;
+    fi;
+    endfor;
+    N=n;
+    for k=1 upto N:
+    ang[k]=(#3/total[N])*total[k];
+    endfor;
+    n:=0;
+    for p_=t:
+    if numeric p_:
+    n:=n+1;
+    A[n]=A[n-1] rotatedabout(O,p_*(#3/total[N]));
+    draw A[n-1]--O--A[n];
+    % Affichage des angles associés
+    if #4=1:
+    if round(p_*(#3/total[N]))>15:
+    if (n mod 2)=0:
+    marque_a:=0.9*20
+    else:
+    marque_a:=1.1*20/0.9
+    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;
+    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);
+    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)):
+    D[n]=C[n]+(0.5cm,0);
+    draw C[n]--D[n];
+    label.urt(TEX(p_),D[n]);
+    fi;
+    if (xpart(C[n])<xpart(O)) and (ypart(C[n])>ypart(O)):
+    D[n]=C[n]-(0.5cm,0);
+    draw C[n]--D[n];
+    label.ulft(TEX(p_),D[n]);
+    fi;
+    if (xpart(C[n])<xpart(O)) and (ypart(C[n])<ypart(O)):
+    D[n]=C[n]-(0.5cm,0);
+    draw C[n]--D[n];
+    label.llft(TEX(p_),D[n]);
+    fi;
+    if (xpart(C[n])>xpart(O)) and (ypart(C[n])<ypart(O)):
+    D[n]=C[n]+(0.5cm,0);
+    draw C[n]--D[n];
+    label.lrt(TEX(p_),D[n]);
+    fi;
+    fi;
+    endfor;
+    enddef;
+    Figure(-10u,-10u,10u,10u);
+    toto(#2);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    pair A[],O,B[],C[],D[];
+    O=(0,0);
+    n:=0;
+    numeric total[],ang[];
+    total[0]=0;
+    ang[0]:=0;
+    path cc;
+    cc=(fullcircle scaled (2*#1));
+    if #3=360:
+    draw cc;
+    else:
+    draw (subpath(0,length cc/2) of cc)--cycle;
+    fi;
+    A[0]=point(0) of cc;
+    vardef toto(text t)=
+    for p_=t:
+    if numeric p_:
+    n:=n+1;
+    total[n]:=total[n-1]+p_;
+    fi;
+    endfor;
+    N=n;
+    for k=1 upto N:
+    ang[k]=(#3/total[N])*total[k];
+    endfor;
+    n:=0;
+    for p_=t:
+    if numeric p_:
+    n:=n+1;
+    A[n]=A[n-1] rotatedabout(O,p_*(#3/total[N]));
+    draw A[n-1]--O--A[n];
+    % Affichage des angles associés
+    if #4=1:
+    if round(p_*(#3/total[N]))>15:
+    if (n mod 2)=0:
+    marque_a:=0.9*20
+    else:
+    marque_a:=1.1*20/0.9
+    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;
+    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);
+    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)):
+    D[n]=C[n]+(0.5cm,0);
+    draw C[n]--D[n];
+    label.urt(LATEX(p_),D[n]);
+    fi;
+    if (xpart(C[n])<xpart(O)) and (ypart(C[n])>ypart(O)):
+    D[n]=C[n]-(0.5cm,0);
+    draw C[n]--D[n];
+    label.ulft(LATEX(p_),D[n]);
+    fi;
+    if (xpart(C[n])<xpart(O)) and (ypart(C[n])<ypart(O)):
+    D[n]=C[n]-(0.5cm,0);
+    draw C[n]--D[n];
+    label.llft(LATEX(p_),D[n]);
+    fi;
+    if (xpart(C[n])>xpart(O)) and (ypart(C[n])<ypart(O)):
+    D[n]=C[n]+(0.5cm,0);
+    draw C[n]--D[n];
+    label.lrt(LATEX(p_),D[n]);
+    fi;
+    fi;
+    endfor;
+    enddef;
+    Figure(-10u,-10u,10u,10u);
+    toto(#2);
+  \end{mpost}
+  \fi
+}
+
+%Pour la médiane.
+\DTLgnewdb{mtdb}%
+\dtlexpandnewvalue%
+\newcount\nbdonnees%
+
+
+\newcommand\Stat[2][]{%
+  \useKVdefault[ClesStat]%
+  \setKV[ClesStat]{#1}%
+  \ifboolKV[ClesStat]{Liste}{%
+    \setsepchar{,}\ignoreemptyitems%
+    \readlist*\Liste{#2}%
+    \xdef\foo{}%
+    \setsepchar[*]{,*/}\ignoreemptyitems%
+    \xintFor* ##1 in {\xintSeq {1}{\Listelen}}\do{%
+      \xdef\foo{\foo 1/\Liste[##1],}%
+    }%
+    \readlist*\ListeComplete{\foo}%
+    \setKV[ClesStat]{Qualitatif}%
+  }{%
+    %  % on lit la liste écrite sous la forme valeur/effectif
+    \setsepchar[*]{,*/}\ignoreemptyitems%
+    \readlist*\ListeComplete{#2}%
+  }
+  % 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
+  \foreachitem\x\in\ListeComplete{%
+    \DTLnewrow{mtdb}%
+    \itemtomacro\ListeComplete[\xcnt,2]\y%
+    \DTLnewdbentry{mtdb}{Numeric}{\y}%
+  }%
+  \dtlsort{Numeric}{mtdb}{\dtlicompare}%
+  %  % on réinitialise les valeurs des critères de position et de
+  % dispersion
+  \renewcommand\NbDonnees{}
+  \renewcommand\SommeDonnees{}%
+  \renewcommand\EffectifTotal{}%
+  \renewcommand\Moyenne{}%
+  \renewcommand\Etendue{}%
+  \renewcommand\Mediane{}%
+  \renewcommand\DonneeMax{0}%
+  \renewcommand\EffectifMax{0}%
+  \renewcommand\DonneeMin{999999999}%
+  \ifboolKV[ClesStat]{Qualitatif}{%Début qualitatif
+    % Calculs
+    %  %% 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
+    }{}
+    %  %% celui de la moyenne
+    \xdef\Moyenne{\fpeval{\SommeDonnees/\ListeCompletelen}}%
+    \ifboolKV[ClesStat]{Moyenne}{%
+      La somme des données est :%
+      \xintifboolexpr{\ListeCompletelen<\useKV[ClesStat]{Coupure}}{%
+        \[
+          \num{\ListeComplete[1,2]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{%
+            +\num{\ListeComplete[##1,2]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}
+          }=\num{\SommeDonnees}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}%
+      \]}{%
+      \[
+        \num{\ListeComplete[1,2]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}\xintFor* ##1 in {\xintSeq {2}{3}}\do{%
+          +\num{\ListeComplete[##1,2]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}}+\dots\xintFor* ##1 in {\xintSeq {\ListeCompletelen-1}{\ListeCompletelen}}\do{%
+          +\num{\ListeComplete[##1,2]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}
+        }=\num{\SommeDonnees}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}%
+      \]%
+    }%
+      \ifboolKV[ClesStat]{SET}{}{L'effectif total est \num{\ListeCompletelen}.\\}%
+      Donc la moyenne est égale à :%
+      \[\frac{\num{\SommeDonnees}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}}{\num{\ListeCompletelen}}%\IfInteger{\fpeval{round(\fpeval{\SommeDonnees/\ListeCompletelen},\useKV[ClesStat]{Precision})}}{=}{\approx}
+        \opdiv*{\SommeDonnees}{\ListeCompletelen}{resultatmoy}{restemoy}%
+        \opround{resultatmoy}{\useKV[ClesStat]{Precision}}{resultatmoy1}%
+              \opcmp{resultatmoy}{resultatmoy1}\ifopeq=\else\approx\fi%
+        \num{\fpeval{round(\fpeval{\SommeDonnees/\ListeCompletelen},\useKV[ClesStat]{Precision})}}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}.}{.}%
+      \]%
+    }{}%
+    %    %  %% celui de l'étendue
+    \xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{%
+      \xintifboolexpr{\ListeComplete[##1,2]>\DonneeMax}{%
+        \xdef\DonneeMax{\ListeComplete[##1,2]}%
+      }{}%
+      \xintifboolexpr{\ListeComplete[##1,2]<\DonneeMin}{%
+        \xdef\DonneeMin{\ListeComplete[##1,2]}%
+      }{}%
+    }%
+    \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]{Mediane}{%
+      %%%%%%%%%%%%%%%%%%%%%%%%
+      
+      On range les données par ordre croissant :%
+      \nbdonnees=0%
+      \xintifboolexpr{\ListeCompletelen<\useKV[ClesStat]{Coupure}}{%
+        \[\DTLforeach{mtdb}{\numeroDonnee=Numeric}{\num{\numeroDonnee}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}\DTLiflastrow{.}{;}}\]%
+      }{%
+      \medskip%
+      \begin{center}
+        \begin{minipage}{0.9\linewidth}
+          \DTLforeach*{mtdb}{\numeroDonnee=Numeric}{\num{\numeroDonnee}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}\DTLiflastrow{.}{;
+          }\nbdonnees=\fpeval{\nbdonnees+1}\modulo{\nbdonnees}{\useKV[ClesStat]{Coupure}}\xintifboolexpr{\remainder=0}{\\}{}}
+        \end{minipage}
+      \end{center}%
+      \medskip%
+      }%
+      \newcount\med%
+      \newcount\meda%
+      \ifodd\number\ListeCompletelen%odd impair
+      \med=\fpeval{(\ListeCompletelen+1)/2}\relax%
+      L'effectif total est \num{\ListeCompletelen}. Or, $\num{\ListeCompletelen}=\num{\fpeval{\med-1}}+1+\num{\fpeval{\med-1}}$.\\
+      \else% pair
+      \med=\fpeval{\ListeCompletelen/2}\relax
+      \meda=\numexpr\med+1\relax
+      L'effectif total est \num{\ListeCompletelen}. Or, $\num{\ListeCompletelen}=\num{\the\med}+\num{\the\med}$.\\
+      \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}.}{.}%
+        \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}.}{.}
+        \fi
+      }
+      %%%%%%%%%%%%%%%%%%%%%%%% 
+    }{}
+    % construction du tableau
+    \ifboolKV[ClesStat]{Tableau}{\ifboolKV[ClesStat]{Total}{\buildtabqt}{\buildtabq}}{}
+    % Construction du graphique ??
+    \ifboolKV[ClesStat]{Graphique}{%
+      \ifboolKV[ClesStat]{Angle}{\buildgraphcq{360}}{\ifboolKV[ClesStat]{SemiAngle}{\buildgraphcq{180}}{}}
+      \ifboolKV[ClesStat]{Batons}{\buildgraphq}{}
+    }{}
+  }{%%%%%%%%%%%%%%%%%%%%%Début quantitatif
+   %  % on effectue les calculs
+   %  %% celui de la somme des données
+   \foreachitem\don\in\ListeComplete{\xdef\SommeDonnees{\fpeval{\SommeDonnees+\ListeComplete[\doncnt,1]*\ListeComplete[\doncnt,2]}}}%
+    %  %% celui de l'effectif total
+    \foreachitem\don\in\ListeComplete{\xdef\EffectifTotal{\fpeval{\EffectifTotal+\ListeComplete[\doncnt,2]}}}%
+    %  %% celui de l'étendue
+    \xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{%
+      \xintifboolexpr{\ListeComplete[##1,1]>\DonneeMax}{%
+        \xdef\DonneeMax{\ListeComplete[##1,1]}%
+      }{}%
+      \xintifboolexpr{\ListeComplete[##1,1]<\DonneeMin}{%
+        \xdef\DonneeMin{\ListeComplete[##1,1]}%
+      }{}%
+    }%
+%    \xdef\EffectifMax{\DonneeMax}%
+    \xdef\Etendue{\fpeval{\DonneeMax-\DonneeMin}}%%
+    %  %% celui de la moyenne
+    \xdef\Moyenne{\fpeval{\SommeDonnees/\EffectifTotal}}%
+    \ifboolKV[ClesStat]{EffectifTotal}{%
+      L'effectif total est : \[\ListeComplete[1,2]\xintFor* ##1 in
+      {\xintSeq {2}{\ListeCompletelen}}\do{%
+        +\ListeComplete[##1,2]}=\num{\EffectifTotal}\]
+    }{}%
+    \ifboolKV[ClesStat]{Moyenne}{%
+      La somme des données est :%
+      \xintifboolexpr{\ListeCompletelen<\useKV[ClesStat]{Coupure}}{%
+        \[
+          \ifnum\ListeComplete[1,2]=1\else\num{\ListeComplete[1,2]}\times\fi\num{\ListeComplete[1,1]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{%
+            +\ifnum\ListeComplete[##1,2]=1\else\num{\ListeComplete[##1,2]}\times\fi\num{\ListeComplete[##1,1]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}
+          }=\num{\SommeDonnees}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}
+        \]
+      }{%
+        \[
+          \ifnum\ListeComplete[1,2]=1\else\num{\ListeComplete[1,2]}\times\fi\num{\ListeComplete[1,1]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}\xintFor* ##1 in {\xintSeq {2}{2}}\do{%
+            +\ifnum\ListeComplete[##1,2]=1\else\num{\ListeComplete[##1,2]}\times\fi\num{\ListeComplete[##1,1]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}
+          }+\dots\xintFor* ##1 in {\xintSeq {\ListeCompletelen-1}{\ListeCompletelen}}\do{%
+            +\ifnum\ListeComplete[##1,2]=1\else\num{\ListeComplete[##1,2]}\times\fi\num{\ListeComplete[##1,1]}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}
+          }=\num{\SommeDonnees}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}
+        \]
+      }
+      \ifboolKV[ClesStat]{SET}{}{L'effectif total est :%
+        \ifboolKV[ClesStat]{Liste}{ \num{\EffectifTotal}\\}{%
+          \[\num{\ListeComplete[1,2]}\xintFor* ##1 in {\xintSeq {2}{\ListeCompletelen}}\do{%
+              +\num{\ListeComplete[##1,2]}
+            }=\num{\EffectifTotal}
+          \]%
+        }%
+      }
+      Donc la moyenne est égale à :%
+      \[\frac{\num{\SommeDonnees}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}}{}}{\num{\EffectifTotal}}%
+        \opdiv*{\SommeDonnees}{\EffectifTotal}{resultatmoy}{restemoy}%
+        \opround{resultatmoy}{\useKV[ClesStat]{Precision}}{resultatmoy1}%
+        % Moy=\opprint{resultatmoy}--Moy1=\opprint{resultatmoy1}
+        \opcmp{resultatmoy}{resultatmoy1}\ifopeq=\else\approx\fi%
+        \num{\fpeval{round(\SommeDonnees/\EffectifTotal,\useKV[ClesStat]{Precision})}}\ifboolKV[ClesStat]{Concret}{~\text{\useKV[ClesStat]{Unite}}.}{.}
+      \]%
+    }{}%
+    %  % 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}.}{.}}{}%
+    %  %% pour la médiane
+    \ifboolKV[ClesStat]{Mediane}{%
+      
+      \newcount\med%
+      \newcount\meda%
+      \ifodd\number\EffectifTotal%odd impair
+      \med=\fpeval{(\EffectifTotal+1)/2}\relax%
+      L'effectif total est \num{\EffectifTotal}. Or, $\num{\EffectifTotal}=\num{\fpeval{\med-1}}+1+\num{\fpeval{\med-1}}$. %
+      \else% pair
+      \med=\fpeval{\EffectifTotal/2}\relax%
+      \meda=\numexpr\med+1\relax%
+      L'effectif total est \num{\EffectifTotal}. Or, $\num{\EffectifTotal}=\num{\fpeval{\med}}+\num{\fpeval{\med}}$. %
+      \fi%
+      \newcount\k%
+      \k=0%
+      \xintFor* ##1 in {\xintSeq {1}{\ListeCompletelen}}\do{%
+        \xintFor* ##2 in {\xintSeq {1}{\ListeComplete[##1,2]}}\do{%
+          \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}.}{.}%
+          \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}.}{.}%
+          \fi%
+        }%
+      }%
+    }{}%
+    % Construction de tableau
+    \ifboolKV[ClesStat]{Tableau}{\ifboolKV[ClesStat]{Total}{\buildtabt}{\buildtab}}{}%
+    % Construction du graphique ??
+    \ifboolKV[ClesStat]{Graphique}{\buildgraph}{}%
+  }%
+}%
+
+%%%%%%%%%%%%%
+%%% Radar
+%%%%%%%%%%%%%
+\setKVdefault[ClesRadar]{Rayon=3cm,Reference=20,MoyenneClasse=false,Disciplines=false,Pas=5}
+
+\newtoks\toklisteradara%pour la moyenne de l'élève
+\newtoks\toklisteradarb%pour la discipline
+\newtoks\toklisteradarc%pour la moyenne de classe
+
+\def\UpdateRadara#1/#2/#3\nil{\addtotok\toklisteradara{#1,}}
+\def\UpdateRadarb#1/#2/#3\nil{\addtotok\toklisteradarb{"#2",}}
+\def\UpdateRadarc#1/#2/#3\nil{\addtotok\toklisteradarc{#3,}}
+
+\newcommand\MPRadar[6]{%
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    pair O;
+    O=(0,0);
+    path cc;
+    cc=cercles(O,#1);
+    %%etiquettage des disciplines
+    n:=0;%compter le nombre de disciplines
+    for p_=#2:
+    n:=n+1;
+    endfor;
+    for k=1 upto n:
+    N[k]=k*(360/n);
+    trace segment(O,pointarc(cc,N[k]));% dashed evenly;
+    endfor;
+    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])]);
+    fi;
+    endfor;
+    % tracé des pas:
+    pas=#4/#3;
+    for k=1 upto pas-1:
+    trace (k/pas)[O,pointarc(cc,N[1])] for l=2 upto n: --(k/pas)[O,pointarc(cc,N[l])] endfor
+    --cycle dashed evenly withcolor 0.5white;
+    endfor;
+    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 #3 etex,(1/pas)[O,pointarc(cc,0)]);
+    % tracé des résultats élèves
+    pair El[];
+    el=0;
+    for p_=#5:
+    el:=el+1;
+    El[el]=(p_/#4)[O,pointarc(cc,N[el])];
+    endfor;
+    trace El[1] for p=2 upto n:--El[p] endfor --cycle withpen
+    pencircle scaled 1.5 withcolor blue;
+    % tracé des résultats classe
+    pair Cl[];
+    cl=0;
+    for p_=#6:
+    cl:=cl+1;
+    Cl[cl]=(p_/#4)[O,pointarc(cc,N[cl])];
+    endfor;
+    trace Cl[1] for p=2 upto n:--Cl[p] endfor --cycle withcolor rouge;
+  \end{mplibcode}
+  \else
+  \begin{mpost}
+    pair O;
+    O=(0,0);
+    path cc;
+    cc=cercles(O,#1);
+    %%etiquettage des disciplines
+    n:=0;%compter le nombre de disciplines
+    for p_=#2:
+    n:=n+1;
+    endfor;
+    for k=1 upto n:
+    N[k]=k*(360/n);
+    trace segment(O,pointarc(cc,N[k]));% dashed evenly;
+    endfor;
+    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])]);
+    fi;
+    endfor;
+    % tracé des pas:
+    pas=#4/#3;
+    for k=1 upto pas-1:
+    trace (k/pas)[O,pointarc(cc,N[1])] for l=2 upto n: --(k/pas)[O,pointarc(cc,N[l])] endfor
+    --cycle dashed evenly withcolor 0.5white;
+    endfor;
+    trace pointarc(cc,N[1]) for l=2 upto n: --pointarc(cc,N[l]) endfor
+    --cycle;
+    % etiquettage des pas
+    dotlabel.top(LATEX("\noexpand\tiny"&decimal(#4)&"") rotated -90,pointarc(cc,0));
+    dotlabel.urt(LATEX("\noexpand\tiny"&decimal(#3)&""),(1/pas)[O,pointarc(cc,0)]);
+    % tracé des résultats élèves
+    pair El[];
+    el=0;
+    for p_=#5:
+    el:=el+1;
+    El[el]=(p_/#4)[O,pointarc(cc,N[el])];
+    endfor;
+    trace El[1] for p=2 upto n:--El[p] endfor --cycle withpen
+    pencircle scaled 1.5 withcolor blue;
+    % tracé des résultats classe
+    pair Cl[];
+    cl=0;
+    for p_=#6:
+    cl:=cl+1;
+    Cl[cl]=(p_/#4)[O,pointarc(cc,N[cl])];
+    endfor;
+    trace Cl[1] for p=2 upto n:--Cl[p] endfor --cycle withcolor rouge;
+  \end{mpost}
+  \fi
+}
+
+\newcommand\Radar[2][]{%
+  % 1 les paramètres
+  % 2 la répartition des notes
+  \useKVdefault[ClesRadar]%
+  \setKV[ClesRadar]{#1}%
+  \ignoreemptyitems%
+  \readlist*\ListeRadar{#2}%
+  \toklisteradara{}%
+  \foreachitem\compteur\in\ListeRadar{\expandafter\UpdateRadara\compteur\nil}%
+  \ifboolKV[ClesRadar]{Disciplines}{}{%
+    \toklisteradarb{}%
+    \foreachitem\compteur\in\ListeRadar{\expandafter\UpdateRadarb\compteur\nil}%
+  }
+  \ifboolKV[ClesRadar]{MoyenneClasse}{}{%
+    \toklisteradarc{}%
+    \foreachitem\compteur\in\ListeRadar{\expandafter\UpdateRadarc\compteur\nil}%
+  }
+  \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}
+
+\newcommand\Jauge[2][]{%
+  \setlength{\barrewidth}{\linewidth-2\fboxsep}%
+  \useKVdefault[ClesBarre]%
+  \setKV[ClesBarre]{#1}%
+  \xdef\NomComp{\useKV[ClesBarre]{Nom}}%
+  \xdef\TexteOrigine{\useKV[ClesBarre]{Origine}}
+  \xdef\TexteReference{\useKV[ClesBarre]{Reference}}
+  \xdef\CouleurFond{\useKV[ClesBarre]{CouleurFond}}%
+  \xdef\CouleurGrad{\useKV[ClesBarre]{CouleurGraduation}}%
+  \xdef\CouleurBarre{\useKV[ClesBarre]{CouleurBarre}}%
+  \xdef\CouleurI{\useKV[ClesBarre]{CouleurI}}%
+  \xdef\CouleurF{\useKV[ClesBarre]{CouleurF}}%
+  \xdef\CouleurS{\useKV[ClesBarre]{CouleurS}}%
+  \xdef\CouleurM{\useKV[ClesBarre]{CouleurM}}%
+  \ifboolKV[ClesBarre]{Niveau}{%
+    \begin{tikzpicture}[rounded corners=2pt,very thin]
+      \fill [gray!50] (0,0) rectangle (\barrewidth, 0.15);
+      \xintifboolexpr{#2<\useKV[ClesBarre]{LimiteI}}{%
+        \fill [\CouleurI] (0,0) rectangle (#2/100*\barrewidth, 0.15);
+      }{\xintifboolexpr{#2<\useKV[ClesBarre]{LimiteF}}{%
+          \fill [\CouleurF] (0,0) rectangle (#2/100*\barrewidth, 0.15);
+        }{\xintifboolexpr{#2<\useKV[ClesBarre]{LimiteS}}{%
+            \fill [\CouleurS] (0,0) rectangle (#2/100*\barrewidth, 0.15);
+          }{\fill [\CouleurM] (0,0) rectangle (#2/100*\barrewidth, 0.15);}
+        }
+      }
+      \node[anchor=south west] at (0,0.5em) {\NomComp};%
+      \node[anchor=north] at (0,-0.25em) {\TexteOrigine};
+      \node[anchor=north] at (\barrewidth,-0.25em) {\TexteReference};
+      \ifboolKV[ClesBarre]{Graduation}{%
+        \foreach \s in {1,...,\fpeval{\useKV[ClesBarre]{Pas}-1}}%
+        {
+          \draw[\CouleurGrad] (\s/\useKV[ClesBarre]{Pas}*\barrewidth,0)--(\s/\useKV[ClesBarre]{Pas}*\barrewidth,0.15); 
+        }
+      }{}
+      \foreach \s in {\useKV[ClesBarre]{LimiteI},\useKV[ClesBarre]{LimiteF},\useKV[ClesBarre]{LimiteS}}%
+      {
+        \draw[black] (\s/100*\barrewidth,-0.1)--(\s/100*\barrewidth,0.2);%
+      }
+    \end{tikzpicture}%
+  }{%
+    \begin{tikzpicture}[rounded corners=2pt,very thin]
+      \fill [\CouleurFond] (0,0) rectangle (\barrewidth, 0.15);%
+      \fill [\CouleurBarre] (0,0) rectangle (#2/100*\barrewidth, 0.15);%
+      \node[anchor=south west] at (0,0.5em) {\NomComp};%
+      \node[anchor=north] at (0,-0.25em) {\useKV[ClesBarre]{TexteOrigine}};%
+      \node[anchor=north] at (\barrewidth,-0.25em) {\useKV[ClesBarre]{TexteReference}};%
+      \ifboolKV[ClesBarre]{Graduation}{%
+      \foreach \s in {1,...,\fpeval{\useKV[ClesBarre]{Pas}-1}}%
+      {
+        \draw[\CouleurGrad] (\s/\useKV[ClesBarre]{Pas}*\barrewidth,0)--(\s/\useKV[ClesBarre]{Pas}*\barrewidth,0.15); 
+      }}{}%
+    \end{tikzpicture}%
+  }
+}
+
+%%%%%%%%%%%%%%%
+%%% 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}
+
+
+\newcommand\rightcomment[4]%
+  {\begin{tikzpicture}[remember picture,overlay]
+   \draw[Cfleches,-stealth]
+     ($({pic cs:#3}|-{pic cs:#1})+(\useKV[ClesEquation]{Ecart},0)$)
+     .. controls +(0.2,-0.05) and +(0.2,0.1) ..
+     node[right,align=left]{#4}
+     ($({pic cs:#3}|-{pic cs:#2})+(\useKV[ClesEquation]{Ecart},0.1)$);
+   \end{tikzpicture}%
+ }
+
+
+ \newcommand\leftcomment[4]%
+  {\begin{tikzpicture}[remember picture,overlay]
+   \draw[Cfleches,-stealth]
+     ($({pic cs:#3}|-{pic cs:#1})-(\useKV[ClesEquation]{Ecart},0)$)
+     .. controls +(-0.2,-0.05) and +(-0.2,0.1) ..
+     node[left,align=right]{#4}
+     ($({pic cs:#3}|-{pic cs:#2})-(\useKV[ClesEquation]{Ecart},-0.1)$);
+   \end{tikzpicture}%
+ }
+
+ \newcommand\Rightcomment[4]%
+  {\begin{tikzpicture}[remember picture,overlay]
+   \draw[Cfleches,-stealth]
+     ($({pic cs:#3}|-{pic cs:#1})+(\useKV[ClesEquation]{Ecart},0)$)
+     .. controls +(0.2,-0.05) and +(0.2,0.1) ..
+     node[right,align=left]{#4}
+     ($({pic cs:#3}|-{pic cs:#2})+(\useKV[ClesEquation]{Ecart},0.1)$);
+   \end{tikzpicture}%
+ }
+ \newcommand\Leftcomment[4]%
+  {\begin{tikzpicture}[remember picture,overlay]
+   \draw[Cfleches,-stealth]
+     ($({pic cs:#3}|-{pic cs:#1})-(\useKV[ClesEquation]{Ecart},0)$)
+     .. controls +(-0.2,-0.05) and +(-0.2,0.1) ..
+     node[left,align=right]{#4}
+     ($({pic cs:#3}|-{pic cs:#2})-(\useKV[ClesEquation]{Ecart},-0.1)$);
+   \end{tikzpicture}%
+ }
+
+ % Pour "oublier" les tikzmarks. En cas de plusieurs utilisations de la macro \ResolEquation
+\newcounter{Nbequa}
+\setcounter{Nbequa}{0}
+
+%CT
+\newdimen\fdashwidth    \fdashwidth  = 0.8pt % épaisseur traits
+\newdimen\fdashlength   \fdashlength = 0.5mm % longueur des pointillés et séparation entre pointillés
+\newdimen\fdashsep      \fdashsep    = 3pt % séparateur entre contenu et traits
+
+\def\fdash#1{%
+  \leavevmode\begingroup%
+  \setbox0\hbox{#1}%
+  \def\hdash{\vrule height\fdashwidth width\fdashlength\relax}%
+  \def\vdash{\hrule height\fdashlength width\fdashwidth\relax}%
+  \def\dashblank{\kern\fdashlength}%
+  \ifdim\fdashsep>0pt
+  \setbox0\hbox{\vrule width0pt height\dimexpr\ht0+\fdashsep depth\dimexpr\dp0+\fdashsep\kern\fdashsep\unhbox0 \kern\fdashsep}%
+  \fi
+  \edef\hdash{\hbox to\the\wd0{\noexpand\color{Csymbole}\hdash\kern.5\fdashlength\xleaders\hbox{\hdash\dashblank}\hfil\hdash}}%
+  \edef\vdash{\vbox to\the\dimexpr\ht0+\dp0+2\fdashwidth{\noexpand\color{Csymbole}\vdash\kern.5\fdashlength\xleaders\vbox{\vdash\dashblank}\vfil\vdash}}%
+  \hbox{%
+    \vdash
+    \vtop{\vbox{\offinterlineskip\hdash\hbox{\unhbox0 }\hdash}}%
+    \vdash}%
+  \endgroup
+}
+% fin CT
+\def\Fdash#1{\raisebox{-2\fdashsep+\fdashwidth}{\fdash{#1}}}
+
+%Une simplification de a/b est possible ou non ?
+\newboolean{Simplification}
+
+\newcommand{\SSimpliTest}[2]{%
+  % Test d'une simplification possible ou pas de #1/#2
+  \newcount\numerateur\newcount\denominateur\newcount\valabsnum\newcount\valabsdeno%
+  \numerateur=\number#1
+  \denominateur=\number#2
+  \ifnum\number#1<0
+  \valabsnum=\numexpr0-\number#1
+  \else
+  \valabsnum=\number#1
+  \fi
+  \ifnum\number#2<0
+  \valabsdeno=\numexpr0-\number#2
+  \else
+  \valabsdeno=\number#2
+  \fi
+  \ifnum\the\valabsnum=0
+    \setboolean{Simplification}{true}
+  \else
+    \PGCD{\the\valabsnum}{\the\valabsdeno}
+    \ifnum\pgcd>1
+      \setboolean{Simplification}{true}
+    \else
+      \ifnum\the\numerateur<0
+        \ifnum\the\denominateur<0
+          \setboolean{Simplification}{true}
+        \else
+          \ifnum\valabsdeno=1\relax
+            \setboolean{Simplification}{true}
+          \else
+          \setboolean{Simplification}{false}
+          \fi
+        \fi
+      \else
+        \ifnum\valabsdeno=1\relax
+          \setboolean{Simplification}{true}
+        \else
+          \setboolean{Simplification}{false}
+        \fi
+      \fi
+    \fi
+  \fi
+}
+
+\definecolor{Cfleches}{RGB}{100,100,100}%
+
+\input{PfC-EquationSoustraction1}%
+\input{PfC-EquationTerme1}%
+\input{PfC-EquationComposition1}%
+\input{PfC-EquationPose1}%
+\input{PfC-EquationSymbole1}%
+\input{PfC-EquationLaurent1}
+
+\newcommand{\ResolEquation}[5][]{%
+  \useKVdefault[ClesEquation]%
+  \setKV[ClesEquation]{#1}%
+  \colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}%
+  \colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}%
+  \colorlet{Csymbole}{\useKV[ClesEquation]{CouleurSymbole}}%
+  \colorlet{Cdecomp}{\useKV[ClesEquation]{CouleurSous}}%
+  \ifboolKV[ClesEquation]{Carre}{%
+    \ResolEquationCarre[#1]{#2}%
+  }{%
+    \ifboolKV[ClesEquation]{Produit}{%
+      \ResolEquationProduit[#1]{#2}{#3}{#4}{#5}%
+    }{%
+      \ifboolKV[ClesEquation]{Verification}{%
+        \Verification[#1]{#2}{#3}{#4}{#5}%
+      }{%
+        \ifboolKV[ClesEquation]{Symbole}{%
+          \ResolEquationSymbole[#1]{#2}{#3}{#4}{#5}%
+        }{%
+          \ifboolKV[ClesEquation]{Laurent}{%
+            \ResolEquationLaurent[#1]{#2}{#3}{#4}{#5}%
+          }{%
+            \ifboolKV[ClesEquation]{Terme}{%
+              \ResolEquationTerme[#1]{#2}{#3}{#4}{#5}%
+            }{\ifboolKV[ClesEquation]{Composition}{%
+                \ResolEquationComposition[#1]{#2}{#3}{#4}{#5}%
+              }{\ifboolKV[ClesEquation]{Pose}{%
+                  \ResolEquationL[#1]{#2}{#3}{#4}{#5}%
+                }{%
+                  \ResolEquationSoustraction[#1]{#2}{#3}{#4}{#5}%
+                }%
+              }%
+            }%
+          }%
+        }%
+      }%
+    }%
+  }%
+}%
+
+\newcommand\ResolEquationCarre[2][]{%
+  \setKV[ClesEquation]{#1}%
+  \xintifboolexpr{#2<0}{%
+    Comme $\num{#2}$ est négatif, alors l'équation $\useKV[ClesEquation]{Lettre}^2=\num{#2}$ n'a aucune solution.%
+  }{\xintifboolexpr{#2=0}{%
+      L'équation $\useKV[ClesEquation]{Lettre}^2=0$ a une unique solution : $\useKV[ClesEquation]{Lettre}=0$.%
+    }{%
+      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}{\\%
+        \useKV[ClesEquation]{Lettre}&=\num{\fpeval{sqrt(#2)}}&&\text{et}&\useKV[ClesEquation]{Lettre}&=-\num{\fpeval{sqrt(#2)}}}{}%
+      \end{align*}
+    }
+  }
+}
+
+\newcommand\ResolEquationProduit[5][]{%
+  \setKV[ClesEquation]{#1}%
+  \ifboolKV[ClesEquation]{Equivalence}{}{C'est un produit nul donc \ifboolKV[ClesEquation]{Facteurs}{l'un au
+      moins des facteurs est nul}{} :}%
+  \ifboolKV[ClesEquation]{Equivalence}{%
+          \[\Distri{#2}{#3}{#4}{#5}=0\]
+    \begin{align*}%
+      &\makebox[0pt]{$\Longleftrightarrow$}&\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}}}}&=0&\quad&\makebox[0pt]{ou}\quad&\xintifboolexpr{#5=0}{\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\\
+      &\makebox[0pt]{$\Longleftrightarrow$}&\xintifboolexpr{#3=0}{\xdef\Coeffa{1}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{#2=1}{&}{\useKV[ClesEquation]{Lettre}&=0}}{\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}}&&&\xintifboolexpr{#5=0}{\xdef\Coeffc{1}\xdef\Coeffd{\fpeval{0-#5}}\xintifboolexpr{#4=1}{&}{\useKV[ClesEquation]{Lettre}&=0}}{\xdef\Coeffc{#4}\xdef\Coeffd{\fpeval{0-#5}}\xintifboolexpr{\Coeffc=1}{}{\num{\Coeffc}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffd}}%\\
+      \xintifboolexpr{\Coeffa=1 'and' \Coeffc=1}{}{\\%\ifnum\cmtd>1
+      &\makebox[0pt]{$\Longleftrightarrow$}&\xintifboolexpr{\Coeffa=1}{&}{\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}}\xintifboolexpr{\Coeffc=1}{}{&&&\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffd}}{\num{\Coeffc}}}
+      % accolade%\\
+      %%%% 
+      \ifboolKV[ClesEquation]{Entier}{%
+      \xdef\TSimp{}%
+      \SSimpliTest{\Coeffb}{\Coeffa}\ifthenelse{\boolean{Simplification}}{\xintifboolexpr{#3=0}{\xdef\TSimp{0}}{\xdef\TSimp{1}}}{\xdef\TSimp{0}}
+      \SSimpliTest{\Coeffd}{\Coeffc}\ifthenelse{\boolean{Simplification}}{\xintifboolexpr{#5=0}{}{\xdef\TSimp{\fpeval{\TSimp+1}}}}{}
+      \xintifboolexpr{\TSimp=0}{}{\\
+      \ifboolKV[ClesEquation]{Simplification}{%
+      &\makebox[0pt]{$\Longleftrightarrow$}&\SSimpliTest{\Coeffb}{\Coeffa}\xintifboolexpr{\Coeffa=1}{&}{\ifthenelse{\boolean{Simplification}}{\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{&}%\\
+      }
+      }{}
+      &&&\ifboolKV[ClesEquation]{Simplification}{%
+      \SSimpliTest{\Coeffd}{\Coeffc}%
+          \xintifboolexpr{\Coeffc=1}{}{\ifthenelse{\boolean{Simplification}}{\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffd}{\Coeffc}}{}%\\
+      }
+      }{}
+      }
+      }{}
+      }
+    \end{align*}
+  }{%
+    \begin{align*}
+    \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}}}}&=0&&\text{ou}&\xintifboolexpr{#5=0}{\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\\
+    \xintifboolexpr{#3=0}{\xdef\Coeffa{1}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{#2=1}{&}{\useKV[ClesEquation]{Lettre}&=0}}{\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}}&&&\xintifboolexpr{#5=0}{\xdef\Coeffc{1}\xdef\Coeffd{\fpeval{0-#5}}\xintifboolexpr{#4=1}{&}{\useKV[ClesEquation]{Lettre}&=0}}{\xdef\Coeffc{#4}\xdef\Coeffd{\fpeval{0-#5}}\xintifboolexpr{\Coeffc=1}{}{\num{\Coeffc}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffd}}%\\
+      \xintifboolexpr{\Coeffa=1 'and' \Coeffc=1}{}{\\%\ifnum\cmtd>1
+      \xintifboolexpr{\Coeffa=1}{&}{\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}}\xintifboolexpr{\Coeffc=1}{}{&&&\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffd}}{\num{\Coeffc}}}
+       %accolade%\\
+      %%%%   
+      \ifboolKV[ClesEquation]{Entier}{%
+      \xdef\TSimp{}
+      \SSimpliTest{\Coeffb}{\Coeffa}\ifthenelse{\boolean{Simplification}}{\xintifboolexpr{#3=0}{\xdef\TSimp{0}}{\xdef\TSimp{1}}}{\xdef\TSimp{0}}
+      \SSimpliTest{\Coeffd}{\Coeffc}\ifthenelse{\boolean{Simplification}}{\xintifboolexpr{#5=0}{}{\xdef\TSimp{\fpeval{\TSimp+1}}}}{}
+      \xintifboolexpr{\TSimp=0}{}{\\
+      \ifboolKV[ClesEquation]{Simplification}{%
+      \SSimpliTest{\Coeffb}{\Coeffa}
+      \xintifboolexpr{\Coeffa=1}{&}{\ifthenelse{\boolean{Simplification}}{\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{&}%\\
+      }
+      }{}
+      &&&\ifboolKV[ClesEquation]{Simplification}{%
+      \SSimpliTest{\Coeffd}{\Coeffc}%
+          \xintifboolexpr{\Coeffc=1}{}{\ifthenelse{\boolean{Simplification}}{\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffd}{\Coeffc}}{}%\\
+      }
+      }{}
+      }
+      }{}
+      }
+    \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}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffd}{\Coeffc}}{\frac{\num{\Coeffd}}{\num{\Coeffc}}}\fi$.
+    }{}
+}
+
+\newcommand\Verification[5][]{%
+  \setKV[ClesEquation]{#1}
+  \xdef\ValeurTest{\useKV[ClesEquation]{Nombre}}
+  Testons la valeur $\useKV[ClesEquation]{Lettre}=\num{\ValeurTest}$ :
+  \begin{align*}
+    \xintifboolexpr{#2=0}{\num{#3}}{\num{#2}\times\xintifboolexpr{\ValeurTest<0}{(\num{\ValeurTest})}{\num{\ValeurTest}}\xintifboolexpr{#3=0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{\num{#3}}}}&&\xintifboolexpr{#4=0}{\num{#5}}{\num{#4}\times\xintifboolexpr{\ValeurTest<0}{(\num{\ValeurTest})}{\num{\ValeurTest}}\xintifboolexpr{#5=0}{}{\xintifboolexpr{#5>0}{+\num{#5}}{\num{#5}}}}\\
+    \xintifboolexpr{#2=0}{}{\num{\fpeval{#2*\useKV[ClesEquation]{Nombre}}}\xintifboolexpr{#3=0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{\num{#3}}}}&&\xintifboolexpr{#4=0}{}{\num{\fpeval{#4*\useKV[ClesEquation]{Nombre}}}\xintifboolexpr{#5=0}{}{\xintifboolexpr{#5>0}{+\num{#5}}{\num{#5}}}}\\
+    \xintifboolexpr{#2=0}{}{\num{\fpeval{#2*\useKV[ClesEquation]{Nombre}+#3}}}&&\xintifboolexpr{#4=0}{}{\num{\fpeval{#4*\useKV[ClesEquation]{Nombre}+#5}}}
+  \end{align*}
+  \xdef\Testa{\fpeval{#2*\useKV[ClesEquation]{Nombre}+#3}}\xdef\Testb{\fpeval{#4*\useKV[ClesEquation]{Nombre}+#5}}
+  \ifboolKV[ClesEquation]{Egalite}{%
+    Comme \xintifboolexpr{\Testa=\Testb}{$\num{\Testa}=\num{\Testb}$}{$\num{\Testa}\not=\num{\Testb}$}, alors l'égalité $\xintifboolexpr{#2=0}{\num{#3}}{\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3=0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}}=\xintifboolexpr{#4=0}{\num{#5}}{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5=0}{}{\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}}}$ \xintifboolexpr{\Testa=\Testb}{ est vérifiée }{ n'est pas vérifiée } pour $\useKV[ClesEquation]{Lettre}=\num{\useKV[ClesEquation]{Nombre}}$.%
+  }{\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}%Tableau=false :
+                                %inutile ?
+
+\def\Updatetoksmath#1/#2\nil{\addtotok\tabtoksa{&#1}\addtotok\tabtoksb{&#2}}%
+
+\def\buildtabpropor{%
+  \tabtoksa{}\tabtoksb{}%
+  \tabtoksa{\useKV[ClesPropor]{GrandeurA}}\tabtoksb{\useKV[ClesPropor]{GrandeurB}}%
+  \ifboolKV[ClesPropor]{Math}{%
+    \foreachitem\compteur\in\ListeValeur{\expandafter\Updatetoksmath\compteur\nil}%
+  }{\foreachitem\compteur\in\ListeValeur{\expandafter\updatetoks\compteur\nil}%
+  }%
+  \xdef\LongListe{\ListeValeurlen}%
+  \renewcommand{\arraystretch}{\useKV[ClesPropor]{Stretch}}%
+  \begin{tabular}{|>{\columncolor{gray!15}}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\\%
+    \hhline{*{\number\numexpr\ListeValeurlen+1}{-}}%
+    \the\tabtoksb\\%
+    \hhline{*{\number\numexpr\ListeValeurlen+1}{-}}%
+    \multicolumn{1}{c}{\TikzPBD\setcounter{NbPropor}{1}}\xintFor* ##1 in {\xintSeq {1}{\ListeValeurlen}}\do{&\multicolumn{1}{c}{\TikzPB}}\\%
+  \end{tabular}%
+}%
+
+\newcounter{NbPropor}
+
+\newcommand{\TikzPH}{%
+   \tikz[remember picture,overlay]{%
+   \coordinate[name=ProporH-\theNbPropor,yshift=-\the\dp\strutbox*\arraystretch];}%
+   \stepcounter{NbPropor}%
+ }%
+
+ \newcommand{\TikzPHD}{%
+   \setbox1=\hbox{\useKV[ClesPropor]{GrandeurA}}
+   \tikz[remember picture,overlay]{%
+   \coordinate[name=ProporHD,xshift=-0.5*\the\wd1,yshift=-\the\dp\strutbox*\arraystretch];}%
+ }%
+
+ \newcommand{\TikzPB}{%
+   \tikz[remember picture, overlay]{%
+     \coordinate[name=ProporB-\theNbPropor,yshift=\the\ht\strutbox*\arraystretch];}%
+   \stepcounter{NbPropor}%
+ }%
+
+ \newcommand{\TikzPBD}{%
+   \setbox1=\hbox{\useKV[ClesPropor]{GrandeurA}}
+   \tikz[remember picture, overlay]{%
+     \coordinate[name=ProporBD,xshift=-0.5*\the\wd1,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);%
+  \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);%
+  \end{tikzpicture}%
+  \fi%
+}%
+
+\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);%
+  \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);%
+  \end{tikzpicture}%
+  \fi%
+}
+
+\newcommand\Propor[2][]{%
+  \useKVdefault[ClesPropor]%
+  \setKV[ClesPropor]{#1}%
+  \xdef\colorfill{\useKV[ClesPropor]{ColorFill}}%
+  \xdef\EcartLargeur{\useKV[ClesPropor]{Largeur}}
+%  %on lit la liste écrite sous la forme valeur/effectif
+  \setsepchar[*]{,*/}\ignoreemptyitems%
+  \readlist*\ListeValeur{#2}%
+  \buildtabpropor%
+}
+
+\newcommand\FlecheCoef[2][\EcartLargeur]{%
+  \begin{tikzpicture}[remember picture, overlay]%
+    \node[] (Point1) at ($(ProporH-\LongListe)!0.1!(ProporB-\LongListe)$) {};%
+    \node[] (Point2) at ($(ProporH-\LongListe)!0.9!(ProporB-\LongListe)$) {};%
+    \coordinate[right of=Point1,node distance=0.5*#1+\tabcolsep] (point1);%
+    \coordinate[right of=Point2,node distance=0.5*#1+\tabcolsep] (point2);%
+    \draw[-stealth,out=-20,in=20] (point1) to node[midway,right,inner sep=1pt]{#2}(point2);%
+\end{tikzpicture}%
+}%
+
+\newcommand\FlecheCoefDebut[2][1.25\tabcolsep]{%
+  \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}%
+}%
+
+\newcommand\FlecheCoefInv[2][1cm]{%
+  \begin{tikzpicture}[remember picture, overlay]%
+    \node[] (Point1) at ($(ProporH-\LongListe)!0.1!(ProporB-\LongListe)$) {};%
+    \node[] (Point2) at ($(ProporH-\LongListe)!0.9!(ProporB-\LongListe)$) {};%
+    \coordinate[right of=Point1,node distance=0.5*#1+\tabcolsep] (point1);%
+    \coordinate[right of=Point2,node distance=0.5*#1+\tabcolsep] (point2);%
+    \draw[-stealth,out=20,in=-20] (point2) to node[midway,right,inner sep=1pt]{#2}(point1);%
+\end{tikzpicture}%
+}%
+
+\newcommand\FlecheLineaireH[4]{%
+  \begin{tikzpicture}[remember picture,overlay,node distance=\ht\strutbox]
+  \node[inner sep=0pt] (MilieuH) at ($(ProporH-#1)!0.5!(ProporH-#2)$) {};
+  \node[circle,draw,inner sep=0pt] [above of=MilieuH] (aux) {#4} ;
+  \coordinate[above of=aux] (aux1);
+  \draw[-stealth] (ProporH-#1) |- (aux);
+  \draw[-stealth] (ProporH-#2) |- (aux);
+  \draw[-stealth] (aux) -- (aux1) -| (ProporH-#3);
+\end{tikzpicture}
+}
+
+\newcommand\FlecheLineaireB[4]{%
+  \begin{tikzpicture}[remember picture,overlay,node distance=3mm]
+  \node[inner sep=0pt] (MilieuB) at ($(ProporB-#1)!0.5!(ProporB-#2)$) {};
+  \node[circle,draw,inner sep=0pt] [below of=MilieuB] (aux) {#4} ;
+  \coordinate[below of=aux,node distance=3mm] (aux1);
+  \draw[-stealth] (ProporB-#1) |- (aux);
+  \draw[-stealth] (ProporB-#2) |- (aux);
+  \draw[-stealth] (aux) -- (aux1) -| (ProporB-#3);
+\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}
+  
+\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 :
+        \[\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\left(1-\frac{\num{#2}}{100}\right)=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times(1-\num{\fpeval{#2/100}})=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\num{\fpeval{(1-#2/100)}}=\num{\fpeval{#3*(1-#2/100)}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\]
+      }{%
+        Calculons ce que représente la \useKV[ClesPourcentage]{MotReduction} de \num{#2}~\%.
+        \ifboolKV[ClesPourcentage]{AideTableau}{%
+          \xdef\NomA{\useKV[ClesPourcentage]{GrandeurA}}
+          \xdef\NomB{\useKV[ClesPourcentage]{GrandeurB}}
+          \begin{center}
+            \Propor[GrandeurA=\NomA,GrandeurB=\NomB]{/#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}}{}.%
+        }{Pour calculer \num{#2}~\% de \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}, on effectue le calcul :
+        \[\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{#2}}{100}}{\num{\fpeval{#2/100}}}\times\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{\fpeval{#2*#3}}}{100}}{\num{\fpeval{#2*#3/100}}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\ifboolKV[ClesPourcentage]{Fractionnaire}{=\num{\fpeval{#2*#3/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}}{}\]%
+       On obtient une \useKV[ClesPourcentage]{MotReduction} de $\num{\fpeval{#3*#2/100}}$\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}}{}.}
+      }
+  }{%
+    \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 :
+        \[\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\left(1+\frac{\num{#2}}{100}\right)=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times(1+\num{\fpeval{#2/100}})=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\num{\fpeval{(1+#2/100)}}=\num{\fpeval{#3*(1+#2/100)}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\]
+      }{%
+        Calculons ce que représente l'augmentation de \num{#2}~\%. %
+        \ifboolKV[ClesPourcentage]{AideTableau}{%
+          \xdef\NomA{\useKV[ClesPourcentage]{GrandeurA}}%
+          \xdef\NomB{\useKV[ClesPourcentage]{GrandeurB}}%
+          \begin{center}%
+            \Propor[GrandeurA=\NomA,GrandeurB=\NomB]{/#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}}{}.%
+        }{Pour calculer \num{#2}~\% de \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}, on effectue le calcul :
+          \[\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{#2}}{100}}{\num{\fpeval{#2/100}}}\times\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{\fpeval{#2*#3}}}{100}}{\num{\fpeval{#2*#3/100}}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\ifboolKV[ClesPourcentage]{Fractionnaire}{=\num{\fpeval{#2*#3/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}}{}\]%
+          On obtient une augmentation de $\num{\fpeval{#3*#2/100}}$\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}}{}.}
+      }
+    }{%
+      \ifboolKV[ClesPourcentage]{Calculer}{%
+        \xdef\NomA{\useKV[ClesPourcentage]{GrandeurA}}
+        \xdef\NomB{\useKV[ClesPourcentage]{GrandeurB}}
+        \Propor[GrandeurA=\NomA,GrandeurB=\NomB]{#2/#3,/100}%
+        \xdef\colorfill{\useKV[ClesPourcentage]{ColorFill}}%
+        \FlechesPB{2}{1}{\scriptsize$\times\num{\fpeval{#3/100}}$}%
+        \FlechesPH{1}{2}{\scriptsize$\div\num{\fpeval{#3/100}}$}%
+        \xdef\ResultatPourcentage{\fpeval{#2*100/#3}}%
+      }{%
+        Pour calculer \num{#2}~\% de \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}, on effectue le calcul :%
+        \[\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{#2}}{100}}{\num{\fpeval{#2/100}}}\times\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{\fpeval{#2*#3}}}{100}}{\num{\fpeval{#2*#3/100}}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\ifboolKV[ClesPourcentage]{Fractionnaire}{=\num{\fpeval{#2*#3/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}}{}\]%
+      }%
+    }%
+  }%
+}%
+
+%%%%%%%%%%%%%
+%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,NombreUn}
+
+\newcommand\MPTest[9][]{%
+  % #2 : Longueur de la barre unité
+  % #3 : premier nombre
+  % #4 : deuxième nombre
+  % #5 : troisième nombre
+  % #6 : Valeurs du ratio
+  % #7 à #9: Couleurs de remplissage
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    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);
+    B-A=(long,0);
+    C-B=u*(0,0.5);
+    D-C=A-B;
+    n:=0;%n pour savoir si le ratio est a:b ou a:b:c
+    numeric N[];%Pour sauvegarder les éléments du ratio
+    for p_=t:
+    n:=n+1;
+    N[n]=p_;
+    endfor;
+    % on fait la somme totale "du ratio"
+    somme=0;
+    somme:=somme for k=1 upto n:+N[k] endfor;
+    Figure(0,0,long+2u,3u);
+    remplis polygone(A,(N[1]/somme)[A,B],(N[1]/somme)[D,C],D)
+    withcolor #7;
+    remplis polygone(B,(N[1]/somme)[A,B],(N[1]/somme)[D,C],C)
+    withcolor #8;
+    if n>2:
+    remplis
+    polygone((N[1]/somme)[A,B],((N[1]+N[2])/somme)[A,B],((N[1]+N[2])/somme)[D,C],(N[1]/somme)[D,C])
+    withcolor #8;
+    remplis
+    polygone(B,((N[1]+N[2])/somme)[A,B],((N[1]+N[2])/somme)[D,C],C)
+    withcolor #9;
+    fi;
+    drawoptions(withpen pencircle scaled1.5bp);
+    draw polygone(A,B,C,D);
+    for k=1 upto somme-1:
+    draw segment((k/somme)[A,B],(k/somme)[D,C]);
+    endfor;
+    drawoptions();
+    % accolades
+    labeloffset:=labeloffset/2;
+    label.top(TEX("\footnotesize$\overbrace{\hbox
+      to"&decimal(abs(A-B))&"pt{}}$"),iso(D,C));
+    labeloffset:=labeloffset*2;
+    label.bot(TEX("\footnotesize$\underbrace{\hbox
+      to"&decimal(abs((N[1]/somme)[A,B]-A))&"pt{}}$"),iso(A,(N[1]/somme)[A,B]));
+    label.bot(TEX("\footnotesize$\underbrace{\hbox
+      to"&decimal(abs((N[1]/somme)[A,B]-((N[1]+N[2])/somme)[A,B]))&"pt{}}$"),iso(((N[1]+N[2])/somme)[A,B],(N[1]/somme)[A,B]));
+    if n>2:
+    label.bot(TEX("\footnotesize$\underbrace{\hbox
+      to"&decimal(abs(((N[1]+N[2])/somme)[A,B]-B))&"pt{}}$"),iso(B,((N[1]+N[2])/somme)[A,B]));
+    fi;
+    enddef;
+    RatioTrois(#2)(#6);
+    %etiquettage
+    labeloffset:=labeloffset*3;
+    label.top(btex \useKV[ClesRatio]{TexteTotal} etex,iso(D,C));
+    if #3>1:
+    label.bot(btex #3~\useKV[ClesRatio]{TextePart}s
+    etex,iso(A,(N[1]/somme)[A,B]));
+    else:
+    label.bot(btex #3~\useKV[ClesRatio]{TextePart} etex,iso(A,(N[1]/somme)[A,B]));
+    fi;
+    if #4>1:
+    label.bot(btex #4~\useKV[ClesRatio]{TextePart}s etex,iso(((N[1]+N[2])/somme)[A,B],(N[1]/somme)[A,B]));
+    else:
+    label.bot(btex #4~\useKV[ClesRatio]{TextePart}
+    etex,iso(((N[1]+N[2])/somme)[A,B],(N[1]/somme)[A,B]));
+    fi;
+    if n>2:
+    if #5>1:
+    label.bot(btex #5~\useKV[ClesRatio]{TextePart}s etex,iso(B,((N[1]+N[2])/somme)[A,B]));
+    else:
+    label.bot(btex #5~\useKV[ClesRatio]{TextePart} etex,iso(B,((N[1]+N[2])/somme)[A,B]));
+    fi;
+    fi;
+  \end{mplibcode}
+  \else
+  \usempxpackage{simplekv}
+  \mpxcommands{%
+    \setKVdefault[ClesRatio]{TexteTotal=quantité,TextePart=part}
+    \setKV[ClesRatio]{#1}
+  }
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    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);
+    B-A=(long,0);
+    C-B=u*(0,0.5);
+    D-C=A-B;
+    n:=0;%n pour savoir si le ratio est a:b ou a:b:c
+    numeric N[];%Pour sauvegarder les éléments du ratio
+    for p_=t:
+    n:=n+1;
+    N[n]=p_;
+    endfor;
+    % on fait la somme totale "du ratio"
+    somme=0;
+    somme:=somme for k=1 upto n:+N[k] endfor;
+    Figure(0,0,long+2u,3u);
+    remplis polygone(A,(N[1]/somme)[A,B],(N[1]/somme)[D,C],D)
+    withcolor #7;
+    remplis polygone(B,(N[1]/somme)[A,B],(N[1]/somme)[D,C],C)
+    withcolor #8;
+    if n>2:
+    remplis
+    polygone((N[1]/somme)[A,B],((N[1]+N[2])/somme)[A,B],((N[1]+N[2])/somme)[D,C],(N[1]/somme)[D,C])
+    withcolor #8;
+    remplis
+    polygone(B,((N[1]+N[2])/somme)[A,B],((N[1]+N[2])/somme)[D,C],C)
+    withcolor #9;
+    fi;
+    drawoptions(withpen pencircle scaled1.5bp);
+    draw polygone(A,B,C,D);
+    for k=1 upto somme-1:
+    draw segment((k/somme)[A,B],(k/somme)[D,C]);
+    endfor;
+    drawoptions();
+    %accolades
+    label.top(LATEX("\noexpand\footnotesize$\noexpand\overbrace{\noexpand\hbox
+      to"&decimal(abs(A-B))&"pt{}}$"),iso(D,C));
+    label.bot(LATEX("\noexpand\footnotesize$\noexpand\underbrace{\noexpand\hbox
+      to"&decimal(abs((N[1]/somme)[A,B]-A))&"pt{}}$"),iso(A,(N[1]/somme)[A,B]));
+    label.bot(LATEX("\noexpand\footnotesize$\noexpand\underbrace{\noexpand\hbox
+      to"&decimal(abs((N[1]/somme)[A,B]-((N[1]+N[2])/somme)[A,B]))&"pt{}}$"),iso(((N[1]+N[2])/somme)[A,B],(N[1]/somme)[A,B]));
+    if n>2:
+    label.bot(LATEX("\noexpand\footnotesize$\noexpand\underbrace{\noexpand\hbox
+      to"&decimal(abs(((N[1]+N[2])/somme)[A,B]-B))&"pt{}}$"),iso(B,((N[1]+N[2])/somme)[A,B]));
+    fi;
+    enddef;
+    RatioTrois(#2)(#6);
+    %etiquettage
+    labeloffset:=labeloffset*3;
+    label.top(\btex \useKV[ClesRatio]{TexteTotal} etex,iso(D,C));
+    if #3>1:
+    label.bot(btex #3\unexpanded{~\useKV[ClesRatio]{TextePart}}s
+    etex,iso(A,(N[1]/somme)[A,B]));
+    else:
+    label.bot(btex #3\unexpanded{~\useKV[ClesRatio]{TextePart}} etex,iso(A,(N[1]/somme)[A,B]));
+    fi;
+    if #4>1:
+    label.bot(btex #4\unexpanded{~\useKV[ClesRatio]{TextePart}}s etex,iso(((N[1]+N[2])/somme)[A,B],(N[1]/somme)[A,B]));
+    else:
+    label.bot(btex #4\unexpanded{~\useKV[ClesRatio]{TextePart}}
+    etex,iso(((N[1]+N[2])/somme)[A,B],(N[1]/somme)[A,B]));
+    fi;
+    if n>2:
+    if #5>1:
+    label.bot(btex #5\unexpanded{~\useKV[ClesRatio]{TextePart}}s etex,iso(B,((N[1]+N[2])/somme)[A,B]));
+    else:
+    label.bot(btex #5\unexpanded{~\useKV[ClesRatio]{TextePart}} etex,iso(B,((N[1]+N[2])/somme)[A,B]));
+    fi;
+    fi;
+  \end{mpost}
+  \fi
+}
+
+\newtoks\toklisteratio
+\def\UpdateRatio#1\nil{\addtotok\toklisteratio{#1,}}
+
+\def\updateratiotoks#1/#2/#3\nil{\addtotok\tabtoksa{&\num{#2}}\addtotok\tabtoksb{&\num{#3}}\addtotok\tabtoksc{&#1}}
+
+
+\def\buildtabratio{%
+  \tabtoksa{}\tabtoksb{}\tabtoksc{}%
+  \tabtoksa{\useKV[ClesRatio]{GrandeurA}}\tabtoksb{\useKV[ClesRatio]{GrandeurB}}
+  \foreachitem\compteur\in\ListeRatio{\expandafter\updateratiotoks\compteur\nil}%
+  \xdef\LongListe{\ListeRatiolen}%
+  \renewcommand{\arraystretch}{\useKV[ClesRatio]{Stretch}}%
+  \begin{tabular}{|>{\columncolor{gray!15}}c|*{\number\numexpr\ListeRatiolen}{>{\centering\arraybackslash}p{\useKV[ClesRatio]{Largeur}}|}l}
+    \ifboolKV[ClesRatio]{Nom}{%
+    \hhline{~*{\number\numexpr\ListeRatiolen}{-}}
+    \multicolumn{1}{c|}{}\the\tabtoksc\\
+    }{}
+    \hhline{*{\number\numexpr\ListeRatiolen+1}{-}}%
+    \the\tabtoksa&\setcounter{NbPropor}{1}\TikzRH\\%
+    \hhline{*{\number\numexpr\ListeRatiolen+1}{-}}%
+    \the\tabtoksb&\setcounter{NbPropor}{1}\TikzRB\\%
+    \hhline{*{\number\numexpr\ListeRatiolen+1}{-}}%
+  \end{tabular}%
+}%
+
+\newcommand{\TikzRH}{%
+   \tikz[remember picture,overlay]{%
+   \coordinate[name=ProporH-\theNbPropor,yshift=\the\ht\strutbox*\arraystretch];}%
+   \stepcounter{NbPropor}%
+ }%
+
+ \newcommand{\TikzRB}{%
+   \tikz[remember picture, overlay]{%
+     \coordinate[name=ProporB-\theNbPropor,yshift=-\the\dp\strutbox*\arraystretch];}%
+   \stepcounter{NbPropor}%
+ }%
+ 
+\newcommand\FlecheRatio[2][\EcartLargeur]{%
+  \begin{tikzpicture}[remember picture, overlay]%
+    \node[] (Point1) at ($(ProporH-1)!0.1!(ProporB-1)$) {};%
+    \node[] (Point2) at ($(ProporH-1)!0.9!(ProporB-1)$) {};%
+    \coordinate[right of=Point1,node distance=0*#1-\tabcolsep] (point1);%
+    \coordinate[right of=Point2,node distance=0*#1-\tabcolsep] (point2);%
+    \draw[-stealth,out=-20,in=20] (point1) to node[midway,right,inner sep=1pt]{#2}(point2);%
+\end{tikzpicture}%
+}%
+
+\newcommand\FlecheInvRatio[2][\EcartLargeur]{%
+  \begin{tikzpicture}[remember picture, overlay]%
+    \node[] (Point1) at ($(ProporH-1)!0.1!(ProporB-1)$) {};%
+    \node[] (Point2) at ($(ProporH-1)!0.9!(ProporB-1)$) {};%
+    \coordinate[right of=Point1,node distance=0*#1-\tabcolsep] (point1);%
+    \coordinate[right of=Point2,node distance=0*#1-\tabcolsep] (point2);%
+    \draw[-stealth,out=20,in=-20] (point2) to node[midway,right,inner sep=1pt]{#2}(point1);%
+\end{tikzpicture}%
+}%
+
+\newcommand\Ratio[2][]{%
+  \useKVdefault[ClesRatio]%
+  \setKV[ClesRatio]{#1}%
+  \xdef\EcartLargeur{\useKV[ClesRatio]{Largeur}}%
+  \ifboolKV[ClesRatio]{Figure}{%
+    \ignoreemptyitems%
+    \readlist*\ListeRatio{#2}%
+    \toklisteratio{}%
+    \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{}}
+    \MPTest[#1]{\useKV[ClesRatio]{Longueur}}{\NbUn}{\NbDeux}{\NbTrois}{\the\toklisteratio}{\useKV[ClesRatio]{CouleurUn}}{\useKV[ClesRatio]{CouleurDeux}}{\useKV[ClesRatio]{CouleurTrois}}%
+  }{}%
+  \ifboolKV[ClesRatio]{Tableau}{%
+    \setsepchar[*]{,*/}\ignoreemptyitems%
+    \readlist*\ListeRatio{#2}%
+    \buildtabratio%
+  }{}%
+}%
+
+%%%%%%%%%%%%%%%
+%% 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}}%
+
+\newlength{\RoundedBoxWidth}%
+
+\NewEnviron{Bulle}[1][]{%
+  \setKV[ClesMentales]{#1}%
+  \setlength{\RoundedBoxWidth}{\useKV[ClesMentales]{Largeur}}%
+  \xdef\Pointilles{\ifboolKV[ClesMentales]{Pointilles}{dashed}{}}%
+  \xdef\CouleurTrace{\useKV[ClesMentales]{CTrace}}%
+  \xdef\CouleurFond{\useKV[ClesMentales]{CFond}}%
+  \xdef\EpaisseurLigne{\useKV[ClesMentales]{Epaisseur}}%
+  \xdef\RayonCoin{\useKV[ClesMentales]{Rayon}}%
+  \node(\useKV[ClesMentales]{Nom}) [align=justify,draw=\CouleurTrace,line width=\EpaisseurLigne,\Pointilles,fill=\CouleurFond,rounded corners=\RayonCoin,text width=\RoundedBoxWidth] at (\useKV[ClesMentales]{Ancre}) {\begin{minipage}{\RoundedBoxWidth}\BODY\end{minipage}};%
+  \multido{\i=1+1}{9}{%
+    \xdef\x{\fpeval{\i/10}}
+    \coordinate (\useKV[ClesMentales]{Nom}-H-\i) at ($(\useKV[ClesMentales]{Nom}.north west)!\x!(\useKV[ClesMentales]{Nom}.north east)$);
+    \coordinate (\useKV[ClesMentales]{Nom}-D-\i) at ($(\useKV[ClesMentales]{Nom}.north east)!\x!(\useKV[ClesMentales]{Nom}.south east)$);
+    \coordinate (\useKV[ClesMentales]{Nom}-B-\i) at ($(\useKV[ClesMentales]{Nom}.south east)!\x!(\useKV[ClesMentales]{Nom}.south west)$);
+    \coordinate (\useKV[ClesMentales]{Nom}-G-\i) at ($(\useKV[ClesMentales]{Nom}.south west)!\x!(\useKV[ClesMentales]{Nom}.north west)$);
+  }
+}
+
+%%%%%%%%%%%%
+% Pptés des droites (6eme)
+%%%%%%%%%%%
+\setKVdefault[ClesDroites]{Brouillon=false,CitePropriete=false,Num=1,Figure=false,Remediation=false}
+
+\newcommand\Redaction[4][]{%
+  \ifboolKV[ClesDroites]{Remediation}{%
+    \xintifboolexpr{\useKV[ClesDroites]{Num}=1}{%
+      \ifboolKV[ClesDroites]{CitePropriete}{%
+        Les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont parallèles. Les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont parallèles.%
+        
+        Or, si deux droites sont parallèles, alors toute droite parallèle à l'une est parallèle à l'autre.%
+        
+        Donc les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont parallèles.%
+      }{%
+        Comme les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont toutes les deux parallèles à la même droite $(\hbox to2em{\dotfill})$, alors les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont parallèles.%
+      }
+    }{\xintifboolexpr{\useKV[ClesDroites]{Num}=2}{%
+        \ifboolKV[ClesDroites]{CitePropriete}{%
+          Les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont perpendiculaires. Les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont perpendiculaires.%
+          
+          Or, si deux droites sont perpendiculaires à une même droite, alors elles sont parallèles.%
+          
+          Donc les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont perpendiculaires.
+        }{%
+          Comme les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont toutes les deux perpendiculaires à la même droite $(\hbox to2em{\dotfill})$, alors les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont parallèles.
+        }
+      }{%
+        \ifboolKV[ClesDroites]{CitePropriete}{%
+          Les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont parallèles. Les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont perpendiculaires.%
+          
+          Or, si deux droites sont parallèles, alors toute droite droite perpendiculaire à l'une est perpendiculaire à l'autre.%
+          
+          Donc les droites $(\hbox to2em{\dotfill})$ et $(\hbox to2em{\dotfill})$ sont perpendiculaires.
+        }{%
+          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}{%
+        Les droites $(#2)$ et $(#4)$ sont parallèles. Les droites $(#3)$ et $(#4)$ sont parallèles.%
+        
+        Or, si deux droites sont parallèles, alors toute droite parallèle à l'une est parallèle à l'autre.%
+        
+        Donc les droites $(#2)$ et $(#3)$ sont parallèles.
+      }{%
+        Comme les droites $(#2)$ et $(#3)$ sont toutes les deux parallèles à la même droite $(#4)$, alors les droites $(#2)$ et $(#3)$ sont parallèles.
+      }
+    }{\xintifboolexpr{\useKV[ClesDroites]{Num}=2}{%
+        \ifboolKV[ClesDroites]{CitePropriete}{%
+          Les droites $(#2)$ et $(#4)$ sont perpendiculaires. Les droites $(#3)$ et $(#4)$ sont perpendiculaires.%
+          
+          Or, si deux droites sont perpendiculaires à une même droite, alors elles sont parallèles.%
+          
+          Donc les droites $(#2)$ et $(#3)$ sont perpendiculaires.
+        }{%
+          Comme les droites $(#2)$ et $(#3)$ sont toutes les deux perpendiculaires à la même droite $(#4)$, alors les droites $(#2)$ et $(#3)$ sont parallèles.
+        }
+      }{%
+        \ifboolKV[ClesDroites]{CitePropriete}{%
+          Les droites $(#2)$ et $(#4)$ sont parallèles. Les droites $(#3)$ et $(#4)$ sont perpendiculaires.%
+          
+          Or, si deux droites sont parallèles, alors toute droite droite perpendiculaire à l'une est perpendiculaire à l'autre.%
+          
+          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}
+  \ifboolKV[ClesDroites]{Remediation}{%
+    \xintifboolexpr{\useKV[ClesDroites]{Num}=1}{%
+      \[\left.
+          \begin{array}{l}
+            (\hbox to2em{\dotfill})//(\hbox to2em{\dotfill})\\
+            \\
+            (\hbox to2em{\dotfill})//(\hbox to2em{\dotfill})
+          \end{array}
+        \right\}(\hbox to2em{\dotfill})//(\hbox to2em{\dotfill})
+      \]
+    }{\xintifboolexpr{\useKV[ClesDroites]{Num}=2}{%
+        \[\left.
+            \begin{array}{l}
+              (\hbox to2em{\dotfill})\perp(\hbox to2em{\dotfill})\\
+              \\
+              (\hbox to2em{\dotfill})\perp(\hbox to2em{\dotfill})\\
+            \end{array}
+          \right\}(\hbox to2em{\dotfill})//(\hbox to2em{\dotfill})
+        \]
+      }{%
+        \[\left.
+            \begin{array}{l}
+              (\hbox to2em{\dotfill})//(\hbox to2em{\dotfill})\\
+              \\
+              (\hbox to2em{\dotfill})\perp(\hbox to2em{\dotfill})\\
+            \end{array}
+          \right\}(\hbox to2em{\dotfill})\perp(\hbox to2em{\dotfill})
+        \]
+      }
+    }
+  }{
+    \xintifboolexpr{\useKV[ClesDroites]{Num}=1}{%
+      \[\left.
+          \begin{array}{l}
+            (#2)//(#4)\\
+            \\
+            (#3)//(#4)
+          \end{array}
+        \right\}(#2)//(#3)
+      \]
+    }{\xintifboolexpr{\useKV[ClesDroites]{Num}=2}{%
+        \[\left.
+            \begin{array}{l}
+              (#2)\perp(#4)\\
+              \\
+              (#3)\perp(#4)\\
+            \end{array}
+          \right\}(#2)//(#3)
+        \]
+      }{%
+        \[\left.
+            \begin{array}{l}
+              (#2)//(#4)\\
+              \\
+              (#3)\perp(#4)\\
+            \end{array}
+          \right\}(#2)\perp(#3)
+        \]
+      }
+    }
+  }
+}
+
+\def\MPFigureDroite#1#2{%
+  \ifluatex
+    \mplibcodeinherit{enable}
+   \mplibforcehmode
+  \begin{mplibcode}
+    pair A,B,C,D,E,F,G,H,I,J,K;
+    u:=7.5mm;
+    A=u*(1,3);
+    B-A=u*(3,2);
+    C-A=u*(2,-1);
+    E-C=u*(1,-1.5);
+    G-E=u*(1.5,0);
+    I-A=whatever*(B-A);
+    I-G=whatever*((B-A) rotated 90);
+    D-B=C-A;
+    F-D=E-C;
+    H=1.1[G,I];
+    J=(C--D) intersectionpoint (G--H);
+    K=(E--F) intersectionpoint (G--H);
+    path Codeperp[];
+    pair M[];
+    M1-I=7*unitvector(B-I);
+    M3-I=7*unitvector(J-I);
+    M2-M3=M1-I;
+    Codeperp1=M1--M2--M3;
+    Codeperp2=Codeperp1 shifted(J-I);
+    picture Codepara[];
+    pair R,S,T;
+    path cd;
+    Codepara1=image(
+    R=1/3[A,B];
+    T=1/3[E,F];
+    S=1/3[R,T];
+    cd=(fullcircle scaled 6mm) shifted S;
+    drawoptions(withcolor 0.75*white);
+    drawarrow reverse((R{dir(210+angle(R-T))}..{dir(150+angle(R-T))}S) cutafter cd);
+    drawarrow reverse((T{dir(210+angle(T-R))}..{dir(150+angle(T-R))}S) cutafter cd);
+    draw cd;
+    label(btex $//$ etex ,S);
+    drawoptions();
+    );
+    Codepara2=image(
+    R:=1/2[C,D];
+    T:=1/2[E,F];
+    S:=1/2[R,T];
+    cd:=(fullcircle scaled 6mm) shifted S;
+    drawoptions(withcolor 0.75*white);
+    drawarrow reverse((R{dir(210+angle(R-T))}..{dir(150+angle(R-T))}S) cutafter cd);
+    drawarrow reverse((T{dir(210+angle(T-R))}..{dir(150+angle(T-R))}S) cutafter cd);
+    draw cd;
+    label(btex $//$ etex ,S);
+    drawoptions();
+    );
+    path d[];
+    d1=A--B;
+    d2=C--D;
+    d3=E--F;
+    d4=G--H;
+    picture reste;
+    reste=image(
+    %tracés des droites
+    draw d1;
+    if #1=2:
+    draw d2;
+    elseif #1=3:
+    draw d3;
+    fi;
+    if #2=3:
+    draw d3;
+    elseif #2=4:
+    draw d4;
+    fi;
+    % tracés des codes
+    if (#1=2) and (#2=3):
+    draw Codepara1; draw Codepara2;
+    fi;
+    if (#1=2) and (#2=4):
+    draw Codeperp1; draw Codeperp2;
+    fi;
+    if (#1=3) and (#2=4):
+    draw Codepara1; draw Codeperp1;
+    fi;
+    );
+    reste:=reste rotatedabout(u*(3,3),-90+uniformdeviate(180));
+    draw reste;
+  \end{mplibcode}
+  \mplibcodeinherit{disable}
+  \else
+  \begin{mpost}
+    pair A,B,C,D,E,F,G,H,I,J,K;
+    u:=7.5mm;
+    A=u*(1,3);
+    B-A=u*(3,2);
+    C-A=u*(2,-1);
+    E-C=u*(1,-1.5);
+    G-E=u*(1.5,0);
+    I-A=whatever*(B-A);
+    I-G=whatever*((B-A) rotated 90);
+    D-B=C-A;
+    F-D=E-C;
+    H=1.1[G,I];
+    J=(C--D) intersectionpoint (G--H);
+    K=(E--F) intersectionpoint (G--H);
+    path Codeperp[];
+    pair M[];
+    M1-I=7*unitvector(B-I);
+    M3-I=7*unitvector(J-I);
+    M2-M3=M1-I;
+    Codeperp1=M1--M2--M3;
+    Codeperp2=Codeperp1 shifted(J-I);
+    picture Codepara[];
+    pair R,S,T;
+    path cd;
+    Codepara1=image(
+    R=1/3[A,B];
+    T=1/3[E,F];
+    S=1/3[R,T];
+    cd=(fullcircle scaled 6mm) shifted S;
+    drawoptions(withcolor 0.75*white);
+    drawarrow reverse((R{dir(210+angle(R-T))}..{dir(150+angle(R-T))}S) cutafter cd);
+    drawarrow reverse((T{dir(210+angle(T-R))}..{dir(150+angle(T-R))}S) cutafter cd);
+    draw cd;
+    label(btex $//$ etex ,S);
+    drawoptions();
+    );
+    Codepara2=image(
+    R:=1/2[C,D];
+    T:=1/2[E,F];
+    S:=1/2[R,T];
+    cd:=(fullcircle scaled 6mm) shifted S;
+    drawoptions(withcolor 0.75*white);
+    drawarrow reverse((R{dir(210+angle(R-T))}..{dir(150+angle(R-T))}S) cutafter cd);
+    drawarrow reverse((T{dir(210+angle(T-R))}..{dir(150+angle(T-R))}S) cutafter cd);
+    draw cd;
+    label(btex $//$ etex ,S);
+    drawoptions();
+    );
+    path d[];
+    d1=A--B;
+    d2=C--D;
+    d3=E--F;
+    d4=G--H;
+    picture reste;
+    reste=image(
+    %tracés des droites
+    draw d1;
+    if #1=2:
+    draw d2;
+    elseif #1=3:
+    draw d3;
+    fi;
+    if #2=3:
+    draw d3;
+    elseif #2=4:
+    draw d4;
+    fi;
+    % tracés des codes
+    if (#1=2) and (#2=3):
+    draw Codepara1; draw Codepara2;
+    fi;
+    if (#1=2) and (#2=4):
+    draw Codeperp1; draw Codeperp2;
+    fi;
+    if (#1=3) and (#2=4):
+    draw Codepara1; draw Codeperp1;
+    fi;
+    );
+    reste:=reste rotatedabout(u*(3,3),-90+uniformdeviate(180));
+    draw reste;
+  \end{mpost}
+  \fi
+}
+
+\newcommand\FaireFigure[4][]{%
+  \setlength{\abovedisplayskip}{0pt}
+  \xintifboolexpr{\useKV[ClesDroites]{Num}=1}{%
+    \MPFigureDroite{2}{3}%
+  }{\xintifboolexpr{\useKV[ClesDroites]{Num}=2}{%
+      \MPFigureDroite{2}{4}%
+    }{%
+      \MPFigureDroite{3}{4}%
+    }%
+  }%
+}%
+
+\newcommand\ProprieteDroites[4][]{%
+  \useKVdefault[ClesDroites]%
+  \setKV[ClesDroites]{#1}%
+  \ifboolKV[ClesDroites]{Figure}{%
+    \begin{multicols}{2}%
+      \begin{center}%
+        \FaireFigure[#1]{#2}{#3}{#4}%
+      \end{center}%
+      \columnbreak
+      \ifboolKV[ClesDroites]{Brouillon}{\Brouillon[#1]{#2}{#3}{#4}}{}%
+      \Redaction[#1]{#2}{#3}{#4}%
+      \par%
+    \end{multicols}
+  }{%
+      \ifboolKV[ClesDroites]{Brouillon}{\Brouillon[#1]{#2}{#3}{#4}}{}%
+      \Redaction[#1]{#2}{#3}{#4}%
+  }%
+}%
+
+%%%%%%%%%%%%%%%%%%%%
+%%% 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
+  % #2 a ou ordonnée premier point
+  % #3 b ou abscisse deuxième point
+  % #4 {} ou ordonnée deuxième point
+  \useKVdefault[ClesAffine]%A supprimer car appel récursif avec Redaction
+  \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}}}}%
+    }{%
+      \ifboolKV[ClesAffine]{ProgCalcul}{%
+        \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}}}}\\
+          \useKV[ClesAffine]{Nom}&:\num{#2}\stackrel{\times\xintifboolexpr{#3<0}{(\num{#3})}{\num{#3}}}{\longrightarrow}\num{\fpeval{#3*#2}}\xintifboolexpr{#4=0}{}{\xintifboolexpr{#4>0}{\stackrel{+\num{#4}}{\longrightarrow}}{\stackrel{\num{#4}}{\longrightarrow}}\num{\fpeval{#3*#2+#4}}}
+        \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}}}%\\
+          \xintifboolexpr{#4=0}{}{\\
+          \useKV[ClesAffine]{Nom}(\num{#2})&=\num{\fpeval{#3*#2+#4}}%\\
+          }
+        \end{align*}
+      }%
+    }%
+  }{\ifboolKV[ClesAffine]{Antecedent}{%
+      \ifboolKV[ClesAffine]{ProgCalcul}{%
+        La fonction affine $\useKV[ClesAffine]{Nom}$ 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*}
+        Nous cherchons le nombre $\useKV[ClesAffine]{Variable}$ tel que son image par la fonction $\useKV[ClesAffine]{Nom}$ soit $\num{#2}$. Donc on obtient :
+        \begin{align*}
+          \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*}
+        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}}
+            }
+        \end{align*}
+      }%
+    }{%
+      \ifboolKV[ClesAffine]{Retrouve}{%
+        On sait que $\useKV[ClesAffine]{Nom}$ est une fonction affine. Donc elle s'écrit sous la forme : \[\useKV[ClesAffine]{Nom}(\useKV[ClesAffine]{Variable})=a\useKV[ClesAffine]{Variable}+b\]
+        Or, $\useKV[ClesAffine]{Nom}(\num{#2})=\num{#3}$ et $\useKV[ClesAffine]{Nom}(\num{#4})=\num{#5}$. Par conséquent, d'après la propriété des accroissements :
+        \begin{align*}
+          a&=\frac{\useKV[ClesAffine]{Nom}(\num{#2})-\useKV[ClesAffine]{Nom}(\num{#4})}{\num{#2}-\xintifboolexpr{#4<0}{(\num{#4})}{\num{#4}}}\\
+          a&=\frac{\num{#3}-\xintifboolexpr{#5<0}{(\num{#5})}{\num{#5}}}{\num{\fpeval{#2-#4}}}\\
+          a&=\frac{\num{\fpeval{#3-#5}}}{\num{\fpeval{#2-#4}}}%\\
+          \SSimpliTest{\fpeval{#3-#5}}{\fpeval{#2-#4}}\ifthenelse{\boolean{Simplification}}{\\a&=\SSimplifie{\fpeval{#3-#5}}{\fpeval{#2-#4}}}{}%
+        \end{align*}
+        La fonction $\useKV[ClesAffine]{Nom}$ s'écrit alors sous la forme $\displaystyle\useKV[ClesAffine]{Nom}(\useKV[ClesAffine]{Variable})=\SSimplifie{\fpeval{#3-#5}}{\fpeval{#2-#4}}\useKV[ClesAffine]{Variable}+b$.
+        \\De plus, comme $\useKV[ClesAffine]{Nom}(\num{#2})=\num{#3}$, alors :
+        \begin{align*}
+          \SSimplifie{\fpeval{#3-#5}}{\fpeval{#2-#4}}\times\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}+b&=\num{#3}\\
+          \SSimplifie{\fpeval{(#3-#5)*#2}}{\fpeval{#2-#4}}+b&=\num{#3}\\
+          b&=\num{\fpeval{#3-(#3-#5)*#2/(#2-#4)}}
+        \end{align*}
+        \xdef\OrdOrigine{\fpeval{#3-(#3-#5)*#2/(#2-#4)}}
+        La fonction affine $\useKV[ClesAffine]{Nom}$ cherchée est :
+        \[\useKV[ClesAffine]{Nom}:\useKV[ClesAffine]{Variable}\mapsto\SSimplifie{\fpeval{#3-#5}}{\fpeval{#2-#4}}\useKV[ClesAffine]{Variable}\xintifboolexpr{\OrdOrigine=0}{}{\xintifboolexpr{\OrdOrigine>0}{+\num{\OrdOrigine}}{-\num{\fpeval{0-\OrdOrigine}}}}\]
+      }{%
+        %
+      }%
+    }%
+  }%
+  \ifboolKV[ClesAffine]{Graphique}{%
+    \ifboolKV[ClesAffine]{VoirCoef}{%
+      \MPFonctionAffine{\useKV[ClesAffine]{Unitex}}{\useKV[ClesAffine]{Unitey}}{#2}{#3}{#4}{#5}{\useKV[ClesAffine]{ACoef}}%
+    }{%
+      \MPFonctionAffine{\useKV[ClesAffine]{Unitex}}{\useKV[ClesAffine]{Unitey}}{#2}{#3}{#4}{#5}{""}}{}%
+  }{}%
+  \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 $(\num{#4};\num{\fpeval{#2*#4+#3}})$.
+      }{%
+        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 $(\num{#5};\num{\fpeval{#2*#5+#3}})$.%        
+      }%
+    }%
+  }%
+  {}%
+  \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}}}}}}{}%
+}%
+
+\def\MPFonctionAffine#1#2#3#4#5#6#7{%
+  % #1 Unitex #2 Unitey
+    % #2 a pour f1 - #4 b pour f1
+    % #5 abscisse du premier point
+    % #6 abscisse du deuxième point
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    XMin=-2;
+    XMax=2;
+    if #5<XMin:
+    XMin:=#5;
+    fi;
+    if #6<XMin:
+    XMin:=#6;
+    fi;
+    if #5>XMax:
+    XMax:=#5;
+    fi;
+    if #6>XMax:
+    XMax:=#6;
+    fi;
+    YMax=2;
+    YMin=-2;
+    if (#5*#3+(#4))>YMax:
+    YMax:=(#5*#3+(#4));
+    fi;
+    if (#6*#3+(#4))>YMax:
+    YMax:=(#6*#3+(#4));
+    fi;
+    if (#5*#3+(#4))<YMin:
+    YMin:=(#5*#3+(#4));
+    fi;
+    if (#6*#3+(#4))<YMin:
+    YMin:=(#6*#3+(#4));
+    fi;
+    unitex:=#1*cm;
+    unitey:=#2*cm;
+    XMax:=XMax+2;
+    XMin:=XMin-2;
+    YMax:=YMax+2;
+    YMin:=YMin-2;
+    %On trace la grille
+    drawoptions(withcolor 0.95white);
+    for k=0 upto (XMax-XMin):
+    draw ((XMin+k)*unitex,YMin*unitey)--((XMin+k)*unitex,YMax*unitey);
+    endfor;
+    for k=0 upto (YMax-YMin):
+    draw (XMin*unitex,(YMin+k)*unitey)--(XMax*unitex,(YMin+k)*unitey);
+    endfor;
+    drawoptions();
+    %On trace les axes
+    drawarrow (XMin*unitex,0)--(XMax*unitex,0);
+    drawarrow (0,YMin*unitey)--(0,YMax*unitey);
+    label.llft(btex O etex,(0,0));
+    dotlabel.bot(btex 1 etex,(unitex,0));
+    dotlabel.lft(btex 1 etex,(0,unitey));
+    % On trace la droite
+    pair A[];
+    A1=(#5*unitex,(#5*#3+(#4))*unitey);
+    A2=(#6*unitex,(#6*#3+(#4))*unitey);
+    draw 2[A1,A2]--2[A2,A1];
+    clip currentpicture to ((XMin*unitex,YMin*unitey)--(XMax*unitex,YMin*unitey)--(XMax*unitex,YMax*unitey)--(XMin*unitex,YMax*unitey)--cycle);
+    %On labellise les points
+    fill (fullcircle scaled 1mm) shifted A1;
+    fill (fullcircle scaled 1mm) shifted A2;
+    draw (xpart(A1),0)--A1--(0,ypart(A1)) dashed evenly;
+    draw (xpart(A2),0)--A2--(0,ypart(A2)) dashed evenly;
+    if (#5*#3+(#4))=0:
+    else:
+    if (#5*#3+(#4))<0:
+    label.top(TEX("\num{"&decimal(#5)&"}"),(xpart(A1),0));
+    else:
+    label.bot(TEX("\num{"&decimal(#5)&"}"),(xpart(A1),0));
+    fi;
+    fi;
+    if (#6*#3+(#4))=0:
+    else:
+    if (#6*#3+(#4))<0:
+    label.top(TEX("\num{"&decimal(#6)&"}"),(xpart(A2),0));
+    else:
+    label.bot(TEX("\num{"&decimal(#6)&"}"),(xpart(A2),0));
+    fi;
+    fi;
+    if #3=0:
+    label.urt(TEX("\num{"&decimal(#5*#3+(#4))&"}"),(0,ypart(A1)));
+    else:
+    if #3>0:
+    if (#5*#3+(#4))=0:
+    else:
+    if (#5*#3+(#4))<0:
+    label.rt(TEX("\num{"&decimal(#5*#3+(#4))&"}"),(0,ypart(A1)));
+    else:
+    label.lft(TEX("\num{"&decimal(#5*#3+(#4))&"}"),(0,ypart(A1)));
+    fi;
+    fi;
+    if (#6*#3+(#4))=0:
+    else:
+    if (#6*#3+(#4))<0:
+    label.rt(TEX("\num{"&decimal(#6*#3+(#4))&"}"),(0,ypart(A2)));
+    else:
+    label.lft(TEX("\num{"&decimal(#6*#3+(#4))&"}"),(0,ypart(A2)));
+    fi;
+    fi;
+    else:
+    if (#5*#3+(#4))=0:
+    else:
+    if (#5*#3+(#4))<0:
+    label.lft(TEX("\num{"&decimal(#5*#3+(#4))&"}"),(0,ypart(A1)));
+    else:
+    label.rt(TEX("\num{"&decimal(#5*#3+(#4))&"}"),(0,ypart(A1)));
+    fi;
+    fi;
+    if (#6*#3+(#4))=0:
+    else:
+    if (#6*#3+(#4))<0:
+    label.lft(TEX("\num{"&decimal(#6*#3+(#4))&"}"),(0,ypart(A2)));
+    else:
+    label.rt(TEX("\num{"&decimal(#6*#3+(#4))&"}"),(0,ypart(A2)));
+    fi;
+    fi;
+    fi;
+    fi;
+    % On affiche ou pas "la marche" du coef directeur
+    for p_=#7:
+    if numeric p_:
+    draw ((#7*unitex,(#7*#3+(#4))*unitey)--((#7+1)*unitex,(#7*#3+(#4))*unitey)--((#7+1)*unitex,((#7+1)*#3+(#4))*unitey)) withcolor red;
+    fi;
+    endfor;
+  \end{mplibcode}
+  \else
+  \begin{mpost}
+    % On définit les constantes
+    XMin=-2;
+    XMax=2;
+    if #5<XMin:
+    XMin:=#5;
+    fi;
+    if #6<XMin:
+    XMin:=#6;
+    fi;
+    if #5>XMax:
+    XMax:=#5;
+    fi;
+    if #6>XMax:
+    XMax:=#6;
+    fi;
+    YMax=2;
+    YMin=-2;
+    if (#5*#3+(#4))>YMax:
+    YMax:=(#5*#3+(#4));
+    fi;
+    if (#6*#3+(#4))>YMax:
+    YMax:=(#6*#3+(#4));
+    fi;
+    if (#5*#3+(#4))<YMin:
+    YMin:=(#5*#3+(#4));
+    fi;
+    if (#6*#3+(#4))<YMin:
+    YMin:=(#6*#3+(#4));
+    fi;
+    unitex:=#1*cm;
+    unitey:=#2*cm;
+    XMax:=XMax+2;
+    XMin:=XMin-2;
+    YMax:=YMax+2;
+    YMin:=YMin-2;
+    %On trace la grille
+    drawoptions(withcolor 0.95white);
+    for k=0 upto (XMax-XMin):
+    draw ((XMin+k)*unitex,YMin*unitey)--((XMin+k)*unitex,YMax*unitey);
+    endfor;
+    for k=0 upto (YMax-YMin):
+    draw (XMin*unitex,(YMin+k)*unitey)--(XMax*unitex,(YMin+k)*unitey);
+    endfor;
+    drawoptions();
+    %On trace les axes
+    drawarrow (XMin*unitex,0)--(XMax*unitex,0);
+    drawarrow (0,YMin*unitey)--(0,YMax*unitey);
+    label.llft(btex O etex,(0,0));
+    dotlabel.bot(btex 1 etex,(unitex,0));
+    dotlabel.lft(btex 1 etex,(0,unitey));
+    % On trace la droite
+    pair A[];
+    A1=(#5*unitex,(#5*#3+(#4))*unitey);
+    A2=(#6*unitex,(#6*#3+(#4))*unitey);
+    draw 2[A1,A2]--2[A2,A1];
+    clip currentpicture to ((XMin*unitex,YMin*unitey)--(XMax*unitex,YMin*unitey)--(XMax*unitex,YMax*unitey)--(XMin*unitex,YMax*unitey)--cycle);
+    %On labellise les points
+    fill (fullcircle scaled 1mm) shifted A1;
+    fill (fullcircle scaled 1mm) shifted A2;
+    draw (xpart(A1),0)--A1--(0,ypart(A1)) dashed evenly;
+    draw (xpart(A2),0)--A2--(0,ypart(A2)) dashed evenly;
+    if (#5*#3+(#4))=0:
+    else:
+    if (#5*#3+(#4))<0:
+    label.top(LATEX("\num{"&decimal(#5)&"}"),(xpart(A1),0));
+    else:
+    label.bot(LATEX("\num{"&decimal(#5)&"}"),(xpart(A1),0));
+    fi;
+    fi;
+    if (#6*#3+(#4))=0:
+    else:
+    if (#6*#3+(#4))<0:
+    label.top(LATEX("\num{"&decimal(#6)&"}"),(xpart(A2),0));
+    else:
+    label.bot(LATEX("\num{"&decimal(#6)&"}"),(xpart(A2),0));
+    fi;
+    fi;
+    if #3=0:
+    label.urt(LATEX("\num{"&decimal(#5*#3+(#4))&"}"),(0,ypart(A1)));
+    else:
+    if #3>0:
+    if (#5*#3+(#4))=0:
+    else:
+    if (#5*#3+(#4))<0:
+    label.rt(LATEX("\num{"&decimal(#5*#3+(#4))&"}"),(0,ypart(A1)));
+    else:
+    label.lft(LATEX("\num{"&decimal(#5*#3+(#4))&"}"),(0,ypart(A1)));
+    fi;
+    fi;
+    if (#6*#3+(#4))=0:
+    else:
+    if (#6*#3+(#4))<0:
+    label.rt(LATEX("\num{"&decimal(#6*#3+(#4))&"}"),(0,ypart(A2)));
+    else:
+    label.lft(LATEX("\num{"&decimal(#6*#3+(#4))&"}"),(0,ypart(A2)));
+    fi;
+    fi;
+    else:
+    if (#5*#3+(#4))=0:
+    else:
+    if (#5*#3+(#4))<0:
+    label.lft(LATEX("\num{"&decimal(#5*#3+(#4))&"}"),(0,ypart(A1)));
+    else:
+    label.rt(LATEX("\num{"&decimal(#5*#3+(#4))&"}"),(0,ypart(A1)));
+    fi;
+    fi;
+    if (#6*#3+(#4))=0:
+    else:
+    if (#6*#3+(#4))<0:
+    label.lft(LATEX("\num{"&decimal(#6*#3+(#4))&"}"),(0,ypart(A2)));
+    else:
+    label.rt(LATEX("\num{"&decimal(#6*#3+(#4))&"}"),(0,ypart(A2)));
+    fi;
+    fi;
+    fi;
+    fi;
+    % On affiche ou pas "la marche" du coef directeur
+    for p_=#7:
+    if numeric p_:
+    draw ((#7*unitex,(#7*#3+(#4))*unitey)--((#7+1)*unitex,(#7*#3+(#4))*unitey)--((#7+1)*unitex,((#7+1)*#3+(#4))*unitey)) withcolor red;
+    fi;
+    endfor;
+  \end{mpost}
+  \fi
+}
+
+
+%%%%%%%%%%%%%%%
+% 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%
+    }{}
+}
+
+\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 droit,Figure=false,Angle=0,Ancre={(0,0)},Largeur=5cm}
+
+\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);
+    draw codeperp(A,B,C,5);
+    draw codeperp(B,C,D,5);
+    draw codeperp(C,D,A,5);
+    draw codeperp(D,A,B,5);
+    marque_s:=marque_s/3;
+    draw Codelongueur(A,B,B,C,C,D,D,A,2);
+    marque_s:=marque_s*3;
+    draw appelation(A,B,-3mm,btex $c$ etex);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    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);
+    draw codeperp(A,B,C,5);
+    draw codeperp(B,C,D,5);
+    draw codeperp(C,D,A,5);
+    draw codeperp(D,A,B,5);
+    marque_s:=marque_s/3;
+    draw Codelongueur(A,B,B,C,C,D,D,A,2);
+    marque_s:=marque_s*3;
+    draw appelation(A,B,-3mm,btex $c$ etex);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigurePolygone{%
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    pair A,B,C,D,E,F;
+    A=u*(1,1);
+    B-A=u*(2,0);
+    C=3/5[B,rotation(A,B,-120)];
+    D-C=u*(0,1);
+    E-D=u*(-1.25,-1);
+    F-E=u*(-1,1);
+    draw polygone(A,B,C,D,E,F);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    pair A,B,C,D,E,F;
+    A=u*(1,1);
+    B-A=u*(2,0);
+    C=3/5[B,rotation(A,B,-120)];
+    D-C=u*(0,1);
+    E-D=u*(-1.25,-1);
+    F-E=u*(-1,1);
+    draw polygone(A,B,C,D,E,F);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureParallelogramme{%
+  \ifluatex
+   \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C,D;
+    A=u*(1,1);
+    B-A=u*(2.25,0.25);
+    D=4/5[A,rotation(B,A,40)];
+    C-D=B-A;
+    draw polygone(A,B,C,D);
+    drawoptions(withcolor gris);
+    draw marque_para(droite(A,B),droite(C,D),0.455);
+    draw marque_para(droite(B,C),droite(A,D),0.43);
+    draw segment(B,2.5[C,B]) dashed evenly;
+    draw segment(A,1.5[D,A]) dashed evenly;
+    draw segment(A,1.55[B,A]) dashed evenly;
+    draw segment(D,2[C,D]) dashed evenly;
+    drawoptions();
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C,D;
+    A=u*(1,1);
+    B-A=u*(2.25,0.25);
+    D=4/5[A,rotation(B,A,40)];
+    C-D=B-A;
+    draw polygone(A,B,C,D);
+    drawoptions(withcolor gris);
+    draw marque_para(droite(A,B),droite(C,D),0.455);
+    draw marque_para(droite(B,C),droite(A,D),0.43);
+    draw segment(B,2.5[C,B]) dashed evenly;
+    draw segment(A,1.5[D,A]) dashed evenly;
+    draw segment(A,1.55[B,A]) dashed evenly;
+    draw segment(D,2[C,D]) dashed evenly;
+    drawoptions();
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureParallelogrammeAire{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    Figure(-5u,-5u,10u,5u);
+    pair A,B,C,D,I,J;
+    A=u*(1,1);
+    B-A=u*(2,0.5);
+    D=3/5[A,rotation(B,A,40)];
+    C-D=B-A;
+    I=projection(D,A,B);
+    draw polygone(A,B,C,D) withcolor gris;
+    draw segment(A,B);
+    draw segment(D,I);
+    draw codeperp(D,I,B,5);
+    A:=A+3*u*(1,0);
+    B:=A+u*(2,0.5);
+    D:=3/5[A,rotation(B,A,40)];
+    C:=D+B-A;
+    J=projection(B,A,D);
+    draw polygone(A,B,C,D) withcolor gris;
+    draw segment(D,1.5[A,D]) dashed evenly withcolor gris;
+    draw segment(A,D);
+    draw segment(B,J);
+    draw codeperp(B,J,A,5);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    Figure(-5u,-5u,10u,5u);
+    pair A,B,C,D,I,J;
+    A=u*(1,1);
+    B-A=u*(2,0.5);
+    D=3/5[A,rotation(B,A,40)];
+    C-D=B-A;
+    I=projection(D,A,B);
+    draw polygone(A,B,C,D) withcolor gris;
+    draw segment(A,B);
+    draw segment(D,I);
+    draw codeperp(D,I,B,5);
+    A:=A+3*u*(1,0);
+    B:=A+u*(2,0.5);
+    D:=3/5[A,rotation(B,A,40)];
+    C:=D+B-A;
+    J=projection(B,A,D);
+    draw polygone(A,B,C,D) withcolor gris;
+    draw segment(D,1.5[A,D]) dashed evenly withcolor gris;
+    draw segment(A,D);
+    draw segment(B,J);
+    draw codeperp(B,J,A,5);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureSphere{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    typetrace:="3D";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,0,10,500);
+    color O,A,B,C;
+    O=(0,0,0);
+    A-O=(0,1/2,0);
+    C-O=(-1/2,0,0);
+    B-O=(0,0,1/2);
+    path cc,cd;
+    cc=cercles(O,A,O,A,C);
+    cd=cercles(O,A,O,A,B);
+    draw cd;
+    draw (subpath(0,length cc/2) of cc) dashed evenly;
+    draw subpath(length cc/2,length cc) of cc;
+    draw cotationmil(O,A,0,18,btex rayon $r$ etex);
+    marque_p:="plein";
+    pointe(O);
+    marque_p:="non";
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    typetrace:="3D";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,0,10,500);
+    color O,A,B,C;
+    O=(0,0,0);
+    A-O=(0,1/2,0);
+    C-O=(-1/2,0,0);
+    B-O=(0,0,1/2);
+    path cc,cd;
+    cc=cercles(O,A,O,A,C);
+    cd=cercles(O,A,O,A,B);
+    draw cd;
+    draw (subpath(0,length cc/2) of cc) dashed evenly;
+    draw subpath(length cc/2,length cc) of cc;
+    draw cotationmil(O,A,0,18,btex rayon $r$ etex);
+    marque_p:="plein";
+    pointe(O);
+    marque_p:="non";
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigurePave{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,30,20,115);
+    color A,B,C,D,E,F,G,H;
+    draw Pave(A,B,C,D,E,F,G,H)(0.5,1,1/3) withcolor gris;
+    draw segment(A,B);
+    draw segment(E,F);
+    draw segment(A,F);
+    draw appelation(A,B,-2mm,\btex $\ell$ etex);
+    draw appelation(F,E,2mm,\btex $p$ etex);
+    draw appelation(A,F,2mm,\btex $h$ etex);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,30,20,115);
+    color A,B,C,D,E,F,G,H;
+    draw Pave(A,B,C,D,E,F,G,H)(0.5,1,1/3) withcolor gris;
+    draw segment(A,B);
+    draw segment(E,F);
+    draw segment(A,F);
+    draw appelation(A,B,-2mm,\btex $\ell$ etex);
+    draw appelation(F,E,2mm,\btex $p$ etex);
+    draw appelation(A,F,2mm,\btex $h$ etex);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigurePrisme{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,30,20,115);
+    color A,B,C,D,E,F,G,H;
+    D=(0.75,0,0);
+    G=(0,1,0);
+    H=(0,0,0);
+    A-D=(0,0,0.5);
+    C-D=G-H;
+    E-H=A-D;
+    F-E=(0,0.6,0);
+    B-A=F-E;
+    NbS:=8;
+    Sommet1:=A;
+    Sommet2:=B;
+    Sommet3:=C;
+    Sommet4:=D;
+    Sommet5:=E;
+    Sommet6:=F;
+    Sommet7:=G;
+    Sommet8:=H;
+    NF:=6;
+    Fc[100]:=4;Fc[101]:=1;Fc[102]:=4;Fc[103]:=3;Fc[104]:=2;
+    Fc[200]:=4;Fc[201]:=4;Fc[202]:=1;Fc[203]:=5;Fc[204]:=8;
+    Fc[300]:=4;Fc[301]:=4;Fc[302]:=8;Fc[303]:=7;Fc[304]:=3;
+    Fc[400]:=4;Fc[401]:=8;Fc[402]:=5;Fc[403]:=6;Fc[404]:=7;
+    Fc[500]:=4;Fc[501]:=1;Fc[502]:=2;Fc[503]:=6;Fc[504]:=5;
+    Fc[600]:=4;Fc[601]:=2;Fc[602]:=3;Fc[603]:=7;Fc[604]:=6;
+    CoulTrace:=gris;
+    DessineObjet;
+    drawoptions(withcolor gris);
+    draw codeperp(B,A,E,5);
+    draw codeperp(A,B,F,5);
+    draw codeperp(H,D,C,5);
+    draw codeperp(D,C,G,5);
+    drawoptions();
+    draw polygone(A,B,C,D);
+    draw hachurage(polygone(A,B,C,D),60,0.3,0);
+    draw segment(A,E);
+    draw appelation(A,E,3mm,btex hauteur etex);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,30,20,115);
+    color A,B,C,D,E,F,G,H;
+    D=(0.75,0,0);
+    G=(0,1,0);
+    H=(0,0,0);
+    A-D=(0,0,0.5);
+    C-D=G-H;
+    E-H=A-D;
+    F-E=(0,0.6,0);
+    B-A=F-E;
+    NbS:=8;
+    Sommet1:=A;
+    Sommet2:=B;
+    Sommet3:=C;
+    Sommet4:=D;
+    Sommet5:=E;
+    Sommet6:=F;
+    Sommet7:=G;
+    Sommet8:=H;
+    NF:=6;
+    Fc[100]:=4;Fc[101]:=1;Fc[102]:=4;Fc[103]:=3;Fc[104]:=2;
+    Fc[200]:=4;Fc[201]:=4;Fc[202]:=1;Fc[203]:=5;Fc[204]:=8;
+    Fc[300]:=4;Fc[301]:=4;Fc[302]:=8;Fc[303]:=7;Fc[304]:=3;
+    Fc[400]:=4;Fc[401]:=8;Fc[402]:=5;Fc[403]:=6;Fc[404]:=7;
+    Fc[500]:=4;Fc[501]:=1;Fc[502]:=2;Fc[503]:=6;Fc[504]:=5;
+    Fc[600]:=4;Fc[601]:=2;Fc[602]:=3;Fc[603]:=7;Fc[604]:=6;
+    CoulTrace:=gris;
+    DessineObjet;
+    drawoptions(withcolor gris);
+    draw codeperp(B,A,E,5);
+    draw codeperp(A,B,F,5);
+    draw codeperp(H,D,C,5);
+    draw codeperp(D,C,G,5);
+    drawoptions();
+    draw polygone(A,B,C,D);
+    draw hachurage(polygone(A,B,C,D),60,0.3,0);
+    draw segment(A,E);
+    draw appelation(A,E,3mm,btex hauteur etex);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureCylindre{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,0,20,70);
+    color O,O',A,A',B,B',C,C';
+    O=(0,0,0);
+    O'-O=(0,0,1);
+    A-O=(0,1,0);
+    A'-A=O'-O;
+    C=symetrie(A,O);
+    C'-C=O'-O;
+    B-O=(-1/2,0,0);
+    B'-B=O'-O;
+    path cc,cd;
+    cc=cercles(O,A,O,A,B);
+    cd=cercles(O',A',O',A',B');
+    draw cd;
+    draw segment(C,C');
+    draw segment(A,A');
+    draw (subpath(0,length cc/2) of cc) dashed evenly;
+    draw subpath(length cc/2,length cc) of cc;
+    draw segment(O,A);
+    draw cotationmil(C,C',3mm,25,btex hauteur $h$ etex);
+    draw appelation(O,A,2mm,btex rayon $r$ etex);
+    marque_p:="croix";
+    pointe(O);
+    marque_p:="non";
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,0,20,70);
+    color O,O',A,A',B,B',C,C';
+    O=(0,0,0);
+    O'-O=(0,0,1);
+    A-O=(0,1,0);
+    A'-A=O'-O;
+    C=symetrie(A,O);
+    C'-C=O'-O;
+    B-O=(-1/2,0,0);
+    B'-B=O'-O;
+    path cc,cd;
+    cc=cercles(O,A,O,A,B);
+    cd=cercles(O',A',O',A',B');
+    draw cd;
+    draw segment(C,C');
+    draw segment(A,A');
+    draw (subpath(0,length cc/2) of cc) dashed evenly;
+    draw subpath(length cc/2,length cc) of cc;
+    draw segment(O,A);
+    draw cotationmil(C,C',3mm,25,btex hauteur $h$ etex);
+    draw appelation(O,A,2mm,btex rayon $r$ etex);
+    marque_p:="croix";
+    pointe(O);
+    marque_p:="non";
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureCone{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,0,10,70);
+    color O,O',A,B,C;
+    O=(0,0,0);
+    O'-O=(0,0,1.5);
+    A-O=(0,1,0);
+    C=symetrie(A,O);
+    B-O=(-1/2,0,0);
+    path cc;
+    cc=cercles(O,A,O,A,B);
+    draw chemin(C,O',A);
+    draw (subpath(0,length cc/2) of cc) dashed evenly;
+    draw subpath(length cc/2,length cc) of cc;
+    draw chemin(O',O,A);
+    draw appelation(O,O',2mm,btex hauteur etex);
+    draw appelation(O,A,1mm,btex rayon $r$ etex);
+    marque_p:="croix";
+    pointe(O);
+    marque_p:="non";
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,0,10,70);
+    color O,O',A,B,C;
+    O=(0,0,0);
+    O'-O=(0,0,1.5);
+    A-O=(0,1,0);
+    C=symetrie(A,O);
+    B-O=(-1/2,0,0);
+    path cc;
+    cc=cercles(O,A,O,A,B);
+    draw chemin(C,O',A);
+    draw (subpath(0,length cc/2) of cc) dashed evenly;
+    draw subpath(length cc/2,length cc) of cc;
+    draw chemin(O',O,A);
+    draw appelation(O,O',2mm,btex hauteur etex);
+    draw appelation(O,A,1mm,btex rayon $r$ etex);
+    marque_p:="croix";
+    pointe(O);
+    marque_p:="non";
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigurePyramide{%
+  \ifluatex
+  \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;
+    z2=(4,2)*u;
+    z3=(-0.5,2.75)*u;
+    z4=(-3,1.5)*u;
+    z5=(0.5,6)*u;
+    z6=(0.5,1.5)*u;
+    z7=z6 shifted (5u,0);
+    draw z5--z0 withcolor gris;
+    draw z5--z1 withcolor gris;
+    draw z5--z2 withcolor gris;
+    draw z5--z4 withcolor gris;
+    draw z5--z3 dashed evenly withcolor gris;
+    draw hachurage(polygone(z4,z0,z1,z2,z3,z4),60,0.4,0);
+    remplis codeperp(z7,z6,z5,8)--z6--cycle withcolor white;
+    draw z4--z0--z1--z2;
+    draw z2--z3--z4 dashed evenly;
+    draw z5--z6 dashed evenly;
+    draw codeperp(z7,z6,z5,8);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    Figure(-10u,-10u,10u,10u);
+    u:=0.5cm;
+    z0=(-0.5,0)*u;
+    z1=(2.5,0.5)*u;
+    z2=(4,2)*u;
+    z3=(-0.5,2.75)*u;
+    z4=(-3,1.5)*u;
+    z5=(0.5,6)*u;
+    z6=(0.5,1.5)*u;
+    z7=z6 shifted (5u,0);
+    draw z5--z0 withcolor gris;
+    draw z5--z1 withcolor gris;
+    draw z5--z2 withcolor gris;
+    draw z5--z4 withcolor gris;
+    draw z5--z3 dashed evenly withcolor gris;
+    draw hachurage(polygone(z4,z0,z1,z2,z3,z4),60,0.4,0);
+    remplis codeperp(z7,z6,z5,8)--z6--cycle withcolor white;
+    draw z4--z0--z1--z2;
+    draw z2--z3--z4 dashed evenly;
+    draw z5--z6 dashed evenly;
+    draw codeperp(z7,z6,z5,8);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureCube{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,30,20,80);
+    color A,B,C,D,E,F,G,H;
+    draw Cube(A,B,C,D,E,F,G,H) withcolor gris;
+    draw segment(E,H);
+    draw appelation(E,H,2mm,btex $a$ etex);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-10u,-10u,10u,10u);
+    Initialisation(5,30,20,80);
+    color A,B,C,D,E,F,G,H;
+    draw Cube(A,B,C,D,E,F,G,H) withcolor gris;
+    draw segment(E,H);
+    draw appelation(E,H,2mm,btex $a$ etex);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureLosange{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C,D;
+    A=u*(1,1);
+    B-A=u*(2,0.5);
+    D=rotation(B,A,40);
+    C-D=B-A;
+    draw polygone(A,B,C,D);
+    marque_s:=marque_s/3;
+    draw Codelongueur(A,B,B,C,C,D,D,A,2);
+    marque_s:=marque_s*3;
+    draw appelation(A,B,-3mm,btex $c$ etex);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C,D;
+    A=u*(1,1);
+    B-A=u*(2,0.5);
+    D=rotation(B,A,40);
+    C-D=B-A;
+    draw polygone(A,B,C,D);
+    marque_s:=marque_s/3;
+    draw Codelongueur(A,B,B,C,C,D,D,A,2);
+    marque_s:=marque_s*3;
+    draw appelation(A,B,-3mm,btex $c$ etex);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureLosangeAire{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C,D;
+    A=u*(1,1);
+    B-A=u*(2,0.5);
+    D=rotation(B,A,40);
+    C-D=B-A;
+    draw polygone(A,B,C,D) withcolor gris;
+    draw segment(A,C);
+    draw segment(B,D);
+    marque_s:=marque_s/3;
+    draw Codelongueur(A,B,B,C,C,D,D,A,2);
+    marque_s:=marque_s*3;
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C,D;
+    A=u*(1,1);
+    B-A=u*(2,0.5);
+    D=rotation(B,A,40);
+    C-D=B-A;
+    draw polygone(A,B,C,D) withcolor gris;
+    draw segment(A,C);
+    draw segment(B,D);
+    marque_s:=marque_s/3;
+    draw Codelongueur(A,B,B,C,C,D,D,A,2);
+    marque_s:=marque_s*3;
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureRectangle{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    pair A,B,C,D;
+    A=u*(1,1);
+    B-A=u*(3,0);
+    C=2/3[B,rotation(A,B,-90)];
+    D-C=A-B;
+    draw polygone(A,B,C,D);
+    draw codeperp(A,B,C,5);
+    draw codeperp(B,C,D,5);
+    draw codeperp(C,D,A,5);
+    draw codeperp(D,A,B,5);
+    marque_s:=marque_s/3;
+    draw Codelongueur(A,B,C,D,2);
+    draw Codelongueur(A,D,C,B,5);
+    marque_s:=marque_s*3;
+    draw appelation(A,B,-3mm,btex $L$ etex);
+    label.lft(btex $\ell$ etex,iso(A,D));
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    pair A,B,C,D;
+    A=u*(1,1);
+    B-A=u*(3,0);
+    C=2/3[B,rotation(A,B,-90)];
+    D-C=A-B;
+    draw polygone(A,B,C,D);
+    draw codeperp(A,B,C,5);
+    draw codeperp(B,C,D,5);
+    draw codeperp(C,D,A,5);
+    draw codeperp(D,A,B,5);
+    marque_s:=marque_s/3;
+    draw Codelongueur(A,B,C,D,2);
+    draw Codelongueur(A,D,C,B,5);
+    marque_s:=marque_s*3;
+    draw appelation(A,B,-3mm,btex $L$ etex);
+    label.lft(btex $\ell$ etex,iso(A,D));
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureTriangle{%
+    \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C;
+    A=u*(1,1);
+    B-A=u*(3,0);
+    C=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45));
+    draw polygone(A,B,C);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C;
+    A=u*(1,1);
+    B-A=u*(3,0);
+    C=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45));
+    draw polygone(A,B,C);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureCercle{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C;
+    A=u*(2.5,2.5);
+    path cc;
+    cc=cercles(A,1.25u);
+    B=pointarc(cc,195);
+    C=symetrie(B,A);
+    draw cc withcolor gris;
+    draw segment(B,C);
+    marque_p:="croix";
+    pointe(A);
+    draw appelation(B,C,3mm,\btex diamètre etex);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C;
+    A=u*(2.5,2.5);
+    path cc;
+    cc=cercles(A,1.25u);
+    B=pointarc(cc,195);
+    C=symetrie(B,A);
+    draw cc withcolor gris;
+    draw segment(B,C);
+    marque_p:="croix";
+    pointe(A);
+    draw appelation(B,C,3mm,\btex diamètre etex);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureDisque{%
+  \ifluatex
+  \mplibforcehmode
+  \begin{mplibcode}
+    drawoptions( dashed dashpattern(on1cm));
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C;
+    A=u*(2.5,2.5);
+    path cc;
+    cc=cercles(A,1.25u);
+    B=pointarc(cc,195);
+    C=symetrie(B,A);
+    draw cc withcolor gris;
+    draw segment(A,C);
+    marque_p:="croix";
+    pointe(A);
+    draw appelation(A,C,3mm,\btex rayon $r$ etex);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C;
+    A=u*(2.5,2.5);
+    path cc;
+    cc=cercles(A,1.25u);
+    B=pointarc(cc,195);
+    C=symetrie(B,A);
+    draw cc withcolor gris;
+    draw segment(A,C);
+    marque_p:="croix";
+    pointe(A);
+    draw appelation(A,C,3mm,\btex rayon $r$ etex);
+  \end{mpost}
+  \fi
+}
+
+\def\MPFigureTriangleAire{%
+    \ifluatex
+  \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);
+    C=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45));
+    H=projection(C,A,B);
+    I=projection(A,B,C);
+    J=projection(B,C,A);
+    draw polygone(A,B,C) withcolor gris;
+    drawoptions();
+    draw segment(C,H);
+    draw segment(A,B);
+    draw codeperp(C,H,B,5);
+    drawoptions();
+    A:=A+u*(2.5,0);
+    B:=A+u*(1.4,0);
+    C:=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45));
+    I:=projection(A,B,C);
+    J:=projection(B,C,A);
+    draw polygone(A,B,C) withcolor gris;
+    drawoptions();
+    draw segment(A,I);
+    draw segment(C,B);
+    draw codeperp(A,I,B,5);
+    drawoptions();
+    A:=A-u*(1.25,1);
+    B:=A+u*(1.4,0);
+    C:=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45));
+    J:=projection(B,C,A);
+    draw polygone(A,B,C) withcolor gris;
+    drawoptions();
+    draw segment(B,J);
+    draw segment(C,A);
+    draw codeperp(B,J,C,5);
+    drawoptions();
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    Figure(-5u,-5u,5u,5u);
+    pair A,B,C,H,I,J;
+    A=u*(0.5,1);
+    B-A=u*(1.4,0);
+    C=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45));
+    H=projection(C,A,B);
+    I=projection(A,B,C);
+    J=projection(B,C,A);
+    draw polygone(A,B,C) withcolor gris;
+    drawoptions();
+    draw segment(C,H);
+    draw segment(A,B);
+    draw codeperp(C,H,B,5);
+    drawoptions();
+    A:=A+u*(2.5,0);
+    B:=A+u*(1.4,0);
+    C:=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45));
+    I:=projection(A,B,C);
+    J:=projection(B,C,A);
+    draw polygone(A,B,C) withcolor gris;
+    drawoptions();
+    draw segment(A,I);
+    draw segment(C,B);
+    draw codeperp(A,I,B,5);
+    drawoptions();
+    A:=A-u*(1.25,1);
+    B:=A+u*(1.4,0);
+    C:=demidroite(A,rotation(B,A,60)) intersectionpoint demidroite(B,rotation(A,B,-45));
+    J:=projection(B,C,A);
+    draw polygone(A,B,C) withcolor gris;
+    drawoptions();
+    draw segment(B,J);
+    draw segment(C,A);
+    draw codeperp(B,J,C,5);
+    drawoptions();
+  \end{mpost}
+  \fi
+}
+
+\newcommand\Formule[1][]{%
+  \useKVdefault[ClesFormule]
+  \setKV[ClesFormule]{#1}
+  \setlength{\RoundedBoxWidth}{\useKV[ClesFormule]{Largeur}}
+  \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}%
+          \IfStrEqCase{\useKV[ClesFormule]{Surface}}{%
+            {carré}{\begin{center}
+                \MPFigureCarre\par
+                Périmètre d'un carré :\par$4\times c$
+              \end{center}}%
+            {polygone}{%
+              \begin{center}
+                \MPFigurePolygone\par
+                Périmètre d'un polygone : \par$\text{Somme des côtés}$
+              \end{center}
+            }%
+            {rectangle}{
+              \begin{center}
+                \MPFigureRectangle\par
+                Périmètre d'un rectangle : \par$2\times(L+\ell)$
+              \end{center}
+              }%
+              {losange}{%
+                \begin{center}
+                \MPFigureLosange\par
+                Périmètre d'un losange : \par$4\times c$
+              \end{center}
+              }%
+            {triangle}{%
+              \begin{center}
+                \MPFigureTriangle\par
+                Périmètre d'un triangle : \par Somme des côtés
+              \end{center}
+            }%
+            {cercle}{%
+              \begin{center}
+                \MPFigureCercle\par
+                Périmètre d'un cercle : \par$\pi\times\text{diamètre}$
+              \end{center}
+            }%
+            {parallélogramme}{
+              \begin{center}
+                \MPFigureParallelogramme\par
+                Périmètre d'un parallélogramme : \par Somme des côtés
+              \end{center}
+            }}
+        \end{minipage}};
+    \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}%
+            \IfStrEqCase{\useKV[ClesFormule]{Surface}}{%
+              {carré}{\begin{center}
+                  \MPFigureCarre\par
+                  Aire d'un carré :\par$c\times c$
+              \end{center}}%
+            {rectangle}{%
+              \begin{center}
+                  \MPFigureRectangle\par
+                  Aire d'un rectangle :\par$L\times\ell$
+              \end{center}
+              }%
+              {losange}{%
+                \begin{center}
+                  \MPFigureLosangeAire\par
+                  Aire d'un losange :\par$\dfrac{\text{grande diagonale}\times\text{petite diagonale}}{2}$
+              \end{center}
+              }%
+            {triangle}{%
+              \begin{center}
+                \MPFigureTriangleAire\par\vspace{1em}\par
+                Aire d'un triangle : $\displaystyle\frac{\text{côté}\times\text{hauteur relative à ce côté}}{2}$
+              \end{center}
+            }%
+            {disque}{%
+              \begin{center}
+                \MPFigureDisque\par
+                Aire d'un disque :\par$\pi\times r\times r$
+              \end{center}
+            }%
+            {parallélogramme}{%
+              \begin{center}
+                \MPFigureParallelogrammeAire\par
+                Aire d'un parallélogramme : $\text{côté}\times\text{hauteur relative à ce côté}$
+                \end{center}
+            }
+            {sphère}{%
+              \begin{center}
+                \MPFigureSphere\par
+                Aire d'une sphère : $4\times\pi\times r^2$
+              \end{center}
+            }}
+        \end{minipage}};
+    \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}%
+            \IfStrEqCase{\useKV[ClesFormule]{Solide}}{%
+              {boule}{\begin{center}
+                \MPFigureSphere\par
+                Volume d'une boule : $\dfrac{4\times\pi\times r^3}{3}$
+              \end{center}}%
+            {cube}{%
+              \begin{center}
+                \MPFigureCube\par
+                Volume d'une cube : $a^3\quad(a\times a\times a)$
+              \end{center}
+            }%
+              {pavé}{%
+                \begin{center}
+                  \MPFigurePave\par
+                  Volume d'un pavé droit : $\ell\times h\times p$
+              \end{center}
+              }
+              {prisme}{%
+                \begin{center}
+                  \MPFigurePrisme\par
+                  Volume d'un prisme droit : $\text{Aire de la base}\times\mbox{hauteur}$
+                \end{center}
+              }
+              {cylindre}{%
+                \begin{center}
+                  \MPFigureCylindre\par
+                  Volume d'un cylindre de révolution : $\pi\times r^2\times h$
+                \end{center}
+              }
+              {pyramide}{%
+                \begin{center}
+                  \MPFigurePyramide\par
+                  Volume d'une pyramide : $\dfrac{\text{Aire de la base}\times\text{hauteur}}{3}$
+                \end{center}
+              }
+              {cône}{%
+                \begin{center}
+                  \MPFigureCone\par
+                  Volume d'un cône de révolution : $\displaystyle\dfrac{\pi\times r^2\times h}{3}$
+                \end{center}
+              }
+              }
+          \end{minipage}};
+      \end{tikzpicture}
+    }
+  }
+}
+
+%%%%%%%%%%
+%%% Proba
+%%%%%%%%%%
+\setKVdefault[ClesProba]{Echelle=false,Arbre=false,Branche=2,Angle=60,Rayon=0.25,LongueurEchelle=5,Affichage=0,Grille=0}
+
+\def\Updatetoksproba#1/#2\nil{\addtotok\toklistepointproba{"#1","\footnotesize #2",}}
+\def\Updatetoksprobaechelle#1/#2/#3\nil{\addtotok\toklistepointproba{#1,#2,"#3",}}
+
+\newtoks\toklistepointproba
+
+% Pour construire l'arbre de probabilité
+\def\buildarbreproba{%
+  \toklistepointproba{}%
+  \foreachitem\compteur\in\ListeProba{\expandafter\Updatetoksproba\compteur\nil}%
+  \MPArbreProba{\useKV[ClesProba]{Branche}}{\useKV[ClesProba]{Angle}}{\the\toklistepointproba}{\useKV[ClesProba]{Rayon}}%
+}
+
+% Pour construire l'échelle de probabilité
+\def\buildechelleproba{%
+  \toklistepointproba{}%
+  \foreachitem\compteur\in\ListeProba{\expandafter\Updatetoksprobaechelle\compteur\nil}%
+  \MPEchelleProbaUn{\useKV[ClesProba]{LongueurEchelle}}{\the\toklistepointproba}{\useKV[ClesProba]{Affichage}}{\useKV[ClesProba]{Grille}}%
+}
+
+\def\MPEchelleProbaUn#1#2#3#4{%
+  % #1:longueur du segment représentant l'échelle
+  % #2:Liste des évènements/proba
+  % #3: pour l'affichage des labels (0 : rien, 1: fleches, 2 : fleches+evènements, 3: fleches+proba, 4 : tout)
+  % #4 : dimension de "la grille" associée
+  \ifluatex
+  \begin{mplibcode}
+    pair A,B,C[],D[];%les noeuds de l'arbre
+    Figure(-10u,-10u,10u,10u);
+    A=u*(1,1);
+    B-A=u*(#1,0);
+    draw segment(A,B);
+    draw marquesegment(A,B);
+    marque_s:=marque_s/2;
+    if #4>1:
+      for k=0 upto (#4-1):
+        D[k]=(k/#4)[A,B];
+      endfor;
+      if (#4 mod 2)=0:
+        for k=0 step 2 until (#4-1):
+          draw marquesegment(D[k],D[k+1]);
+        endfor;
+      else:
+        for k=1 step 2 until (#4-1):
+          draw marquesegment(D[k],D[k+1]);
+        endfor;
+      fi;
+    fi;
+    marque_s:=marque_s*2;
+    labeloffset:=labeloffset*3;
+    label.bot(btex 0 etex,A);
+    label.bot(btex 1 etex,B);
+    labeloffset:=labeloffset/3;
+    n:=1;%compter les informations
+    k:=1;% compter les informations noeud pour les placer
+    vardef toto(text t)=
+      for p_=t:
+        if (n mod 3)=1:
+          num:=p_;
+        fi;
+        if (n mod 3)=2:
+        deno:=p_;
+        fi;
+        if (n mod 3=0):
+          C[k]=(num/deno)[A,B];
+          if (#3>0):
+          drawarrow (C[k]-u*(0,0.5))--(C[k]-u*(0,0.15));
+          fi;
+          if (#3=2) or (#3=4):
+            dotlabel.top(TEX(p_),C[k]);
+          fi;
+          if (#3=1) or (#3=3):
+            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.
+          fi;
+          k:=k+1;
+        fi;
+      n:=n+1;
+      endfor;
+    enddef;
+    toto(#2);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    pair A,B,C[],D[];%les noeuds de l'arbre
+    Figure(-10u,-10u,10u,10u);
+    A=u*(1,1);
+    B-A=u*(#1,0);
+    draw segment(A,B);
+    draw marquesegment(A,B);
+    marque_s:=marque_s/2;
+    if #4>1:
+      for k=0 upto (#4-1):
+        D[k]=(k/#4)[A,B];
+      endfor;
+      if (#4 mod 2)=0:
+        for k=0 step 2 until (#4-1):
+          draw marquesegment(D[k],D[k+1]);
+        endfor;
+      else:
+        for k=1 step 2 until (#4-1):
+          draw marquesegment(D[k],D[k+1]);
+        endfor;
+      fi;
+    fi;
+    marque_s:=marque_s*2;
+    labeloffset:=labeloffset*3;
+    label.bot(btex 0 etex,A);
+    label.bot(btex 1 etex,B);
+    labeloffset:=labeloffset/3;
+    n:=1;%compter les informations
+    k:=1;% compter les informations noeud pour les placer
+    vardef toto(text t)=
+      for p_=t:
+        if (n mod 3)=1:
+          num:=p_;
+        fi;
+        if (n mod 3)=2:
+        deno:=p_;
+        fi;
+        if (n mod 3=0):
+          C[k]=(num/deno)[A,B];
+          if (#3>0):
+          drawarrow (C[k]-u*(0,0.5))--(C[k]-u*(0,0.15));
+          fi;
+          if (#3=2) or (#3=4):
+            dotlabel.top(LATEX(p_),C[k]);
+          fi;
+          if (#3=1) or (#3=3):
+            dotlabel.top("",C[k]);
+          fi;
+          if (#3>2):
+            label.bot(LATEX("$\noexpand\frac{"&decimal(num)&"}{"&decimal(deno)&"}$"),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.
+          fi;
+          k:=k+1;
+        fi;
+      n:=n+1;
+      endfor;
+    enddef;
+    toto(#2);
+  \end{mpost}
+  \fi
+}
+
+\def\MPArbreProba#1#2#3#4{%
+  % #1:longueur d'une branche
+  % #2:angle entre deux branches de même origine
+  % #3:Liste des évènements/proba
+  \ifluatex
+  \begin{mplibcode}
+    pair A[],B[];%les noeuds de l'arbre
+    Figure(-10u,-10u,10u,10u);
+    A0=u*(1,1);
+    B0-A0=u*(#1,0);
+    A1=rotation(B0,A0,#2/2);
+    A2=rotation(B0,A0,-#2/2);
+    B1-A1=B0-A0;
+    A3=rotation(B1,A1,#2/3);
+    A4=rotation(B1,A1,-#2/3);
+    B2-A2=B0-A0;
+    A5=rotation(B2,A2,#2/3);
+    A6=rotation(B2,A2,-#2/3);
+    draw segment(A4,A1);
+    draw segment(A5,A2);
+    draw chemin(A3,A1,A0,A2,A6);
+    for k=1 upto 6:
+    fill cercles(A[k],#4*cm) withcolor white;
+    endfor;
+    n:=1;%compter les informations
+    k:=1;% compter les informations noeud pour les placer
+    l:=1;% compter les informations "numériques"
+    vardef toto(text t)=
+    for p_=t:
+    if (n mod 2)=1:
+    if p_<>"":
+    label(TEX(p_),A[k]);
+    fi;
+    k:=k+1;
+    else:
+    if (l mod 2)=1:
+    if p_<>"":
+    draw appelation(A[(l-1) div 2],A[l],4mm,TEX(p_));
+    fi;
+    else:
+    if p_<>"":
+    draw appelation(A[(l-1) div 2],A[l],-4mm,TEX(p_));
+    fi;
+    fi;
+    l:=l+1;
+    fi;
+    n:=n+1;
+    endfor;
+    enddef;
+    toto(#3);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    pair A[],B[];%les noeuds de l'arbre
+    Figure(-10u,-10u,10u,10u);
+    A0=u*(1,1);
+    B0-A0=u*(#1,0);
+    A1=rotation(B0,A0,#2/2);
+    A2=rotation(B0,A0,-#2/2);
+    B1-A1=B0-A0;
+    A3=rotation(B1,A1,#2/3);
+    A4=rotation(B1,A1,-#2/3);
+    B2-A2=B0-A0;
+    A5=rotation(B2,A2,#2/3);
+    A6=rotation(B2,A2,-#2/3);
+    draw segment(A4,A1);
+    draw segment(A5,A2);
+    draw chemin(A3,A1,A0,A2,A6);
+    for k=1 upto 6:
+    fill cercles(A[k],#4*cm) withcolor white;
+    endfor;
+    n:=1;%compter les informations
+    k:=1;% compter les informations noeud pour les placer
+    l:=1;% compter les informations "numériques"
+    vardef toto(text t)=
+    for p_=t:
+    if (n mod 2)=1:
+    label(LATEX(p_),A[k]);
+    k:=k+1;
+    else:
+    if (l mod 2)=1:
+    draw appelation(A[(l-1) div 2],A[l],4mm,LATEX(p_));
+    else:
+    draw appelation(A[(l-1) div 2],A[l],-4mm,LATEX(p_));
+    fi;
+    l:=l+1;
+    fi;
+    n:=n+1;
+    endfor;
+    enddef;
+    toto(#3);
+  \end{mpost}
+  \fi
+}
+
+\newcommand\Proba[2][]{%
+  \useKVdefault[ClesProba]%
+  \setKV[ClesProba]{#1}%
+  % On liste les différents éléments sous la forme Evènement/proba
+  \setsepchar[*]{,*/}\ignoreemptyitems%
+  \readlist*\ListeProba{#2}
+  \ifboolKV[ClesProba]{Echelle}{%
+    \buildechelleproba%
+  }{\ifboolKV[ClesProba]{Arbre}{%
+      \buildarbreproba%
+    }{}
+  }
+}
+
+%%%%%%%%%%%%%%
+%%%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}
+% ValeurOrigine permet de faire des morceaux de demi-droite graduée en passant par droite :)
+
+\def\Updatetoksdroite#1/#2\nil{\addtotok\toklistepointdroite{#1,"#2",}}
+\def\Updatetoksrepere#1/#2/#3\nil{\addtotok\toklistepointrepere{#1,#2,"#3",}}
+\def\Updatetoksespace#1/#2/#3/#4\nil{\addtotok\toklistepointespace{#1,#2,#3,"#4",}}
+
+\newtoks\toklistepointrepere
+\newtoks\toklistepointdroite
+\newtoks\toklistepointespace
+
+% Pour construire le repère de l'espace
+\def\buildespace{%
+  \toklistepointespace{}%
+  \ifboolKV[ClesReperage]{Sphere}{%
+    \foreachitem\compteur\in\ListePointEspace{\expandafter\Updatetoksrepere\compteur\nil}%
+  }{%
+    \foreachitem\compteur\in\ListePointEspace{\expandafter\Updatetoksespace\compteur\nil}%
+  }
+  \ifboolKV[ClesReperage]{AffichageNom}{%
+    \ifboolKV[ClesReperage]{AffichageCoord}{%
+      \[\MPEspacePave{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\useKV[ClesReperage]{Unitey}}{\useKV[ClesReperage]{Pasy}}{\useKV[ClesReperage]{Unitez}}{\useKV[ClesReperage]{Pasz}}{\the\toklistepointespace}{3}{\useKV[ClesReperage]{EchelleEspace}}\]%
+    }{%
+      \[\MPEspacePave{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\useKV[ClesReperage]{Unitey}}{\useKV[ClesReperage]{Pasy}}{\useKV[ClesReperage]{Unitez}}{\useKV[ClesReperage]{Pasz}}{\the\toklistepointespace}{2}{\useKV[ClesReperage]{EchelleEspace}}\]%
+    }
+  }{%
+    \ifboolKV[ClesReperage]{AffichageCoord}{%
+      \[\MPEspacePave{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\useKV[ClesReperage]{Unitey}}{\useKV[ClesReperage]{Pasy}}{\useKV[ClesReperage]{Unitez}}{\useKV[ClesReperage]{Pasz}}{\the\toklistepointespace}{1}{\useKV[ClesReperage]{EchelleEspace}}\]%
+    }{%
+      \[\MPEspacePave{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\useKV[ClesReperage]{Unitey}}{\useKV[ClesReperage]{Pasy}}{\useKV[ClesReperage]{Unitez}}{\useKV[ClesReperage]{Pasz}}{\the\toklistepointespace}{0}{\useKV[ClesReperage]{EchelleEspace}}\]%
+    }
+  }%
+}%
+
+\def\MPEspacePave#1#2#3#4#5#6#7#8#9{%
+  \ifluatex
+  \begin{mplibcode}
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-20u,-20u,20u,20u);
+    Initialisation(1500,30,20,abs(#9));
+    %marque_r:=marque_r/2;
+    marque_p:="plein";
+    color A,B,C,D,E,F,G,H,M[],N[];
+    draw Pave(A,B,C,D,E,F,G,H)(#1,#3,#5);
+    if #9>0:
+    drawarrow Projette(A)--Projette(1.5[D,A]);
+    drawarrow Projette(C)--Projette(1.5[D,C]);
+    drawarrow Projette(E)--Projette(1.5[D,E]);
+    label.ulft(btex 1 etex,Projette((1/#2)[D,A]));
+    label.bot(btex 1 etex,Projette((1/#4)[D,C]));
+    label.lft(btex 1 etex,Projette((1/#6)[D,E]));
+    for k=1 upto (#2):
+    pointe((k/#2)[D,A]);
+    endfor;
+    for k=1 upto (#4):
+    pointe((k/#4)[D,C]);
+    endfor;
+    for k=1 upto (#6):
+    pointe((k/#6)[D,E]);
+    endfor;
+    else:
+    drawarrow Projette(D)--Projette(1.5[A,D]) dashed evenly;
+    drawarrow Projette(B)--Projette(1.5[A,B]);
+    drawarrow Projette(F)--Projette(1.5[A,F]);
+    label.ulft(btex 1 etex,Projette((1/#2)[A,D]));
+    label.bot(btex 1 etex,Projette((1/#4)[A,B]));
+    label.lft(btex 1 etex,Projette((1/#6)[A,F]));
+    for k=1 upto (#2):
+    pointe((k/#2)[A,D]);
+    endfor;
+    for k=1 upto (#4):
+    pointe((k/#4)[A,B]);
+    endfor;
+    for k=1 upto (#6):
+    pointe((k/#6)[A,F]);
+    endfor;
+    fi;
+    vardef tata(text t)=
+    n:=1;%pour compter combien de points
+    k:=0;%pour garder l'abscisse
+    l:=0;%pour garder l'ordonnée
+    m:=0;%pour garder l'altitude
+    if #8>0:
+    for p_=t:
+    if (n mod 4)=1:
+    k:=p_;
+    fi;
+    if (n mod 4)=2:
+    l:=p_;
+    fi;
+    if (n mod 4)=3:
+    m:=p_;
+    fi;
+    if (n mod 4)=0:
+    M[n]=(k/#2)[D,A]+(l/#4)*(C-D)+(m/#6)*(E-D);
+    N[n]=(k/#2)[D,A]+(l/#4)*(C-D);
+    if (#8>1):
+    label.top(TEX(p_),Projette(M[n]));
+    pointe(M[n]);
+    fi;
+    if (#8=1) or (#8=3) :
+    drawoptions(dashed evenly withcolor gris);
+    draw segment(M[n],(0,0,bluepart(M[n])));
+    draw segment(M[n],N[n]);
+    draw segment(N[n],(redpart(M[n]),0,0));
+    draw segment(N[n],(0,greenpart(M[n]),0));
+    drawoptions();
+    fi;
+    fi;
+    n:=n+1;
+    endfor;
+    fi;
+    enddef;
+    vardef toto(text t)=
+    n:=1;%pour compter combien de points
+    k:=0;%pour garder l'abscisse
+    l:=0;%pour garder l'ordonnée
+    m:=0;%pour garder l'altitude
+    if #8>0:
+    for p_=t:
+    if (n mod 4)=1:
+    k:=p_;
+    fi;
+    if (n mod 4)=2:
+    l:=p_;
+    fi;
+    if (n mod 4)=3:
+    m:=p_;
+    fi;
+    if (n mod 4)=0:
+    % message("je suis ici : "&p_);
+    M[n]=(k/#2)[A,D]+(l/#4)*(B-A)+(m/#6)*(F-A);
+    N[n]=(k/#2)[A,D]+(l/#4)*(B-A);
+    if (#8>1):
+    label.top(TEX(p_),Projette(M[n]));
+    pointe(M[n]);
+    fi;
+    if (#8=1) or (#8=3) :
+    drawoptions(dashed evenly withcolor gris);
+    draw segment(M[n],A+(0,0,bluepart(M[n])));
+    draw segment(M[n],N[n]);
+    draw segment(N[n],A+(l/#4)*(B-A));
+    draw segment(N[n],A+(k/#2)*(D-A));
+    drawoptions();
+    fi;
+    fi;
+    n:=n+1;
+    endfor;
+    fi;
+    enddef;
+    if #9>0:
+    tata(#7);
+    else:
+    toto(#7);
+    fi;
+    draw Pave(A,B,C,D,E,F,G,H)(#1,#3,#5);
+  \end{mplibcode}
+  \else
+  \begin{mpost}[mpsettings={input PfC-Geometrie;}]
+    typetrace:="3D";
+    typerepre:="persp";
+    Figure(-20u,-20u,20u,20u);
+    Initialisation(1500,30,20,abs(#9));
+    %marque_r:=marque_r/2;
+    marque_p:="plein";
+    color A,B,C,D,E,F,G,H,M[],N[];
+    draw Pave(A,B,C,D,E,F,G,H)(#1,#3,#5);
+    if #9>0:
+    drawarrow Projette(A)--Projette(1.5[D,A]);
+    drawarrow Projette(C)--Projette(1.5[D,C]);
+    drawarrow Projette(E)--Projette(1.5[D,E]);
+    label.ulft(btex 1 etex,Projette((1/#2)[D,A]));
+    label.bot(btex 1 etex,Projette((1/#4)[D,C]));
+    label.lft(btex 1 etex,Projette((1/#6)[D,E]));
+    for k=1 upto (#2):
+    pointe((k/#2)[D,A]);
+    endfor;
+    for k=1 upto (#4):
+    pointe((k/#4)[D,C]);
+    endfor;
+    for k=1 upto (#6):
+    pointe((k/#6)[D,E]);
+    endfor;
+    else:
+    drawarrow Projette(D)--Projette(1.5[A,D]) dashed evenly;
+    drawarrow Projette(B)--Projette(1.5[A,B]);
+    drawarrow Projette(F)--Projette(1.5[A,F]);
+    label.ulft(btex 1 etex,Projette((1/#2)[A,D]));
+    label.bot(btex 1 etex,Projette((1/#4)[A,B]));
+    label.lft(btex 1 etex,Projette((1/#6)[A,F]));
+    for k=1 upto (#2):
+    pointe((k/#2)[A,D]);
+    endfor;
+    for k=1 upto (#4):
+    pointe((k/#4)[A,B]);
+    endfor;
+    for k=1 upto (#6):
+    pointe((k/#6)[A,F]);
+    endfor;
+    fi;
+    vardef tata(text t)=
+    n:=1;%pour compter combien de points
+    k:=0;%pour garder l'abscisse
+    l:=0;%pour garder l'ordonnée
+    m:=0;%pour garder l'altitude
+    if #8>0:
+    for p_=t:
+    if (n mod 4)=1:
+    k:=p_;
+    fi;
+    if (n mod 4)=2:
+    l:=p_;
+    fi;
+    if (n mod 4)=3:
+    m:=p_;
+    fi;
+    if (n mod 4)=0:
+    M[n]=(k/#2)[D,A]+(l/#4)*(C-D)+(m/#6)*(E-D);
+    N[n]=(k/#2)[D,A]+(l/#4)*(C-D);
+    if (#8>1):
+    label.top(LATEX(p_),Projette(M[n]));
+    pointe(M[n]);
+    fi;
+    if (#8=1) or (#8=3) :
+    drawoptions(dashed evenly withcolor gris);
+    draw segment(M[n],(0,0,bluepart(M[n])));
+    draw segment(M[n],N[n]);
+    draw segment(N[n],(redpart(M[n]),0,0));
+    draw segment(N[n],(0,greenpart(M[n]),0));
+    drawoptions();
+    fi;
+    fi;
+    n:=n+1;
+    endfor;
+    fi;
+    enddef;
+    vardef toto(text t)=
+    n:=1;%pour compter combien de points
+    k:=0;%pour garder l'abscisse
+    l:=0;%pour garder l'ordonnée
+    m:=0;%pour garder l'altitude
+    if #8>0:
+    for p_=t:
+    if (n mod 4)=1:
+    k:=p_;
+    fi;
+    if (n mod 4)=2:
+    l:=p_;
+    fi;
+    if (n mod 4)=3:
+    m:=p_;
+    fi;
+    if (n mod 4)=0:
+    % message("je suis ici : "&p_);
+    M[n]=(k/#2)[A,D]+(l/#4)*(B-A)+(m/#6)*(F-A);
+    N[n]=(k/#2)[A,D]+(l/#4)*(B-A);
+    if (#8>1):
+    label.top(LATEX(p_),Projette(M[n]));
+    pointe(M[n]);
+    fi;
+    if (#8=1) or (#8=3) :
+    drawoptions(dashed evenly withcolor gris);
+    draw segment(M[n],A+(0,0,bluepart(M[n])));
+    draw segment(M[n],N[n]);
+    draw segment(N[n],A+(l/#4)*(B-A));
+    draw segment(N[n],A+(k/#2)*(D-A));
+    drawoptions();
+    fi;
+    fi;
+    n:=n+1;
+    endfor;
+    fi;
+    enddef;
+    if #9>0:
+    tata(#7);
+    else:
+    toto(#7);
+    fi;
+    draw Pave(A,B,C,D,E,F,G,H)(#1,#3,#5);
+  \end{mpost}
+  \fi
+}%
+
+% Pour construire le repère du plan
+\def\buildrepere{%
+  \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}{%
+        \[\MPPlan{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\useKV[ClesReperage]{Unitey}}{\useKV[ClesReperage]{Pasy}}{\the\toklistepointrepere}{1}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurUnitey}}\]%
+      }{%
+        \[\MPPlan{\useKV[ClesReperage]{Unitex}}{\useKV[ClesReperage]{Pasx}}{\useKV[ClesReperage]{Unitey}}{\useKV[ClesReperage]{Pasy}}{\the\toklistepointrepere}{0}{\useKV[ClesReperage]{ValeurUnitex}}{\useKV[ClesReperage]{ValeurUnitey}}\]%
+      }
+    }%
+  }%
+}
+
+\def\MPPlan#1#2#3#4#5#6#7#8{%
+  \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)=
+    for p_=t:
+    if (n mod 3)=1:
+      if p_>maxx:
+        maxx:=p_;
+      fi;
+      if p_<minx:
+        minx:=p_;
+      fi;
+    fi;
+    if (n mod 3)=2:
+      if p_>maxy:
+        maxy:=p_;
+      fi;
+      if p_<miny:
+        miny:=p_;
+      fi;
+      fi;
+      n:=n+1;
+    endfor;
+    maxx:=maxx+1;
+    minx:=minx-1;
+    if maxx<(#2+1):
+    maxx:=#2+1;
+    fi;
+    if minx>(-#2-1):
+    minx:=-#2-1;
+    fi;
+    maxy:=maxy+1;
+    miny:=miny-1;
+    if maxy<(#4+1):
+    maxy:=#2+1;
+    fi;
+    if miny>(-#4-1):
+    miny:=-#4-1;
+    fi;
+    enddef;
+    toto(#5);
+    Figure((minx-1)*unitpx,(miny-1)*unitpy,(maxx+1)*unitpx,(maxy+1)*unitpy);
+    pair A,B,C,D,E;
+    A=(0,0);
+    B=(minx*unitpx,0);
+    C=(maxx*unitpx,0);
+    D=(0,miny*unitpy);
+    E=(0,maxy*unitpy);
+    for k=0 upto (maxx-minx):
+    draw ((xpart(B),ypart(D)-0.75*unitpy)--(xpart(B),ypart(E)+0.75*unitpy)) shifted (k*unitpx,0) withcolor gris;
+    endfor;
+    for k=0 upto (maxy-miny):
+    draw ((xpart(B)-0.75*unitpx,ypart(D))--(xpart(C)+0.75*unitpx,ypart(D))) shifted (0,k*unitpy) withcolor gris;
+    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);
+    % 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:
+    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 #6>1:
+    message("p = "&p_);
+  %  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.ulft(TEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k=0) and (l<0):
+    label.llft(TEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k<0) and (l<0):
+    label.llft(TEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k<0) and (l=0):
+    label.llft(TEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k>0) and (l<0):
+    label.lrt(TEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    pointe((k*unitpx,l*unitpy));
+ %   fi;
+    fi;
+    if (#6=1) or (#6=3):
+    draw (0,l*unitpy)--(k*unitpx,l*unitpy)--(k*unitpx,0) dashed evenly;
+    fi;
+    fi;
+    n:=n+1;
+    endfor;
+    fi;
+    enddef;
+    tata(#5);
+  \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)=
+    for p_=t:
+    if (n mod 3)=1:
+      if p_>maxx:
+        maxx:=p_;
+      fi;
+      if p_<minx:
+        minx:=p_;
+      fi;
+    fi;
+    if (n mod 3)=2:
+      if p_>maxy:
+        maxy:=p_;
+      fi;
+      if p_<miny:
+        miny:=p_;
+      fi;
+      fi;
+      n:=n+1;
+    endfor;
+    maxx:=maxx+1;
+    minx:=minx-1;
+    if maxx<(#2+1):
+    maxx:=#2+1;
+    fi;
+    if minx>(-#2-1):
+    minx:=-#2-1;
+    fi;
+    maxy:=maxy+1;
+    miny:=miny-1;
+    if maxy<(#4+1):
+    maxy:=#2+1;
+    fi;
+    if miny>(-#4-1):
+    miny:=-#4-1;
+    fi;
+    enddef;
+    toto(#5);
+    Figure((minx-1)*unitpx,(miny-1)*unitpy,(maxx+1)*unitpx,(maxy+1)*unitpy);
+    pair A,B,C,D,E;
+    A=(0,0);
+    B=(minx*unitpx,0);
+    C=(maxx*unitpx,0);
+    D=(0,miny*unitpy);
+    E=(0,maxy*unitpy);
+    for k=0 upto (maxx-minx):
+    draw ((xpart(B),ypart(D)-0.75*unitpy)--(xpart(B),ypart(E)+0.75*unitpy)) shifted (k*unitpx,0) withcolor gris;
+    endfor;
+    for k=0 upto (maxy-miny):
+    draw ((xpart(B)-0.75*unitpx,ypart(D))--(xpart(C)+0.75*unitpx,ypart(D))) shifted (0,k*unitpy) withcolor gris;
+    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);
+    % 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:
+    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 #6>1:
+    if (k>0) and (l>0):
+    label.urt(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k=0) and (l>0):
+    label.urt(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k>0) and (l=0):
+    label.urt(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k<0) and (l>0):
+    label.ulft(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k=0) and (l<0):
+    label.llft(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k<0) and (l<0):
+    label.llft(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k<0) and (l=0):
+    label.llft(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k>0) and (l<0):
+    label.lrt(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    pointe((k*unitpx,l*unitpy));
+    fi;
+    if (#6=1) or (#6=3):
+    draw (0,l*unitpy)--(k*unitpx,l*unitpy)--(k*unitpx,0) dashed evenly;
+    fi;
+    fi;
+    n:=n+1;
+    endfor;
+    fi;
+    enddef;
+    tata(#5);
+  \end{mpost}
+  \fi
+}
+
+\def\MPPlanTrace#1#2#3#4#5#6#7#8#9{%
+  \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)=
+    for p_=t:
+    if (n mod 3)=1:
+      if p_>maxx:
+        maxx:=p_;
+      fi;
+      if p_<minx:
+        minx:=p_;
+      fi;
+    fi;
+    if (n mod 3)=2:
+      if p_>maxy:
+        maxy:=p_;
+      fi;
+      if p_<miny:
+        miny:=p_;
+      fi;
+      fi;
+      n:=n+1;
+    endfor;
+    maxx:=maxx+1;
+    minx:=minx-1;
+    if maxx<(#2+1):
+    maxx:=#2+1;
+    fi;
+    if minx>(-#2-1):
+    minx:=-#2-1;
+    fi;
+    maxy:=maxy+1;
+    miny:=miny-1;
+    if maxy<(#4+1):
+    maxy:=#2+1;
+    fi;
+    if miny>(-#4-1):
+    miny:=-#4-1;
+    fi;
+    enddef;
+    toto(#5);
+    Figure((minx-1)*unitpx,(miny-1)*unitpy,(maxx+1)*unitpx,(maxy+1)*unitpy);
+    pair A,B,C,D,E;
+    A=(0,0);
+    B=(minx*unitpx,0);
+    C=(maxx*unitpx,0);
+    D=(0,miny*unitpy);
+    E=(0,maxy*unitpy);
+    for k=0 upto (maxx-minx):
+    draw ((xpart(B),ypart(D)-0.75*unitpy)--(xpart(B),ypart(E)+0.75*unitpy)) shifted (k*unitpx,0) withcolor gris;
+    endfor;
+    for k=0 upto (maxy-miny):
+    draw ((xpart(B)-0.75*unitpx,ypart(D))--(xpart(C)+0.75*unitpx,ypart(D))) shifted (0,k*unitpy) withcolor gris;
+    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);
+    % 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:
+    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 #6>1:
+    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.ulft(TEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k=0) and (l<0):
+    label.llft(TEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k<0) and (l<0):
+    label.llft(TEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k<0) and (l=0):
+    label.llft(TEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k>0) and (l<0):
+    label.lrt(TEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    pointe((k*unitpx,l*unitpy));
+    fi;
+    if (#6=1) or (#6=3):
+    draw (0,l*unitpy)--(k*unitpx,l*unitpy)--(k*unitpx,0) dashed evenly;
+    fi;
+    fi;
+    n:=n+1;
+    endfor;
+    fi;
+    enddef;    
+    vardef Tracage(text t)(text ls)=%on trace les segments
+    pair A[];
+    n:=0;%pour parcourir la liste
+    m:=0;%pour lister les points par leur nombre
+    for p_=t:
+    n:=n+1;
+    if (n mod 3)=1:
+    k:=p_;
+    fi;
+    if (n mod 3)=2:
+    l:=p_;
+    fi;
+    if (n mod 3)=0:
+    m:=m+1;
+    A[m]=(k*unitpx,l*unitpy);
+    fi;
+    endfor;
+    for p_=ls:
+    draw segment(A[p_ div 10],A[p_ mod 10]);
+    endfor;
+    enddef;
+    tata(#5);
+    Tracage(#5)(#9);
+  \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)=
+    for p_=t:
+    if (n mod 3)=1:
+      if p_>maxx:
+        maxx:=p_;
+      fi;
+      if p_<minx:
+        minx:=p_;
+      fi;
+    fi;
+    if (n mod 3)=2:
+      if p_>maxy:
+        maxy:=p_;
+      fi;
+      if p_<miny:
+        miny:=p_;
+      fi;
+      fi;
+      n:=n+1;
+    endfor;
+    maxx:=maxx+1;
+    minx:=minx-1;
+    if maxx<(#2+1):
+    maxx:=#2+1;
+    fi;
+    if minx>(-#2-1):
+    minx:=-#2-1;
+    fi;
+    maxy:=maxy+1;
+    miny:=miny-1;
+    if maxy<(#4+1):
+    maxy:=#2+1;
+    fi;
+    if miny>(-#4-1):
+    miny:=-#4-1;
+    fi;
+    enddef;
+    toto(#5);
+    Figure((minx-1)*unitpx,(miny-1)*unitpy,(maxx+1)*unitpx,(maxy+1)*unitpy);
+    pair A,B,C,D,E;
+    A=(0,0);
+    B=(minx*unitpx,0);
+    C=(maxx*unitpx,0);
+    D=(0,miny*unitpy);
+    E=(0,maxy*unitpy);
+    for k=0 upto (maxx-minx):
+    draw ((xpart(B),ypart(D)-0.75*unitpy)--(xpart(B),ypart(E)+0.75*unitpy)) shifted (k*unitpx,0) withcolor gris;
+    endfor;
+    for k=0 upto (maxy-miny):
+    draw ((xpart(B)-0.75*unitpx,ypart(D))--(xpart(C)+0.75*unitpx,ypart(D))) shifted (0,k*unitpy) withcolor gris;
+    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);
+    % 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:
+    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 #6>1:
+    if (k>0) and (l>0):
+    label.urt(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k=0) and (l>0):
+    label.urt(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k>0) and (l=0):
+    label.urt(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k<0) and (l>0):
+    label.ulft(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k=0) and (l<0):
+    label.llft(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k<0) and (l<0):
+    label.llft(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k<0) and (l=0):
+    label.llft(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    if (k>0) and (l<0):
+    label.lrt(LATEX(p_),(k*unitpx,l*unitpy));
+    fi;
+    pointe((k*unitpx,l*unitpy));
+    fi;
+    if (#6=1) or (#6=3):
+    draw (0,l*unitpy)--(k*unitpx,l*unitpy)--(k*unitpx,0) dashed evenly;
+    fi;
+    fi;
+    n:=n+1;
+    endfor;
+    fi;
+    enddef;    
+    vardef Tracage(text t)(text ls)=%on trace les segments
+    pair A[];
+    n:=0;%pour parcourir la liste
+    m:=0;%pour lister les points par leur nombre
+    for p_=t:
+    n:=n+1;
+    if (n mod 3)=1:
+    k:=p_;
+    fi;
+    if (n mod 3)=2:
+    l:=p_;
+    fi;
+    if (n mod 3)=0:
+    m:=m+1;
+    A[m]=(k*unitpx,l*unitpy);
+    fi;
+    endfor;
+    for p_=ls:
+    draw segment(A[p_ div 10],A[p_ mod 10]);
+    endfor;
+    enddef;
+    tata(#5);
+    Tracage(#5)(#9);
+  \end{mpost}
+  \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
+  % #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)
+  \ifluatex
+  \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_<minx:
+            minx:=p_;
+          fi;
+        fi;
+      endfor;
+      maxx:=maxx+1;
+      minx:=minx-1;
+      if maxx<(#2+1):
+      maxx:=#2+1;
+      fi;
+      if minx>(-#2-1):
+      minx:=-#2-1;
+      fi;
+    enddef;
+    toto(#3);
+    Figure((minx-1)*u,-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));
+    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;
+    m_c:=m_c*3;
+    marque_p:="croix";
+    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));
+    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_:
+    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;
+    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_<minx:
+            minx:=p_;
+          fi;
+        fi;
+      endfor;
+      maxx:=maxx+1;
+      minx:=minx-1;
+      if maxx<(#2+1):
+      maxx:=#2+1;
+      fi;
+      if minx>(-#2-1):
+      minx:=-#2-1;
+      fi;
+    enddef;
+    toto(#3);
+    Figure((minx-1)*u,-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));
+    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;
+    m_c:=m_c*3;
+    marque_p:="croix";
+    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));
+    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_:
+    label.top(LATEX(p_),unitp*(k,0));
+    if p_<>"":
+    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}%
+      \buildrepere%
+    }{\ifboolKV[ClesReperage]{Droite}{%
+        \setsepchar[*]{,*/}\ignoreemptyitems%
+        \readlist*\ListePointDroite{#2}%
+        \builddemidroite%
+      }{%
+        \setsepchar[*]{,*/}\ignoreemptyitems%
+        \readlist*\ListePointDroite{#2}%
+        \builddemidroite%
+      }%
+    }%
+  }%
+}%
+
+
+%%%%%%%%
+%% 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}}}}%
+  }
+}
+
+%%%%%%%%% 
+%% Tableaux d'unités
+%%%%%%%%%
+\setKVdefault[ClesTableaux]{Decimaux=false,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}
+
+\newcommand\Tableau[1][]{%
+  \useKVdefault[ClesTableaux]
+  \setKV[ClesTableaux]{#1}
+  \ifboolKV[ClesTableaux]{Decimaux}{%
+    \setlength{\tabcolsep}{0.01\tabcolsep}
+    \begin{center}
+      \begin{tabular}{|*{12}{>{\centering\arraybackslash}m{4.75em}|}>{\columncolor{gray!15},}{c}|*{3}{>{\centering\arraybackslash}m{4.75em}|}}
+        \ifboolKV[ClesTableaux]{Partie}{\multicolumn{12}{c}{\bfseries Partie Entière}&\multicolumn{1}{c}{\cellcolor{gray!15},}&\multicolumn{3}{c}{\bfseries Partie décimale}\\}{}
+        \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 des milliers}&\multicolumn{3}{c|}{\cellcolor{\useKV[ClesTableaux]{Couleuru}}Classe des unités}&&&&\\}{}
+        \hline
+        \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%
+        &\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%
+        &%
+        &\fontsize{4.5}{4.5}\selectfont dixièmes%
+        &\fontsize{4.5}{4.5}\selectfont centièmes%
+        &\fontsize{4.5}{4.5}\selectfont millièmes\\
+        \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}%
+        &\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}%
+        &%
+        &\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 $\dfrac{\strut1}{\strut\num{1000}}$%
+        \\
+        }{}
+        \hline
+       &&&&&&&&&&&&&&&\\
+       &&&&&&&&&&&&&&&\\
+      \end{tabular}
+    \end{center}
+    \setlength{\tabcolsep}{100\tabcolsep}
+  }{}
+  \ifboolKV[ClesTableaux]{Metre}{%
+    \[\renewcommand{\arraystretch}{1.15}%
+      \begin{tabular}{|*{7}{p{7.5mm}|}}%
+        \multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (A);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (B);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (C);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (D);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (E);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (F);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (G);}}\\%
+        \hline
+        \multicolumn{1}{|c|}{km}&\multicolumn{1}{c|}{hm}&\multicolumn{1}{c|}{dam}&\multicolumn{1}{c|}{m}&\multicolumn{1}{c|}{dm}&\multicolumn{1}{c|}{cm}&\multicolumn{1}{c|}{mm}\\
+        \hline
+        &&&&&&\\
+        \multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (G1);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (F1);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (E1);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (D1);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (C1);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (B1);}}%
+        &\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (A1);}}\\%
+      \end{tabular}
+    \]
+    \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);}
+    }{}
+  }
+  {}
+  \ifboolKV[ClesTableaux]{Carre}{%
+    \[\renewcommand{\arraystretch}{1.15}\ifboolKV[ClesTableaux]{Colonnes}{\begin{tabular}{|*{7}{p{2.5mm}!{\color{gray!50}\vrule}p{2.5mm}|}}}{\begin{tabular}{|*{7}{p{2.5mm}p{2.5mm}|}}}
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate (A);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate
+    (B);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate
+    (C);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate
+    (D);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate
+    (E);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate
+    (F);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate (G);}}\\%
+\hline
+\multicolumn{2}{|c|}{km$^2$}&\multicolumn{2}{c|}{hm$^2$}&\multicolumn{2}{c|}{dam$^2$}&\multicolumn{2}{c|}{m$^2$}&\multicolumn{2}{c|}{dm$^2$}&\multicolumn{2}{c|}{cm$^2$}&\multicolumn{2}{c|}{mm$^2$}\\
+\hline
+&&&&&&&&&&&&&\\
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em] (G1);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em]
+    (F1);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em]
+    (E1);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em]
+    (D1);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em]
+    (C1);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em]
+    (B1);}}&%
+\multicolumn{2}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=0.6em] (A1);}}\\%
+\end{tabular}
+\]
+\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);}
+}{}
+  }
+  {}
+  \ifboolKV[ClesTableaux]{Cube}{%
+    {\setlength{\tabcolsep}{0.625\tabcolsep}
+\[\renewcommand{\arraystretch}{1.15}\ifboolKV[ClesTableaux]{Colonnes}{\begin{tabular}{|*{7}{p{2.5mm}!{\color{gray!50}\vrule}p{2.5mm}!{\color{gray!50}\vrule}p{2.5mm}|}}}{\begin{tabular}{|*{7}{p{2.5mm}p{2.5mm}p{2.5mm}|}}}
+\multicolumn{3}{c}{\tikz[remember picture,overlay]{\coordinate (A);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay]{\coordinate
+    (B);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay]{\coordinate
+    (C);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay]{\coordinate
+    (D);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay]{\coordinate
+    (E);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay]{\coordinate
+    (F);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay]{\coordinate (G);}}\\%
+\hline
+\multicolumn{3}{|c|}{km$^3$}&\multicolumn{3}{c|}{hm$^3$}&\multicolumn{3}{c|}{dam$^3$}&\multicolumn{3}{c|}{m$^3$}&\multicolumn{3}{c|}{dm$^3$}&\multicolumn{3}{c|}{cm$^3$}&\multicolumn{3}{c|}{mm$^3$}\\
+\hline
+&&&&&&&&&&&&&&&&&&&&\\
+\multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate (G1);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate
+    (F1);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate
+    (E1);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate
+    (D1);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate
+    (C1);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate
+    (B1);}}&%
+\multicolumn{3}{c}{\tikz[remember picture,overlay,yshift=\ht\strutbox]{\coordinate (A1);}}\\%
+\end{tabular}
+\]
+\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);}
+}{}
+  }
+  {}
+  \ifboolKV[ClesTableaux]{Litre}{%
+   \[\renewcommand{\arraystretch}{1.15}\begin{tabular}{|*{7}{p{7.5mm}|}}
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (A);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate
+    (B);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate
+    (C);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate
+    (D);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate
+    (E);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate
+    (F);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (G);}}\\%
+\hline
+\multicolumn{1}{|c|}{kL}&\multicolumn{1}{c|}{hL}&\multicolumn{1}{c|}{daL}&\multicolumn{1}{c|}{L}&\multicolumn{1}{c|}{dL}&\multicolumn{1}{c|}{cL}&\multicolumn{1}{c|}{mL}\\
+\hline
+&&&&&&\\
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (G1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em]
+    (F1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em]
+    (E1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em]
+    (D1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em]
+    (C1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em]
+    (B1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (A1);}}\\%
+\end{tabular}
+\]
+\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);}
+}{}
+  }
+  {}
+  \ifboolKV[ClesTableaux]{Gramme}{%
+   \[\renewcommand{\arraystretch}{1.15}\begin{tabular}{|*{7}{p{7.5mm}|}}
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (A);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate
+    (B);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate
+    (C);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate
+    (D);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate
+    (E);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate
+    (F);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate (G);}}\\%
+\hline
+\multicolumn{1}{|c|}{kg}&\multicolumn{1}{c|}{hg}&\multicolumn{1}{c|}{dag}&\multicolumn{1}{c|}{g}&\multicolumn{1}{c|}{dg}&\multicolumn{1}{c|}{cg}&\multicolumn{1}{c|}{mg}\\
+\hline
+&&&&&&\\
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (G1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em]
+    (F1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em]
+    (E1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em]
+    (D1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em]
+    (C1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em]
+    (B1);}}&%
+\multicolumn{1}{c}{\tikz[remember picture,overlay]{\coordinate[yshift=1em] (A1);}}\\%
+\end{tabular}
+\]
+\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);}
+}{}%
+  }%
+  {}%
+}%
\ No newline at end of file
diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check
index fbb626c771b..96a72a4cf30 100755
--- a/Master/tlpkg/bin/tlpkg-ctan-check
+++ b/Master/tlpkg/bin/tlpkg-ctan-check
@@ -600,7 +600,7 @@ my @TLP_working = qw(
     prelim2e preprint prerex present
     pressrelease prettyref preview prftree
     principia printlen proba probsoln procIAGssymp
-    prodint productbox program
+    prodint productbox profcollege program
     progress progressbar
     proof-at-the-end proofread prooftrees proposal properties
     prosper protex protocol prtec przechlewski-book
diff --git a/Master/tlpkg/libexec/ctan2tds b/Master/tlpkg/libexec/ctan2tds
index 30a16d0a4a1..a8ea6838022 100755
--- a/Master/tlpkg/libexec/ctan2tds
+++ b/Master/tlpkg/libexec/ctan2tds
@@ -1024,6 +1024,7 @@ chomp (my $ctan_root = `tlpkginfo --ctan-root`);
  'presentations',     "die 'skipping, author request'",
  'presentations-en',  "die 'skipping, author request'",
  'preview-latex',     "die 'skipping, use preview'",
+ 'profcollege', "&MAKEflatten",
  'progkeys',    "die 'skipping, noinfo license, author unfindable'",
  'proofs',      "die 'skipping, nosell license'",
  'ps2eps',      "die 'skipping, must go into sources'",
@@ -2092,6 +2093,7 @@ $standardtex
  'pdfx',        '\.(def|dfu|icc|xmp)$|(glyph|Profiles).*tex|pdfx\.sty|ICC_LIC',
  'pdfxup',	'(template\.tex|\.xup)$',
  'petri-nets',  'pnets\.tex|pntext\.tex|\.sty|pndraw\.tex|pnversion\.tex|\.sty|pndraw\.tex',
+ 'profcollege',	'PfC-.*\.tex|' . $standardtex,
  'pgf-blur',    'tikzlibraryshadows.blur.code.tex',
  'pgf-spectra', 'spectra.data.tex|' . $standardtex,
  'pgfmolbio',   'pgfmolbio\..*\.|' . $standardtex, # .lua+.tex submodules
diff --git a/Master/tlpkg/tlpsrc/collection-langfrench.tlpsrc b/Master/tlpkg/tlpsrc/collection-langfrench.tlpsrc
index 3ee50eaea95..93f83cf78d2 100644
--- a/Master/tlpkg/tlpsrc/collection-langfrench.tlpsrc
+++ b/Master/tlpkg/tlpsrc/collection-langfrench.tlpsrc
@@ -32,6 +32,7 @@ depend l2tabu-french
 depend latex2e-help-texinfo-fr
 depend lshort-french
 depend mafr
+depend profcollege
 depend tabvar
 depend tdsfrmath
 depend texlive-fr
diff --git a/Master/tlpkg/tlpsrc/profcollege.tlpsrc b/Master/tlpkg/tlpsrc/profcollege.tlpsrc
new file mode 100644
index 00000000000..e69de29bb2d
--- /dev/null
+++ b/Master/tlpkg/tlpsrc/profcollege.tlpsrc