repere (21jun16)

git-svn-id: svn://tug.org/texlive/trunk@41513 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 557 insertions, 236 deletions

diff --git a/Master/texmf-dist/metapost/repere/repere.mp b/Master/texmf-dist/metapost/repere/repere.mp
index 1d8b70c73a5..2b6d86e5b8b 100644
--- a/Master/texmf-dist/metapost/repere/repere.mp
+++ b/Master/texmf-dist/metapost/repere/repere.mp
@@ -1,8 +1,8 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%                        repere.mp                           %%
 %%   Macros pour la construction de figures dans un repère    %%
-%%                    o.peault@gmail.com                      %%
-%%               Version 13.12 (Décembre 2013)                %%
+%%                 o.peault@openmailbox.org                   %%
+%%                 Version 16.06 (Juin 2016)                  %%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %
 % This work may be distributed and/or modified under the conditions of
@@ -13,18 +13,20 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 input format;
+if not known mplib: input latexmp fi;
 
 warningcheck:=0;
 
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%   REPERE   %%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 numeric _nfig,_nbaxes,theta,taillegrad,taillepoint,taillecroix,facteurx,facteury;
-boolean flecheaxe,displayfrac,coupe;
+boolean flecheaxe,displayfrac,coupe,boolgradxpart,boolgradypart;
 _nfig:=1;
 path cadre;
 numeric _diag,_largcadre,_hautcadre,_tfig;
-pair _O,_I,_J;
+pair _O,_I,_J,_O_;
 transform _T;
 picture _axorlab; pair poslabO;
 
@@ -35,10 +37,35 @@ facteury:=1;
 boolean rep_groupe;
 rep_groupe:=false;
 
+%%%%%%%%%%% Sauvegarde macros plain
 
 let oldbeginfig=beginfig;
 let oldendfig=endfig;
 
+let olddraw = draw;
+let olddrawarrow = drawarrow;
+let olddrawdblarrow = drawdblarrow;
+let oldfill = fill;
+vardef theoldlabel@#(expr s,z) =  % Position s near z
+  save p; picture p;
+  if picture s:  p=s
+  else:    p = s infont defaultfont scaled defaultscale
+  fi;
+  p shifted (z + labeloffset*laboff@# -
+     (labxf@#*lrcorner p + labyf@#*ulcorner p
+       + (1-labxf@#-labyf@#)*llcorner p
+     )
+  )
+enddef;
+vardef oldbbox primary p =
+  llcorner p-(bboxmargin,bboxmargin) -- lrcorner p+(bboxmargin,-bboxmargin)
+  -- urcorner p+(bboxmargin,bboxmargin) -- ulcorner p+(-bboxmargin,bboxmargin)
+  -- cycle
+enddef;
+
+
+%%%%%%% Redéfinition beginfig
+
 def beginfig(expr c)=
   oldbeginfig(c);
   _nfig:=c;
@@ -51,9 +78,11 @@ def endfig=
   rep_groupe:=false
 enddef;
 
+
+%%%%%%%%%% Définition du repère
+
 vardef repere@#(text t)=
  if (str @#="") or (str @#="larg") or (str @#="orth") or (str @#="prop"): 
-%    _nfig:=_nfig+1;definitionrepere@#(t)
     definitionrepere@#(t)
  else:
     reperenum@#(t)
@@ -84,15 +113,73 @@ vardef definitionrepere@#(text t) =
   _T:=identity xscaled Ux yscaled Uy slanted cosd(theta) yscaled sind(theta);
   _defcadre;
   settout(Xmin,Xmax,Ymin,Ymax);
-  _O:=_c(0,0); xO:=0 ; yO:=0;
-  _I:=_c(1,0); _J:=_c(0,1);
+  _O:=_cart(0,0); xO:=0 ; yO:=0;_O_:=(0,0);
+  _I:=_cart(1,0); _J:=_cart(0,1);
   taillegrad:=0.8mm;taillepoint:=3;taillecroix:=1mm;_nbaxes:=0;_axorlab:=nullpicture;poslabO:=(0,0);
   marque_p := "plein";displayfrac:=false;flecheaxe:=true;coupe:=true;
+  boolgradxpart:=true;boolgradypart:=true;
   defaultscale:=1;
   unitex:=abs(_I);unitey:=abs(_J);unite:=unitex;
   facteurx:=1;facteury:=1;
   string extranumx,extranumy;
   extranumx=extranumy="";
+  init_traces;
+enddef;
+
+%%%% Initialisations tracés (redéfinition draw etc.)
+def init_traces =
+  %% draw
+  def draw expr p =
+    addto currentpicture
+    if picture p:
+      also p
+    else:
+      doublepath p transformed _T withpen currentpen
+    fi
+    _op_
+  enddef;
+  %% fill
+  def fill expr c =
+    if path c:
+       addto currentpicture contour (c transformed _T) _op_
+    else:
+      olddraw c
+    fi
+  enddef;
+  %% thelabel
+  vardef thelabel@#(expr s,z) =  % Position s near z
+    save p; picture p;
+    if picture s:  p=s
+    else:    p = s infont defaultfont scaled defaultscale
+    fi;
+    p shifted (_cart(z) + labeloffset*laboff@# -
+       (labxf@#*lrcorner p + labyf@#*ulcorner p
+         + (1-labxf@#-labyf@#)*llcorner p
+       )
+    )
+  enddef;
+  %% drawarrow
+  def drawarrow expr p = _apth:=p transformed _T; _finarr enddef;
+  def drawdblarrow expr p = _apth:=p transformed _T; _findarr enddef;
+  %% bbox
+  vardef bbox primary p =
+    if picture p: oldbbox p transformed inverse _T
+    else: oldbbox p
+    fi
+  enddef;
+enddef;
+
+def _finarr text t =
+  olddraw _apth t;
+  filldraw arrowhead _apth  t
+enddef;
+
+vardef arrowhead expr p = %redéfinition flèches
+  save q,e; path q; pair e;
+  e = point length p of p;
+  q = gobble(p shifted -e cutafter makepath(pencircle scaled 2ahlength))
+    cuttings;
+  (q rotated .5ahangle & reverse q rotated -.5ahangle -- 0.5*(point 0 of q)-- cycle)  shifted e
 enddef;
 
 def setaxes(expr a,b,c,d)=
@@ -121,16 +208,19 @@ enddef;
 let setall=settout;
 
 def fin =
-  if _nbaxes=1: draw _axorlab fi;
-  if coupe: clip currentpicture to cadre fi;
+  if _nbaxes=1: olddraw _axorlab fi;
+  if coupe: clip currentpicture to (cadre transformed _T) fi;
   if bf: oldendfig; bf:=false;_nfig:=_nfig+1 fi;
 enddef;
 
 def _defcadre=
-   cadre:=_c(Xmin,Ymin)--_c(Xmin,Ymax)--_c(Xmax,Ymax)--_c(Xmax,Ymin)--cycle;
+   cadre:=(Xmin,Ymin)--(Xmin,Ymax)--(Xmax,Ymax)--(Xmax,Ymin)--cycle;
    _diag:=abs(llcorner cadre - urcorner cadre);
+   _diag_:=abs(llcorner _cart(cadre) - urcorner _cart(cadre));
    _largcadre:=abs(llcorner cadre - lrcorner cadre);
+   _largcadre_:=abs(llcorner _cart(cadre) - lrcorner _cart(cadre));
    _hautcadre:=abs(llcorner cadre - ulcorner cadre);
+   _hautcadre_:=abs(llcorner _cart(cadre) - ulcorner _cart(cadre));
    _tfig:=max(_largcadre,_hautcadre);         % compatibilité geometriesyr
 enddef;
 
@@ -139,7 +229,7 @@ enddef;
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 def interaxes(expr a,b) =
-  _O:=_c(a,b);
+  _O:=_cart(a,b);_O_:=(a,b);
   xO:=a;
   yO:=b;
 enddef;
@@ -163,7 +253,7 @@ vardef _etiqx_@#(expr ab,dec,st)=   %étiquettes axe des abscisses
   if numeric st: pic:=LaTeX("$\num{" & decimal(st) & extranumx & "}$")
   elseif string st: pic:=LaTeX(st)
   else: pic:=st fi;
-  thelabel.@#(pic,_c(ab,yO) shifted (dec*_posgradx@#))
+  theoldlabel.@#(pic,_cart(ab,yO) shifted (dec*_posgradx@#))
 enddef;
 
 vardef _etiqy_@#(expr ro,dec,st)=   %étiquettes axe des ordonnées
@@ -172,17 +262,17 @@ vardef _etiqy_@#(expr ro,dec,st)=   %étiquettes axe des ordonnées
   if numeric st: pic:=LaTeX("$\num{" & decimal(st) & extranumy & "}$")
   elseif string st: pic:=LaTeX(st)
   else: pic:=st fi;
-  thelabel.@#(pic,_c(xO,ro) shifted (dec*_posgrady@#))
+  theoldlabel.@#(pic,_cart(xO,ro) shifted (dec*_posgrady@#))
 enddef;
 
 
 vardef graduationx(expr x)=          %%%%%%% graduation axe des abscisses
-   ((0,taillegrad)--(0,-taillegrad)) rotated (theta-90) shifted _c(x,yO)
+   ((0,taillegrad)--(0,-taillegrad)) rotated (theta-90) shifted _cart(x,yO)
 enddef;
 
 
 vardef graduationy(expr y)=          %%%%%%% graduation axe des ordonnées
-   ((taillegrad,0)--(-taillegrad,0)) shifted _c(xO,y)
+   ((taillegrad,0)--(-taillegrad,0)) shifted _cart(xO,y)
 enddef;
 
 vardef etiquettex@#(expr x)=
@@ -195,9 +285,9 @@ vardef etiquettey@#(expr y)=
 enddef;
 
 
-vardef dessinaxex=_c(AxeXmin,yO)--_c(AxeXmax,yO) enddef;
+vardef dessinaxex=_cart(AxeXmin,yO)--_cart(AxeXmax,yO) enddef;
 
-vardef dessinaxey=_c(xO,AxeYmin)--_c(xO,AxeYmax) enddef;
+vardef dessinaxey=_cart(xO,AxeYmin)--_cart(xO,AxeYmax) enddef;
 
 
 vardef graduationsaxex(expr grad)=      %%%% ensemble des graduations abscisses
@@ -205,10 +295,10 @@ vardef graduationsaxex(expr grad)=      %%%% ensemble des graduations abscisses
    $=image(%
     imax:=floor((GradXmax-xO)/grad);imin:=ceiling((GradXmin-xO)/grad);
     for i=imin upto imax-1:
-     draw graduationx(arrondimil(i*grad)+xO) withpen pencircle scaled 0.5bp;
+     olddraw graduationx(arrondimil(i*grad)+xO) withpen pencircle scaled 0.5bp;
     endfor
     % dernière graduation
-    if AxeXmax*Ux-(imax*grad+xO)*Ux>ahlength: draw graduationx(arrondimil(imax*grad)+xO) withpen pencircle scaled 0.5bp fi);
+    if AxeXmax*Ux-(imax*grad+xO)*Ux>ahlength: olddraw graduationx(arrondimil(imax*grad)+xO) withpen pencircle scaled 0.5bp fi);
    $
 enddef;
 
@@ -217,10 +307,10 @@ vardef graduationsaxey(expr grad)=      %%%% ensemble des graduations ordonnées
    $=image(%
     imax:=floor((GradYmax-yO)/grad);imin:=ceiling((GradYmin-yO)/grad);
     for i=imin upto imax-1:
-     draw graduationy(arrondimil(i*grad)+yO) withpen pencircle scaled 0.5bp;
+     olddraw graduationy(arrondimil(i*grad)+yO) withpen pencircle scaled 0.5bp;
     endfor;
     % dernière graduation
-    if AxeYmax*Uy-(imax*grad+yO)*Uy>ahlength: draw graduationy(arrondimil(imax*grad)+yO) withpen pencircle scaled 0.5bp fi);
+    if AxeYmax*Uy-(imax*grad+yO)*Uy>ahlength: olddraw graduationy(arrondimil(imax*grad)+yO) withpen pencircle scaled 0.5bp fi);
    $
 enddef;
 
@@ -242,15 +332,15 @@ vardef etiquettesaxex@#(expr val)=       %%% ensemble des étiquettes abscisses
 	   else: labmax:=nullpicture
    	fi;
    	% tracé première étiquette
-	   if xpart ((ulcorner labmin) transformed inverse _T)>=Xmin: draw labmin fi;
+	   if xpart ((ulcorner labmin) transformed inverse _T)>=Xmin: olddraw labmin fi;
    	% tracé autres étiquettes
    	for i=imin+1 upto imax-1:
     		if (i<>0):
-    		  draw etiquettex.@#(arrondimil(i*val)+xO)
+    		  olddraw etiquettex.@#(arrondimil(i*val)+xO)
     		fi;
    	endfor;
    	% tracé dernière étiquette
-   	if xpart ((lrcorner labmax) transformed inverse _T)<=Xmax: draw labmax fi;
+   	if xpart ((lrcorner labmax) transformed inverse _T)<=Xmax: olddraw labmax fi;
         );
       $
 enddef;
@@ -272,15 +362,15 @@ vardef etiquettesaxey@#(expr val)=       %%% ensemble des étiquettes ordonnées
 	   else: labmax:=nullpicture
    	fi;
    	% tracé première étiquette
-   	if ypart (llcorner labmin) >=ypart _c(Xmin,Ymin): draw labmin fi;
+   	if ypart (llcorner labmin) >=ypart _cart(Xmin,Ymin): olddraw labmin fi;
    	% tracé autres étiquettes
    	for i=imin+1 upto imax-1:
     		if (i<>0):
-    		  draw etiquettey.@#(arrondimil(i*val)+yO)
+    		  olddraw etiquettey.@#(arrondimil(i*val)+yO)
     		fi;
    	endfor;
    	% tracé dernière étiquette
-   	if ypart (ulcorner labmax) <=ypart _c(Xmax,Ymax): draw labmax fi
+   	if ypart (ulcorner labmax) <=ypart _cart(Xmax,Ymax): olddraw labmax fi
          );
       $
 enddef;
@@ -290,38 +380,38 @@ vardef _axex_@#(expr grad,val,nn)=
    picture $;
    $=image(
    %    axe
-   if flecheaxe: drawarrow  else: draw fi dessinaxex;
+   if flecheaxe: olddrawarrow  else: olddraw fi dessinaxex;
    %    graduations
-   if grad>0: draw graduationsaxex(grad) fi;
+   if grad>0: olddraw graduationsaxex(grad) fi;
    %    étiquettes
    if val>0:
    	if nn=1:
 	       if str @#<>"":
-		  draw etiquettesaxex@#(val);
+		  olddraw etiquettesaxex@#(val);
 		  _axorlab:=etiquettex@#(xO)
 	       else:
-		  draw etiquettesaxex.bot(val);
+		  olddraw etiquettesaxex.bot(val);
 		  _axorlab:=etiquettex.bot(xO)
 	       fi;
 	       poslabO:=poslabO + unitvector(0,ypart _posgradx@#);
 	       if xO<>yO:
-		  draw _axorlab
+		  olddraw _axorlab
 	       elseif _nbaxes=2:
-		  draw _etiqx_(xO,0,xO) shifted (0.7*abs(llcorner _axorlab - urcorner _axorlab)*poslabO)
+		  olddraw _etiqx_(xO,0,xO) shifted (0.7*abs(llcorner _axorlab - urcorner _axorlab)*poslabO)
 	       fi
 	elseif nn=2:
 	       if str @#<>"":
-		  draw etiquettesaxex@#(val);
-		  draw etiquettex@#(xO)
+		  olddraw etiquettesaxex@#(val);
+		  olddraw etiquettex@#(xO)
 	       else:
-		  draw etiquettesaxex.bot(val);
-		  draw etiquettex.bot(xO)
+		  olddraw etiquettesaxex.bot(val);
+		  olddraw etiquettex.bot(xO)
 	       fi
 	else:
 	       if str @#<>"":
-		  draw etiquettesaxex@#(val)
+		  olddraw etiquettesaxex@#(val)
 	       else:
-		  draw etiquettesaxex.bot(val)
+		  olddraw etiquettesaxex.bot(val)
 	       fi
 	fi
    fi
@@ -334,38 +424,38 @@ vardef _axey_@#(expr grad,val,nn)=
    picture $;
    $=image(
    %    axe
-   if flecheaxe: drawarrow  else: draw fi dessinaxey;
+   if flecheaxe: olddrawarrow  else: olddraw fi dessinaxey;
    %    graduations
-   if grad>0: draw graduationsaxey(grad) fi;
+   if grad>0: olddraw graduationsaxey(grad) fi;
    %    étiquettes
    if val>0:
    	if nn=1:
 	       if str @#<>"":
-		  draw etiquettesaxey@#(val);
+		  olddraw etiquettesaxey@#(val);
 		  _axorlab:=etiquettey@#(yO)
 	       else:
-		  draw etiquettesaxey.lft(val);
+		  olddraw etiquettesaxey.lft(val);
 		  _axorlab:=etiquettey.lft(yO)
 	       fi;
 	       poslabO:=poslabO + unitvector(xpart _posgrady@#,0);
 	       if xO<>yO:
-		  draw _axorlab
+		  olddraw _axorlab
 	       elseif _nbaxes=2:
-		  draw _etiqy_(yO,0,yO) shifted (0.7*abs(llcorner _axorlab - urcorner _axorlab)*poslabO)
+		  olddraw _etiqy_(yO,0,yO) shifted (0.7*abs(llcorner _axorlab - urcorner _axorlab)*poslabO)
 	       fi
 	elseif nn=2:
 	       if str @#<>"":
-		  draw etiquettesaxey@#(val);
-		  draw etiquettey@#(yO)
+		  olddraw etiquettesaxey@#(val);
+		  olddraw etiquettey@#(yO)
 	       else:
-		  draw etiquettesaxey.lft(val);
-		  draw etiquettey.lft(yO)
+		  olddraw etiquettesaxey.lft(val);
+		  olddraw etiquettey.lft(yO)
 	       fi
 	else:
 	       if str @#<>"":
-		  draw etiquettesaxey@#(val)
+		  olddraw etiquettesaxey@#(val)
 	       else:
-		  draw etiquettesaxey.lft(val)
+		  olddraw etiquettesaxey.lft(val)
 	       fi
 	fi
    fi
@@ -535,7 +625,7 @@ vardef etiquettesaxeypi@#(expr n,d)=       %%% ensemble des étiquettes multiple
 	   else: labmax:=nullpicture
    	fi;
    	% tracé première étiquette
-   	if ypart (llcorner labmin) >=ypart _c(Xmin,Ymin): draw labmin fi;
+   	if ypart (llcorner labmin) >=ypart _cart(Xmin,Ymin): draw labmin fi;
    	% tracé autres étiquettes
    	for i=imin+1 upto imax-1:
     		if (i<>0):
@@ -543,7 +633,7 @@ vardef etiquettesaxeypi@#(expr n,d)=       %%% ensemble des étiquettes multiple
     		fi;
    	endfor;
    	% tracé dernière étiquette
-   	if ypart (ulcorner labmax) <=ypart _c(Xmax,Ymax): draw labmax fi
+   	if ypart (ulcorner labmax) <=ypart _cart(Xmax,Ymax): draw labmax fi
          );
       $
 enddef;
@@ -555,7 +645,7 @@ vardef _axexpi_@#(expr num,den,nn)=
    grad:=num*pi/den;
    $=image(
    %    axe
-   if flecheaxe: drawarrow  else: draw fi dessinaxex;
+   if flecheaxe: olddrawarrow  else: olddraw fi dessinaxex;
    %    graduations
    if grad>0: draw graduationsaxex(grad) fi;
    %    étiquettes
@@ -599,7 +689,7 @@ vardef _axeypi_@#(expr num,den,nn)=
    grad:=num*pi/den;
    $=image(
    %    axe
-   if flecheaxe: drawarrow  else: draw fi dessinaxey;
+   if flecheaxe: olddrawarrow  else: olddraw fi dessinaxey;
    %    graduations
    if grad>0: draw graduationsaxey(grad) fi;
    %    étiquettes
@@ -715,8 +805,9 @@ vardef axexpart@#(text t)=
 	for _i=t:
 	   if numeric _i:
 		if var: if str @#="": draw _etiqx_.bot(tmp,taillegrad,tmp) else: draw _etiqx_@#(tmp,taillegrad,tmp) fi fi;
-%		draw ((0,taillegrad)--(0,-taillegrad)) shifted _c(_i,yO) withpen pencircle scaled 0.8bp;
-		draw graduationx(_i) withpen pencircle scaled 0.8bp;
+		if boolgradxpart:
+		   draw graduationx(_i) withpen pencircle scaled 0.8bp
+		fi;
 		tmp:=_i;
 		var:=true
 	   else:
@@ -738,7 +829,7 @@ vardef axeypart@#(text t)=
 	for _i=t:
 	   if numeric _i:
 		if var: if str @#="": draw _etiqy_.lft(tmp,taillegrad,tmp) else: draw _etiqy_@#(tmp,taillegrad,tmp) fi fi;
-		draw ((taillegrad,0)--(-taillegrad,0)) shifted _c(xO,_i) withpen pencircle scaled 0.8bp;
+		draw ((taillegrad,0)--(-taillegrad,0)) shifted _cart(xO,_i) withpen pencircle scaled 0.8bp;
 		tmp:=_i;
 		var:=true
 	   else:
@@ -758,8 +849,8 @@ vardef axesunit=
         draw axes(0,0);
         draw axexpart(1);
         draw axeypart(1);
-        label.llft(LaTeX("$0$"),_c(0,0));
- %       label.llft("0",_c(0,0));
+        label.llft(LaTeX("$0$"),_cart(0,0));
+ %       label.llft("0",_cart(0,0));
           );
   $
 enddef;
@@ -773,22 +864,33 @@ vardef _ccoord(expr xA,yA)=
    (xA,yA) transformed _T
 enddef;
 
+vardef _coord(expr xA,yA)=
+   (xA,yA)
+enddef;
+
 vardef _cobjet(expr obj)=
    obj transformed _T
 enddef;
 
-vardef _c(text t)=
+vardef _cart(text t)=
    if long_texte(t)=2: _ccoord(t)
       else: _cobjet(t)
    fi
 enddef;
 
+vardef _c(text t)=
+   if long_texte(t)=2: _coord(t)
+   else: t
+   fi
+enddef;
+
+
 vardef pol(expr r,theta)=
- _c(r*cos(theta),r*sin(theta))
+ (r*cos(theta),r*sin(theta))
 enddef;
 
 vardef pold(expr r,theta)=
- _c(r*cosd(theta),r*sind(theta))
+ (r*cosd(theta),r*sind(theta))
 enddef;
 
 color coulpoint,coullabel,coullabelfonc;
@@ -799,15 +901,15 @@ vardef MarquePointFig(expr pp)=      % compatibilité geometriesyr15
  save $;
  picture $;
   if marque_p = "plein":
-    $:=image(fill fullcircle scaled taillepoint shifted pp withcolor coulpoint);
+    $:=image(oldfill fullcircle scaled taillepoint shifted _cart(pp) withcolor coulpoint);
   elseif marque_p = "creux":
     $:=image(%
-    fill fullcircle scaled taillepoint shifted pp withcolor background;
-    draw fullcircle scaled taillepoint shifted pp withcolor coulpoint);
+    oldfill fullcircle scaled taillepoint shifted _cart(pp) withcolor background;
+    olddraw fullcircle scaled taillepoint shifted _cart(pp) withcolor coulpoint);
   elseif marque_p = "croix":
   $:=image(%
-    draw ((-taillecroix,0)--(taillecroix,0)) shifted pp withcolor coulpoint;
-    draw ((0,-taillecroix)--(0,taillecroix)) shifted pp withcolor coulpoint)
+    olddraw ((-taillecroix,0)--(taillecroix,0)) shifted _cart(pp) withcolor coulpoint;
+    olddraw ((0,-taillecroix)--(0,taillecroix)) shifted _cart(pp) withcolor coulpoint)
   else: $:=nullpicture
   fi;
   $
@@ -850,12 +952,12 @@ vardef nommecourbe@#(suffix p)(text t)=
    picture dess;
    if long_texte(t)=1: 
       dess:=image(ch:=_chaine(p);
-                  A:=_c(t,fonccourbe.p(t));
+                  A:=(t,fonccourbe.p(t));
                   label@#(LaTeX("$" & ch & "$"),A) withcolor coullabelfonc)
    else:
       dess:=image(%
         for _a=t:
-          if numeric _a: A:=_c(_a,fonccourbe.p(_a))
+          if numeric _a: A:=(_a,fonccourbe.p(_a))
           else: if string _a: label@#(_a,A) else: label@#(_a scaled defaultscale,A) fi withcolor coullabelfonc
           fi;
         endfor)
@@ -868,12 +970,15 @@ enddef;
 vardef nommeobj@#(text t)=
  save $;
  picture $;
+ if long_texte(t)=4: $:=nommeangle@#(t)
+ else:
    for i=t:
      if pair i: $:=nommepoint@#(t)
      else: $:=nommecourbe@#(t)
      fi;
      exitif true;
    endfor
+ fi;
    $
 enddef;
 
@@ -886,11 +991,11 @@ vardef vecteur@#(expr A)(text t)=
    pair m;
    string ch;
    $=image(%
-   if long_texte(t)=1: drawarrow A--A+t;ch:=_chaine(t);label@#(LaTeX("$\vect{" & ijmath(ch) & "}$"),A+t/2)
+   if long_texte(t)=1: drawarrow A--A+t;ch:=_chaine(t);label@#(LaTeX("$\vv{" & ijmath(ch) & "}$"),A+t/2)
    else:
       for u=t:
         if pair u: drawarrow A--A+u; m:=A+u/2
-        else: if string u: if u<>"": label@#(LaTeX("$\vect{" & u & "}$"),m) fi else: label@#(u,m) fi
+        else: if string u: if u<>"": label@#(LaTeX("$\vv{" & u & "}$"),m) fi else: label@#(u,m) fi
         fi;
       endfor
    fi);
@@ -902,7 +1007,7 @@ vardef marquepointcourbefig(suffix p)(text t)=
    picture $;
    $=image(%
    for i=t:
-     MarquePoint(_c(i,fonccourbe.p(i)));
+     MarquePoint((i,fonccourbe.p(i)));
    endfor);
    $
 enddef;
@@ -924,24 +1029,24 @@ def marquepointchemin= draw marquepointcheminfig enddef;
 vardef marquecheminouvertdroitefig(expr p)=
    halfcircle shifted (0,-0.5)
               scaled (2*taillepoint)
-              rotated (90+angle(direction infinity of p))
-              shifted (point infinity of p)
+              rotated (90+angle(direction infinity of _cart(p)))
+              shifted (point infinity of _cart(p))
 enddef;
 
-def marquecheminouvertdroite= draw marquecheminouvertdroitefig enddef;
+def marquecheminouvertdroite= olddraw marquecheminouvertdroitefig enddef;
 
 vardef marquecheminouvertgauchefig(expr p)=
    halfcircle shifted (0,-0.5)
               scaled (2*taillepoint)
-              rotated (-90+angle(direction 0 of p))
-              shifted (point 0 of p)
+              rotated (-90+angle(direction 0 of _cart(p)))
+              shifted (point 0 of _cart(p))
 enddef;
 
-def marquecheminouvertgauche= draw marquecheminouvertgauchefig enddef;
+def marquecheminouvertgauche= olddraw marquecheminouvertgauchefig enddef;
 
-vardef marquecheminouvert(expr p)=
-   marquecheminouvertdroite(p);
-   marquecheminouvertgauche(p)
+def marquecheminouvert(expr p) text t=
+   marquecheminouvertdroite(p) t;
+   marquecheminouvertgauche(p) t
 enddef;
 
 
@@ -964,9 +1069,9 @@ vardef base(suffix a,b,c)=
  picture $;
  O:=_chaine(a); I:=_chaine(b); J:=_chaine(c);
  $:=image(%
- draw vecteur.bot(_O,_c(1,0),ijmath(I)) withpen pencircle scaled 0.8 withcolor coulbase;
- draw vecteur.lft(_O,_c(0,1),ijmath(J)) withpen pencircle scaled 0.8 withcolor coulbase;
- nomme.llft(_O,LaTeX("$" & O & "$")) withcolor coulbase
+ draw vecteur.bot(_O_,(1,0),ijmath(I)) withpen pencircle scaled 0.8 withcolor coulbase;
+ draw vecteur.lft(_O_,(0,1),ijmath(J)) withpen pencircle scaled 0.8 withcolor coulbase;
+ nomme.llft(_O_,LaTeX("$" & O & "$")) withcolor coulbase
  );
  $
 enddef;
@@ -978,7 +1083,7 @@ vardef basep(suffix a,b,c)=
  picture $;
  O:=_chaine(a); I:=_chaine(b); J:=_chaine(c);
  $:=image(%
- nomme.llft(_O,LaTeX("$" & O & "$")) withcolor coulbase;
+ nomme.llft(_O_,LaTeX("$" & O & "$")) withcolor coulbase;
  draw axexpart(1,LaTeX("$" & I & "$")) withcolor coulbase;
  draw axeypart(1,LaTeX("$" & J & "$")) withcolor coulbase;
  );
@@ -990,7 +1095,7 @@ enddef;
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
   numeric ep; color coul;
-  ep:= .2bp;                    %%%%%%%% épaisseur du trait
+  ep:= .3bp;                    %%%%%%%% épaisseur du trait
   coul := .7white;              %%%%%%%% couleur du trait
   def quadstyle= enddef;
 
@@ -999,12 +1104,12 @@ enddef;
    picture $;
  $=image(if quadx>0:
     for i=ceiling((QuadXmin-xO)/quadx) upto floor((QuadXmax-xO)/quadx):
-     draw _c(arrondimil(i*quadx)+xO,QuadYmin)--_c(arrondimil(i*quadx)+xO,QuadYmax) quadstyle withpen pencircle scaled ep withcolor coul;
+     olddraw _cart(arrondimil(i*quadx)+xO,QuadYmin)--_cart(arrondimil(i*quadx)+xO,QuadYmax) quadstyle withpen pencircle scaled ep withcolor coul;
     endfor;
   fi;
   if quady>0:
     for i=ceiling((QuadYmin-yO)/quady) upto floor((QuadYmax-yO)/quady):
-     draw _c(QuadXmin,arrondimil(i*quady)+yO)--_c(QuadXmax,arrondimil(i*quady)+yO) withpen pencircle scaled ep withcolor coul quadstyle;
+     olddraw _cart(QuadXmin,arrondimil(i*quady)+yO)--_cart(QuadXmax,arrondimil(i*quady)+yO) withpen pencircle scaled ep withcolor coul quadstyle;
     endfor;
   fi);
   $
@@ -1016,7 +1121,7 @@ enddef;
  $=image(if (quadx>0) and (quady>0):
     for i=ceiling(QuadXmin/quadx) upto floor(QuadXmax/quadx):
       for j=ceiling(QuadYmin/quady) upto floor(QuadYmax/quady):
-        draw (0,0) shifted _c(i*quadx,j*quady) withpen pencircle scaled 2;
+        olddraw (0,0) shifted _cart(i*quadx,j*quady) withpen pencircle scaled 2;
       endfor;
     endfor;
   fi);
@@ -1033,24 +1138,24 @@ vardef papiermillimetre =
   picture $;
   $=image(%
   for i= ceiling(QuadXmin*Ux*10/cm) upto floor(QuadXmax*Ux*10/cm):
-    if i mod 5 <> 0: draw (i*cm/10,QuadYmin*Uy)--(i*cm/10,QuadYmax*Uy) withpen pencircle scaled pm_epa withcolor pm_coula fi;
+    if i mod 5 <> 0: olddraw (i*cm/10,QuadYmin*Uy)--(i*cm/10,QuadYmax*Uy) withpen pencircle scaled pm_epa withcolor pm_coula fi;
   endfor
   for i= ceiling(QuadYmin*Uy*10/cm) upto floor(QuadYmax*Uy*10/cm):
-    if i mod 5<> 0: draw (QuadXmin*Ux,i*cm/10)--(QuadXmax*Ux,i*cm/10) withpen pencircle scaled pm_epa withcolor pm_coula fi;
+    if i mod 5<> 0: olddraw (QuadXmin*Ux,i*cm/10)--(QuadXmax*Ux,i*cm/10) withpen pencircle scaled pm_epa withcolor pm_coula fi;
   endfor
   %
   for i= ceiling(QuadXmin*Ux/cm)*2+1 step 2 until floor(QuadXmax*Ux/cm)*2-1:
-    draw (i*cm/2,QuadYmin*Uy)--(i*cm/2,QuadYmax*Uy) withpen pencircle scaled pm_epb withcolor pm_coulb;
+    olddraw (i*cm/2,QuadYmin*Uy)--(i*cm/2,QuadYmax*Uy) withpen pencircle scaled pm_epb withcolor pm_coulb;
   endfor
   for i= ceiling(QuadYmin*Uy/cm)*2+1 step 2 until floor(QuadYmax*Uy/cm)*2-1:
-    draw (QuadXmin*Ux,i*cm/2)--(QuadXmax*Ux,i*cm/2) withpen pencircle scaled pm_epb withcolor pm_coulb;
+    olddraw (QuadXmin*Ux,i*cm/2)--(QuadXmax*Ux,i*cm/2) withpen pencircle scaled pm_epb withcolor pm_coulb;
   endfor
   %
   for i= ceiling(QuadXmin*Ux/cm) upto floor(QuadXmax*Ux/cm):
-    draw (i*cm,QuadYmin*Uy)--(i*cm,QuadYmax*Uy) withpen pencircle scaled pm_epc withcolor pm_coulc;
+    olddraw (i*cm,QuadYmin*Uy)--(i*cm,QuadYmax*Uy) withpen pencircle scaled pm_epc withcolor pm_coulc;
   endfor
   for i= ceiling(QuadYmin*Uy/cm) upto floor(QuadYmax*Uy/cm):
-    draw (QuadXmin*Ux,i*cm)--(QuadXmax*Ux,i*cm) withpen pencircle scaled pm_epc withcolor pm_coulc;
+    olddraw (QuadXmin*Ux,i*cm)--(QuadXmax*Ux,i*cm) withpen pencircle scaled pm_epc withcolor pm_coulc;
   endfor);
   $
 enddef;
@@ -1060,47 +1165,51 @@ enddef;
 %%%%%%%%%%  FONCTIONS - COURBES   %%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-vardef courbefonc(suffix f)(expr xmin, xmax, n) =   %Courbe représentative d'une fonction
+vardef courbef_(suffix f)(expr xmin, xmax, n) =   %Courbe représentative d'une fonction
    save $,x;
    path $;
-   $=( _c(xmin,f(xmin))
+   $=((xmin,f(xmin))
     for i=1 upto n-1:
-      .._c(xmin+i*(xmax-xmin)/(n-1),f(xmin+i*(xmax-xmin)/(n-1)))
+      ..(xmin+i*(xmax-xmin)/(n-1),f(xmin+i*(xmax-xmin)/(n-1)))
     endfor );
    $
 enddef;
 
-%%%%%%%%%% TEST %%%%%%%%%%%%%
-vardef courbefonct@#(expr xmin, xmax, n) =   %Courbe représentative d'une fonction
-   save $,x;
-   path $;
-   $=( _c(xmin,@#(xmin))
-    for i=1 upto n-1:
-      .._c(xmin+i*(xmax-xmin)/(n-1),@#(xmin+i*(xmax-xmin)/(n-1)))
-    endfor );
-   $
+
+vardef courbefonc(suffix f)(text t)=
+        save cc;path cc;
+        save k,Val;numeric k,Val[];
+        Val[1]:=Xmin;Val[2]:=Xmax;Val[3]:=60;
+        k:=1;
+        for i=t:
+           Val[k]:=i;
+           k:=k+1;
+        endfor
+        courbef_(f,Val[1],Val[2],Val[3])
 enddef;
-%%%%%%%%%% FINTEST %%%%%%%%%%%%%
+
+
+
 
 vardef courbepoints(suffix f)(expr xmin, xmax, n) =  %Points non reliés
    save $,x;
    picture $;
-   $=image(MarquePoint(_c(xmin,f(xmin)));
+   $=image(MarquePoint((xmin,f(xmin)));
            for i=1 upto n-1:
-              MarquePoint(_c(xmin+i*(xmax-xmin)/(n-1),f(xmin+i*(xmax-xmin)/(n-1))));
+              MarquePoint((xmin+i*(xmax-xmin)/(n-1),f(xmin+i*(xmax-xmin)/(n-1))));
            endfor );
    $
 enddef;
 
 vardef fonccourbe@#(expr x)=    %Ordonnée du point de la courbe @# d'abscisse x (dans le repère utilisateur)
-   ypart ((pointcourbe@#(x)) transformed inverse _T)
+   ypart pointcourbe@#(x)
 enddef;
 
 vardef pointcourbe@#(expr x)=   %Point de la courbe @# d'abscisse x dans le repère utilisateur
 save _P_,t;
   numeric t; pair _P_;
-  (t,whatever)=@# intersectiontimes (_c(x,2*Ymin-Ymax)--_c(x,2*Ymax-Ymin));
-  if t=-1: _P_:=_c(x,0)
+  (t,whatever)=@# intersectiontimes ((x,2*Ymin-Ymax)--(x,2*Ymax-Ymin));
+  if t=-1: _P_:=(x,0)
   else: _P_:=point t of @#
   fi;
   _P_
@@ -1111,10 +1220,10 @@ vardef der@#(expr x)=   %Fonction dérivée
    path pp;
    pair v,w;
    pp:=@#;
-   (t,whatever) = pp intersectiontimes (_c(x,2*Ymin-Ymax)--_c(x,2*Ymax-Ymin));
+   (t,whatever) = pp intersectiontimes ((x,2*Ymin-Ymax)--(x,2*Ymax-Ymin));
    v:=direction t of pp;
-   w:=unitvector(v transformed inverse _T);
-   if xpart w = 0: d:=0 else: d:= (ypart w)/(xpart w) fi;
+%   w:=unitvector(v transformed inverse _T);
+   if xpart v = 0: d:=0 else: d:= (ypart v)/(xpart v) fi;
    d
 enddef;
 
@@ -1134,13 +1243,13 @@ vardef intercourbes(suffix P)(expr p,q)= %renvoie les points d'intersections de
 enddef;
 
 vardef ptantecedents(suffix P)(expr y,p)=
-  intercourbes(P,_c(Xmin,y)--_c(Xmax,y),p)
+  intercourbes(P,(Xmin,y)--(Xmax,y),p)
 enddef;
 
 vardef antecedents(suffix P)(expr y,p)=
   pair PP[];
   ptantecedents(PP,y,p);
-  for i=1 upto 10: P[i]:=xpart (PP[i] transformed inverse _T); endfor
+  for i=1 upto 10: P[i]:=xpart (PP[i]); endfor
 enddef;
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -1160,13 +1269,13 @@ senstan.gauche=(1,0);senstan.droite=(0,1);senstan.double=(1,1);
    picture $;
    for n=tt: i:=incr i ; N[i]:=n; endfor;
    if i=1: N2:=longtan fi;
-   (t,whatever) = p intersectiontimes (_c(N1,Ymin)--_c(N1,Ymax));
+   (t,whatever) = p intersectiontimes ((N1,Ymin)--(N1,Ymax));
    M:=point t of p;
    _v:=N2*unitvector(direction t of p);
    $=image(%
 		MarquePoint(M);
-		if (xpart senstan@#) <> 0: drawarrow M--M-_v*(xpart senstan@#) fi;
-		if (ypart senstan@#) <> 0: drawarrow M--M+_v*(ypart senstan@#) fi;
+		if (xpart senstan@#) <> 0: olddrawarrow _cart(M)--_cart(M)-_v*(xpart senstan@#) fi;
+		if (ypart senstan@#) <> 0: olddrawarrow _cart(M)--_cart(M)+_v*(ypart senstan@#) fi;
     );
    $
 enddef;
@@ -1176,7 +1285,7 @@ vardef tangentedroite(expr p,a) =
  path $;
  numeric m,t;
  pair M;
- (t,whatever) = p intersectiontimes (_c(a,Ymin)--_c(a,Ymax));
+ (t,whatever) = p intersectiontimes ((a,Ymin)--(a,Ymax));
  M:=point t of p;
  $=M-_diag*unitvector(direction t of p)--M+_diag*unitvector(direction t of p);
  $
@@ -1198,7 +1307,7 @@ vardef entrecourbes(expr p,q,xmin,xmax)=
 enddef;
 
 vardef souscourbe(expr p,xmin,xmax)=
- buildcycle(droiteeqx(xmax),p,droiteeqx(xmin),_c(Xmin,0)--_c(Xmax,0))
+ buildcycle(droiteeqx(xmax),p,droiteeqx(xmin),(Xmin,0)--(Xmax,0))
 enddef;
 
 
@@ -1209,9 +1318,9 @@ vardef rectangles@#(suffix p)(expr a,b,n)=   %Riemann, renvoie un chemin fermé
  pas=(b-a)/n;
  _rect_ =
  for i=0 upto n-1:
-   _c(a+i*pas,yO)--_segmrect_@#(p,a+i*pas,pas)--
+   (a+i*pas,yO)--_segmrect_@#(p,a+i*pas,pas)--
  endfor
- _c(b,yO)--cycle;
+ (b,yO)--cycle;
  _rect_
 enddef;
 
@@ -1224,8 +1333,8 @@ vardef _segmrect_@#(suffix p)(expr a,pas)=
  _sousp=subpath (xpart(p intersectiontimes droiteeqx(a)),xpart(p intersectiontimes droiteeqx(a+pas))) of p;
  if _typerect@#=1: llcorner _sousp -- lrcorner _sousp
   elseif _typerect@#=2: ulcorner _sousp -- urcorner _sousp
-   elseif _typerect@#=3: (pointcourbe.p(a))--(pointcourbe.p(a) shifted _c(pas,0))
-    elseif _typerect@#=4: (pointcourbe.p(a+pas) shifted _c(-pas,0))--(pointcourbe.p(a+pas))
+   elseif _typerect@#=3: (pointcourbe.p(a))--(pointcourbe.p(a) shifted (pas,0))
+    elseif _typerect@#=4: (pointcourbe.p(a+pas) shifted (-pas,0))--(pointcourbe.p(a+pas))
  fi
 enddef;
 
@@ -1236,15 +1345,15 @@ vardef droiteeqred(expr a,b)=
  save $;
  path $;
  if (-(Ymax-Ymin)/(Xmax-Xmin)<a) and ((Ymax-Ymin)/(Xmax-Xmin)>a):
-  $:=_c(Xmin,a*Xmin+b)--_c(Xmax,a*Xmax+b);
+  $:=(Xmin,a*Xmin+b)--(Xmax,a*Xmax+b);
  else:
-  $:=_c(Ymin/a-b/a,Ymin)--_c(Ymax/a-b/a,Ymax);
+  $:=(Ymin/a-b/a,Ymin)--(Ymax/a-b/a,Ymax);
  fi;
  $
 enddef;
 
 vardef droiteeqx(expr c)=
-  _c(c,2*Ymin-Ymax)--_c(c,2*Ymax-Ymin)
+  (c,2*Ymin-Ymax)--(c,2*Ymax-Ymin)
 enddef;
 
 vardef droiteeqcart(expr a,b,c)=
@@ -1296,10 +1405,10 @@ vardef demiplaninf(expr d)=
    else: B:=point 0 of d; A:= point infinity of d
   fi;
   $=A--
-  if ypart A>=ypart _c(Xmin,Ymax): _c(Xmin,Ymax)-- fi
-  if ypart A>ypart _c(Xmin,Ymin): _c(Xmin,Ymin)-- fi
-  if ypart B>ypart _c(Xmax,Ymin): _c(Xmax,Ymin)-- fi
-  if ypart B>=ypart _c(Xmax,Ymax): _c(Xmax,Ymax)-- fi
+  if ypart A>=ypart (Xmin,Ymax): (Xmin,Ymax)-- fi
+  if ypart A>ypart (Xmin,Ymin): (Xmin,Ymin)-- fi
+  if ypart B>ypart (Xmax,Ymin): (Xmax,Ymin)-- fi
+  if ypart B>=ypart (Xmax,Ymax): (Xmax,Ymax)-- fi
   B--cycle;
   $
 enddef;
@@ -1313,10 +1422,10 @@ vardef demiplansup(expr d)=
    else: B:=point 0 of d; A:= point infinity of d
   fi;
   $=A--
-  if ypart A<=ypart _c(Xmin,Ymin): _c(Xmin,Ymin)-- fi
-  if ypart A<ypart _c(Xmin,Ymax): _c(Xmin,Ymax)-- fi
-  if ypart B<ypart _c(Xmax,Ymax): _c(Xmax,Ymax)-- fi
-  if ypart B<=ypart _c(Xmax,Ymin): _c(Xmax,Ymin)-- fi
+  if ypart A<=ypart (Xmin,Ymin): (Xmin,Ymin)-- fi
+  if ypart A<ypart (Xmin,Ymax): (Xmin,Ymax)-- fi
+  if ypart B<ypart (Xmax,Ymax): (Xmax,Ymax)-- fi
+  if ypart B<=ypart (Xmax,Ymin): (Xmax,Ymin)-- fi
   B--cycle;
   $
 enddef;
@@ -1325,11 +1434,11 @@ enddef;
 %%%%%%%%%%   PROJECTIONS   %%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 vardef projetex(expr A)=
-  _c(xpart (A transformed inverse _T),yO)
+  (xpart (A),yO)
 enddef;
 
 vardef projetey(expr A)=
-  _c(xO,ypart (A transformed inverse _T))
+  (xO,ypart (A))
 enddef;
 
 vardef projectionx@#(text t)=
@@ -1369,8 +1478,8 @@ vardef projectionaxes(text t)=
   for i=t:
    if not numeric i:
      if pair i: _A:=i;
-     elseif n=1: if ypart _A > ypart _O: draw projectionx.bot(_A,i,-dd) else: draw projectionx.top(_A,i,dd) fi;n:=n+1
-     else: if xpart _A > xpart _O: draw projectiony.lft(_A,i,-dd) else: draw projectiony.rt(_A,i,dd) fi;n:=n+1
+     elseif n=1: if ypart _A > ypart _O_: draw projectionx.bot(_A,i,-dd) else: draw projectionx.top(_A,i,dd) fi;n:=n+1
+     else: if xpart _A > xpart _O_: draw projectiony.lft(_A,i,-dd) else: draw projectiony.rt(_A,i,dd) fi;n:=n+1
      fi;
    fi;
   endfor;
@@ -1391,16 +1500,16 @@ enddef;
 vardef _suiterecfonc_(expr x)=0 enddef;
 numeric _suiterecdeb_, _suiterecfin_, _suiterecinit_;
 
-vardef suiterec(suffix f)(expr deb,fin,init)= 		%escalier un+1=f(un), u_deb=init
+vardef suiterec(suffix f)(expr deb,fin,init)= %escalier un+1=f(un), u_deb=init
   vardef _suiterecfonc_(expr x)=f(x) enddef;
   _suiterecdeb_:=deb;_suiterecfin_:=fin;_suiterecinit_:=init;	%stocke les valeurs pour réutilisation
   save $,un;
   path $;
   numeric un;
   un=init;
-  $=_c(un,yO)
+  $=(un,yO)
   for i=deb upto fin-1:
-    --_c(un,f(un))--_c(f(un),f(un))
+    --(un,f(un))--(f(un),f(un))
     hide(un:=f(un))
   endfor;
   $
@@ -1430,29 +1539,27 @@ vardef suiterecprojx@#(text t)=   	%projections et étiquettes sur axe x, utilis
       deb:=deb+1;un:=_suiterecfonc_(un)
     fi;
     for i=deb upto fin:
-      draw projectionx.@#(_c(un,un));
+      draw projectionx.@#((un,un));
       un:=_suiterecfonc_(un);
     endfor
   elseif nom="_val":
     if deb=_suiterecdeb_:
-%      label.@#(format("%10f",arrondi(10**_prec,un)),_c(un,yO));
       draw etiquettex.@#(arrondi(10**_prec,un));
       deb:=deb+1;un:=_suiterecfonc_(un)
     fi;
     for i=deb upto fin:
-%      draw projectionx.@#(_c(un,un),format("%10f",arrondi(10**_prec,un)));
       lab:=LaTeX("$\num{" &  decimal(arrondi(10**_prec,un)) & "}$");
-      draw projectionx.@#(_c(un,un),lab,-taillegrad);
+      draw projectionx.@#((un,un),lab,-taillegrad);
       un:=_suiterecfonc_(un);
     endfor
   else:
     if deb=_suiterecdeb_:
-      label.@#(LaTeX("$" & nom & "_{" & decimal(deb) & "}" & "$"),_c(un,yO));
+      label.@#(LaTeX("$" & nom & "_{" & decimal(deb) & "}" & "$"),(un,yO));
       deb:=deb+1;un:=_suiterecfonc_(un)
     fi;
     for i=deb upto fin:
       lab:=LaTeX("$" & nom & "_{" & decimal(i) & "}" & "$");
-      draw projectionx.@#(_c(un,un),lab);
+      draw projectionx.@#((un,un),lab);
       un:=_suiterecfonc_(un);
     endfor
   fi);
@@ -1483,7 +1590,7 @@ vardef suiterecprojy@#(text t)=   	%projections et étiquettes sur axe y, utilis
       deb:=deb+1;
     fi;
     for i=deb-1 upto fin-1:
-      draw projectiony.@#(_c(un,_suiterecfonc_(un)));
+      draw projectiony.@#((un,_suiterecfonc_(un)));
       un:=_suiterecfonc_(un);
     endfor
   elseif nom="_val":
@@ -1492,7 +1599,7 @@ vardef suiterecprojy@#(text t)=   	%projections et étiquettes sur axe y, utilis
     fi;
     for i=deb-1 upto fin-1:
       lab:=LaTeX("$\num{" &  decimal(arrondi(10**_prec,un)) & "}$");
-      draw projectiony.@#(_c(un,_suiterecfonc_(un)),lab,-taillegrad);
+      draw projectiony.@#((un,_suiterecfonc_(un)),lab,-taillegrad);
       un:=_suiterecfonc_(un);
     endfor
   else:
@@ -1501,7 +1608,7 @@ vardef suiterecprojy@#(text t)=   	%projections et étiquettes sur axe y, utilis
     fi;
     for i=deb-1 upto fin-1:
       lab:=LaTeX("$" & nom & "_{" & decimal(i+1) & "}" & "$");
-      draw projectiony.@#(_c(un,_suiterecfonc_(un)),lab);
+      draw projectiony.@#((un,_suiterecfonc_(un)),lab);
       un:=_suiterecfonc_(un);
     endfor
   fi);
@@ -1523,11 +1630,11 @@ enddef;
 %%%%%%%%%%   INTERVALLES   %%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 vardef bornex[](expr val)=
- ((1mm,-2mm)--(0,-2mm)--(0,2mm)--(1mm,2mm)) if @<0: xscaled -1 fi shifted _c(val,xO)
+ ((1mm,-2mm)--(0,-2mm)--(0,2mm)--(1mm,2mm)) if @<0: xscaled -1 fi shifted _cart(val,xO)
 enddef;
 
 vardef borney[](expr val)=
- ((2mm,1mm)--(2mm,0)--(-2mm,0)--(-2mm,1mm)) if @<0: yscaled -1 fi shifted _c(yO,val)
+ ((2mm,1mm)--(2mm,0)--(-2mm,0)--(-2mm,1mm)) if @<0: yscaled -1 fi shifted _cart(yO,val)
 enddef;
 
 pair sensborne.FF,sensborne.FO,sensborne.OF,sensborne.OO;
@@ -1537,9 +1644,9 @@ vardef intervallex@#(expr vmin,vmax)=
   save $;
   picture $;
   $=image(%
-   draw _c(vmin,xO)--_c(vmax,xO) withpen pencircle scaled 2pt;
-   draw bornex[xpart sensborne@#](vmin) withpen pencircle scaled 2pt;
-   draw bornex[ypart sensborne@#](vmax) withpen pencircle scaled 2pt);
+   olddraw _cart(vmin,xO)--_cart(vmax,xO) withpen pencircle scaled 2pt;
+   olddraw bornex[xpart sensborne@#](vmin) withpen pencircle scaled 2pt;
+   olddraw bornex[ypart sensborne@#](vmax) withpen pencircle scaled 2pt);
   $
 enddef;
 
@@ -1547,9 +1654,9 @@ vardef intervalley@#(expr vmin,vmax)=
   save $;
   picture $;
   $=image(%
-   draw _c(yO,vmin)--_c(yO,vmax) withpen pencircle scaled 2pt;
-   draw borney[xpart sensborne@#](vmin) withpen pencircle scaled 2pt;
-   draw borney[ypart sensborne@#](vmax) withpen pencircle scaled 2pt);
+   olddraw _cart(yO,vmin)--_cart(yO,vmax) withpen pencircle scaled 2pt;
+   olddraw borney[xpart sensborne@#](vmin) withpen pencircle scaled 2pt;
+   olddraw borney[ypart sensborne@#](vmax) withpen pencircle scaled 2pt);
   $
 enddef;
 
@@ -1574,12 +1681,12 @@ vardef boitemoustache(text t)=
    if known _valeursboitemoustache_[6]: _decboitemoustache_:=_valeursboitemoustache_[6] fi;
    if known _valeursboitemoustache_[7]: _largboitemoustache_:=_valeursboitemoustache_[7] fi;
    $=image(%
-   fill fullcircle scaled 3 shifted _c(_valeursboitemoustache_[1],yO);
-   draw _c(_valeursboitemoustache_[1],yO)--_c(_valeursboitemoustache_[2],yO);
-   draw _c(_valeursboitemoustache_[2],yO) shifted (0,-_largboitemoustache_/2)--_c(_valeursboitemoustache_[2],yO) shifted (0,_largboitemoustache_/2)--_c(_valeursboitemoustache_[4],yO) shifted (0,_largboitemoustache_/2)--_c(_valeursboitemoustache_[4],yO) shifted (0,-_largboitemoustache_/2)--cycle;
-   draw _c(_valeursboitemoustache_[3],yO) shifted (0,-_largboitemoustache_/2)--_c(_valeursboitemoustache_[3],yO) shifted (0,_largboitemoustache_/2);
-   draw _c(_valeursboitemoustache_[4],yO)--_c(_valeursboitemoustache_[5],yO);
-   fill fullcircle scaled 3 shifted _c(_valeursboitemoustache_[5],yO)%
+   oldfill fullcircle scaled 3 shifted _cart(_valeursboitemoustache_[1],yO);
+   olddraw _cart(_valeursboitemoustache_[1],yO)--_cart(_valeursboitemoustache_[2],yO);
+   olddraw _cart(_valeursboitemoustache_[2],yO) shifted (0,-_largboitemoustache_/2)--_cart(_valeursboitemoustache_[2],yO) shifted (0,_largboitemoustache_/2)--_cart(_valeursboitemoustache_[4],yO) shifted (0,_largboitemoustache_/2)--_cart(_valeursboitemoustache_[4],yO) shifted (0,-_largboitemoustache_/2)--cycle;
+   olddraw _cart(_valeursboitemoustache_[3],yO) shifted (0,-_largboitemoustache_/2)--_cart(_valeursboitemoustache_[3],yO) shifted (0,_largboitemoustache_/2);
+   olddraw _cart(_valeursboitemoustache_[4],yO)--_cart(_valeursboitemoustache_[5],yO);
+   oldfill fullcircle scaled 3 shifted _cart(_valeursboitemoustache_[5],yO)%
    ) shifted (0,_decboitemoustache_);
    $
 enddef;
@@ -1615,15 +1722,232 @@ vardef projboitemoustache@#(text t)=
    $=image(%
    for i=1 upto 5:
      if (i=1) or (i=5):
-       A:=_c(_valeursboitemoustache_[i],yO) shifted(0,_decboitemoustache_)
-       else: A:=_c(_valeursboitemoustache_[i],yO) shifted(0,_decboitemoustache_-_largboitemoustache_/2)
+       A:=_cart(_valeursboitemoustache_[i],yO) shifted(0,_decboitemoustache_)
+       else: A:=_cart(_valeursboitemoustache_[i],yO) shifted(0,_decboitemoustache_-_largboitemoustache_/2)
      fi;
-     draw projectionx@#(A,_lab_[i]);
+     draw projectionx@#(A transformed inverse _T,_lab_[i]);
    endfor);
    $
 enddef;
 
 
+numeric diampointsbatons;
+diampointsbatons:=5;
+
+vardef diagrammebatons(text t) =
+   save $;
+   picture $;
+   numeric tmp_taillepoint;
+   string tmp_marque_p;
+   tmp_taillepoint:=taillepoint;
+   tmp_marque_p := marque_p;
+   $=image(%
+     interim linecap:=butt;
+     marque_p:="plein";
+     taillepoint:=diampointsbatons*0.5;
+     for i=t:
+        draw i--projetex(i);
+        MarquePoint(i);
+     endfor
+     );
+   taillepoint:=tmp_taillepoint;
+   marque_p := tmp_marque_p;
+   $
+enddef;
+
+
+numeric largbarres;
+largbarres := 20;
+
+def barrei(expr p)=
+   (projetex(_cart(p)-0.5(largbarres,0))--(_cart(p)-0.5(largbarres,0))--(_cart(p)+0.5(largbarres,0))--projetex(_cart(p)+0.5(largbarres,0))) transformed inverse _T
+enddef;
+
+vardef diagrammebarres(text t)=
+   save $;
+   path $;
+   $:= for i=t: barrei(i)-- endfor cycle;
+   $
+enddef;
+
+
+vardef diagrammebinomiale(expr n,p)=
+   save $,Abin;
+   picture $;
+   pair Abin[];
+   $:=scantokens("diagrammebatons("&
+           "(0," & decimal(binomiale(n,p,0)) & ")" &
+           for i=0 upto n: ",(" & decimal(i) & "," & decimal(binomiale(n,p,i)) & ")" &
+           endfor
+           ")");
+   $
+enddef;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%   POLYGONES   %%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+vardef polygone(text t)=
+  save poly;
+  path poly;
+  poly := 
+    for i=t:
+      i--
+    endfor
+    cycle;
+  poly
+enddef;
+
+if not known typetrace:
+  vardef triangle(expr A,B,C)=
+    polygone(A,B,C)
+  enddef;
+fi
+
+vardef parallelogramme(expr A,O,B)=
+  O--A--(A+B-O)--B--cycle
+enddef;
+
+vardef polygoneregulier(expr A,B,n)=
+  save poly,centre;
+  path poly;pair centre;
+  _cart(B)-centre = (_cart(A)-centre) rotated (360/n);
+  poly:= _cart(A)
+     for i = 1 upto n-1:
+       -- (_cart(A) rotatedaround(centre,(i*360)/n))
+     endfor
+     --cycle;
+  poly transformed inverse _T
+enddef;
+
+vardef equilateral(expr A,B)=
+  polygoneregulier(A,B,3)
+enddef;
+
+vardef carre(expr A,B)=
+  polygoneregulier(A,B,4)
+enddef;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%   CERCLES ET ARCS   %%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+vardef arccercle(expr A,O,B)=
+  path tmp,arc;
+  tmp:=fullcircle scaled (2*(abs(_cart(A)-_cart(O)))) rotated angle(_cart(A)-_cart(O)) shifted _cart(O);
+  if angle(_cart(B)-_cart(O))>angle(_cart(A)-_cart(O)):
+    arc:=subpath(0,(angle(_cart(B)-_cart(O))-angle(_cart(A)-_cart(O)))*(length tmp)/360) of tmp;
+  else:
+    arc:=subpath(0,(360-(angle(_cart(A)-_cart(O))-angle(_cart(B)-_cart(O))))*(length tmp)/360) of tmp;
+  fi
+  arc transformed inverse _T
+enddef;
+
+vardef cerclecr(expr O,r)=
+  fullcircle scaled (2*r*Ux) shifted _cart(O) transformed inverse _T
+enddef;
+
+vardef cerclecp(expr O,A)=
+  fullcircle scaled (2*abs(_cart(A)-_cart(O))) shifted _cart(O) transformed inverse _T
+enddef;
+
+vardef cerclecir(expr A,B,C)=
+  save O;pair O;
+  _cart(O)-0.5[_cart(A),_cart(B)]=whatever * (_cart(B)-_cart(A)) rotated 90;
+  _cart(O)-0.5[_cart(A),_cart(C)]=whatever * (_cart(C)-_cart(A)) rotated 90;
+  cerclecp(O,A)
+enddef;
+
+vardef cercle(text t)=
+   save $;path $;
+   save r;boolean r;
+   r:=false;
+   if long_texte(t)=3:
+     $:=cerclecir(t)
+   else:
+     for i=t:
+       if numeric i: r:=true fi;
+     endfor
+     if r: $:=cerclecr(t) else: $:=cerclecp(t) fi;
+   fi;
+   $   
+enddef;
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%   MARQUES ANGLES, SEGMENTS...   %%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+taille_marque_a:=0.4cm;
+sep_marque_a:=1.5;
+
+
+vardef arc_marqueangle(expr A,O,B,t)=
+  arccercle((_cart(O)+t*unitvector(_cart(A)-_cart(O))) transformed inverse _T,O,(_cart(O)+t*unitvector(_cart(B)-_cart(O))) transformed inverse _T)
+enddef;
+
+vardef marqueanglegeo(expr A,O,B,n)=
+  O--arc_marqueangle(A,O,B,taille_marque_a-(n-1)*sep_marque_a/2)
+  for i=1 upto n-1:
+   --reverse arc_marqueangle(A,O,B,taille_marque_a-(n-1)*sep_marque_a/2+(i-1)*sep_marque_a)--
+   arc_marqueangle(A,O,B,taille_marque_a-(n-1)*sep_marque_a/2+i*sep_marque_a)
+  endfor
+  --cycle
+enddef;
+
+
+vardef marqueangleor(expr A,O,B)=
+  arc_marqueangle(A,O,B,taille_marque_a)
+enddef;
+
+vardef marqueangle(text t)=
+  if long_texte(t)=4: marqueanglegeo(t)
+  else: marqueangleor(t)
+  fi
+enddef;
+
+vardef nommeangle@#(expr A,O,B,p)=
+  save P,a;pair P;path a;
+  a:=arc_marqueangle(A,O,B,taille_marque_a);
+  P:= point (arctime 0.5*arclength a of a) of a;
+  if string p: thelabel@#(p,P)
+  else: thelabel@#(p scaled defaultscale,P)
+  fi
+enddef;
+
+
+
+taille_marque_ad:=0.3cm;
+
+vardef marqueangledroit(expr A,O,B)=
+  parallelogramme((_cart(O)+taille_marque_ad*unitvector(_cart(A)-_cart(O))) transformed inverse _T,O,(_cart(O)+taille_marque_ad*unitvector(_cart(B)-_cart(O))) transformed inverse _T)
+enddef;
+
+taille_marque_s:=0.3cm;
+angle_marque_s:=60;
+sep_marque_s:=2;
+
+vardef milieu(expr A,B)=
+  0.5[A,B]
+enddef;
+
+vardef marqueunique_s(expr A,B)=
+   ((-taille_marque_s*unitvector(_cart(A)-_cart(B))/2)--(taille_marque_s*unitvector(_cart(A)-_cart(B))/2)) rotated angle_marque_s
+enddef;
+
+vardef marquesegment(expr A,B,n)=
+ save $;
+ picture $;
+ $=image(
+    for i=1 upto n:
+      draw marqueunique_s(A,B) shifted ((i-1-(n-1)/2)*sep_marque_s*unitvector(_cart(B)-_cart(A))) transformed inverse _T;
+    endfor
+    );
+  $ shifted milieu(_cart(A),_cart(B))
+enddef;
+
+
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%   FONCTIONS USUELLES   %%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -1677,13 +2001,13 @@ enddef;
 vardef repbriques(expr larg,haut,dec)=
  numeric d;d=0;
  image(%
- for j=0 upto _hautcadre/haut:
-   draw ((0,0)--(_largcadre,0)) shifted (0,j*haut);
+ for j=0 upto _hautcadre_/haut:
+   olddraw ((0,0)--(_largcadre_,0)) shifted (0,j*haut);
    d:=d+dec;if d>larg: d:=d-larg fi;
-   for i=0 upto _largcadre/larg:
-     draw ((0,0)--(0,haut)) shifted (i*larg+d,j*haut);
+   for i=0 upto _largcadre_/larg:
+     olddraw ((0,0)--(0,haut)) shifted (i*larg+d,j*haut);
    endfor;
- endfor) shifted llcorner cadre
+ endfor) shifted llcorner _cart(cadre)
 enddef;
 
 
@@ -1700,9 +2024,9 @@ enddef;
 
 vardef rephachures(expr pas,angle)=
  image(%
- for i=floor(-_diag/(2*pas)) upto ceiling(_diag/(2*pas)):
- draw ((-_diag/2,0)--(_diag/2,0)) shifted (0,i*pas);
- endfor) rotated angle shifted center cadre
+ for i=floor(-_diag_/(2*pas)) upto ceiling(_diag_/(2*pas)):
+ olddraw ((-_diag_/2,0)--(_diag_/2,0)) shifted (0,i*pas);
+ endfor) rotated angle shifted center _cart(cadre)
 enddef;
 
 numeric pervagues,ampvagues,decvagues;
@@ -1719,11 +2043,11 @@ enddef;
 
 vardef repvagues(expr per,amp,dec)=   %D'après le manuel de l'utilisateur de MetaPost
  image(%
- for j=0 upto _hautcadre/dec:
-   for i=0 upto _largcadre/amp:
-    draw ((0,0){curl 0}..(per/4,-amp)..(per/2,0){curl 0}..(3*per/4,amp)..(per,0){curl 0}) shifted (i*per,j*dec);
+ for j=0 upto _hautcadre_/dec:
+   for i=0 upto _largcadre_/amp:
+    olddraw ((0,0){curl 0}..(per/4,-amp)..(per/2,0){curl 0}..(3*per/4,amp)..(per,0){curl 0}) shifted (i*per,j*dec);
    endfor;
- endfor) shifted llcorner cadre
+ endfor) shifted llcorner _cart(cadre)
 enddef;
 
 
@@ -1732,7 +2056,7 @@ primarydef p avec c =
  save _des_;
  picture _des_;
  _des_:=c;
- clip _des_ to p;
+ clip _des_ to (p transformed _T);
  _des_
  endgroup
 enddef;
@@ -1749,12 +2073,7 @@ numeric n_packages;
 n_packages:=0;
 
 def LaTeX_AjoutPackage(expr t)=
-  if known latexmp_module:
      latexmp_packages:=latexmp_packages & "," & t
-  else:
-     n_packages:=n_packages+1;
-     LaTeX_packages[n_packages]:=t
-  fi
 enddef;
 
 def LaTeX_AjoutCommande(expr t)=
@@ -1777,67 +2096,29 @@ def LaTeXsetup =
       latexmp_inputenc:=LaTeX_inputenc;
       if latexmp_inputenc="": latexmp_inputenc:="utf8" fi;
       if latexmp_packages="": latexmp_packages:="fourier" fi;
-      latexmp_packages:=latexmp_packages & ",textcomp,mathtools,mathrsfs,esvect[e],siunitx[output-decimal-marker={,}],babel[frenchb]";
+      latexmp_packages:=latexmp_packages & ",textcomp,mathtools,mathrsfs,esvect[e],siunitx[output-decimal-marker={,}],babel[french]";
       latexmp_preamble:=latexmp_preamble & "\newcommand{\vect}[1]{\vv{#1}}" & "\newcommand{\calc}{\mathscr{C}}" & "\newcommand{\calp}{\mathscr{P}}" & "\DecimalMathComma" ;
    fi
 enddef;
 
-vardef LaTeX primary sc =   %D'après TEX.mp
-  if known latexmp_module: LaTeXsetup; textext(sc) scaled defaultscale
-  else:
-  save n_p;
-  numeric n_p;
-  write "verbatimtex" to "mptextmp.mp";
-  write "%&latex" to "mptextmp.mp";
-  write "\documentclass[10pt]{article}" to "mptextmp.mp";
-  if LaTeX_inputenc="":
-     write "\usepackage[utf8]{inputenc}" to "mptextmp.mp"
-  else:
-     write "\usepackage[" & LaTeX_inputenc &"]{inputenc}" to "mptextmp.mp"
-  fi;
-  write "\usepackage[T1]{fontenc}" to "mptextmp.mp";
-  if known LaTeX_packages[1]:
-       n_p:=1;
-       forever: exitunless known LaTeX_packages[n_p];
-          write "\usepackage{" & LaTeX_packages[n_p] &"}" to "mptextmp.mp";
-          n_p:=n_p+1;
-       endfor
-  else:
-       write "\usepackage{fourier}" to "mptextmp.mp"
-  fi;
-  write "\usepackage{amsmath}" to "mptextmp.mp";
-  write "\usepackage{mathrsfs}" to "mptextmp.mp";
-  write "\usepackage[e]{esvect}" to "mptextmp.mp";
-  write "\usepackage[output-decimal-marker={,}]{siunitx}" to "mptextmp.mp";
-  write "\usepackage[frenchb]{babel}" to "mptextmp.mp";
-  write LaTeX_preamble to "mptextmp.mp";
-  write "\newcommand{\vect}[1]{\vv{#1}}" to "mptextmp.mp";
-  write "\newcommand{\calc}{\mathscr{C}}" to "mptextmp.mp";
-  write "\newcommand{\calp}{\mathscr{P}}" to "mptextmp.mp";
-  write "\begin{document}" to "mptextmp.mp";
-  write "etex" to "mptextmp.mp";
-  write "btex "& sc &" etex" to "mptextmp.mp";
-  write EOF to "mptextmp.mp";
-  scantokens "input mptextmp" scaled defaultscale
+vardef LaTeX primary sc =   
+  if known mplib: textext(sc) scaled defaultscale
+  else: LaTeXsetup; textext(sc) scaled defaultscale
   fi
 enddef;
+%vardef LaTeX primary sc =   
+%   LaTeXsetup; textext(sc) scaled defaultscale
+%enddef;
 
 %%%%%%%%%%%%%%%Figure intermédiaire%%%%%%%%%%%%%%%%%%%
 def figureinter=
-  clip currentpicture to cadre;
+  clip currentpicture to (cadre transformed _T);
   shipit;
   _nfig:=_nfig+1;
   charcode:=charcode+1;
 enddef;
 
 
-vardef arrowhead expr p = %redéfinition flèches
-  save q,e; path q; pair e;
-  e = point length p of p;
-  q = gobble(p shifted -e cutafter makepath(pencircle scaled 2ahlength))
-    cuttings;
-  (q rotated .5ahangle & reverse q rotated -.5ahangle -- 0.5*(point 0 of q)-- cycle)  shifted e
-enddef;
 
 def epaisseur=withpen pencircle scaled enddef;
 def couleur=withcolor enddef;
@@ -1865,6 +2146,8 @@ vardef _chaine(suffix s)= %met les termes en indice si le 2e est un chiffre
 enddef;
 
 
+%%%%%%%%%%%%%%% MATHS %%%%%%%%%%%%%%%%%
+
 vardef arrondi(expr p,x)=              %arrondi de x au p-ième
   round((x-floor(x))*p)/p+floor(x)
 enddef;
@@ -1886,6 +2169,44 @@ vardef pgcd(expr a,b)=
   b_
 enddef;
 
+vardef factorielle(expr n)=  %  Calcul de n!
+  save $;
+  numeric $;
+  $:= 1  for i=1 upto n: * i endfor;
+  $
+enddef;
+
+vardef binom(expr n,k)=    % calcul du coefficient binomial k parmi n
+  save $,p;
+  numeric $,p;
+  p:= min(k,n-k);
+  $:=1;
+  for i=1 upto p:
+   $:= ($*(n-i+1))/i;
+  endfor
+  $
+enddef;
+
+vardef binomiale(expr n,p,k)=
+   save $,ktmp,ptmp;
+   numeric $,ktmp,ptmp;
+   if k>n-k:
+      ktmp:=n-k;
+      ptmp:=1-p
+   else:
+      ktmp:=k;
+      ptmp:=p
+   fi;
+   $:=1;
+   for i=1 upto ktmp:
+      $:=((n-i+1)/i)*ptmp*$;
+   endfor
+   for i=1 upto n-ktmp:
+      $:=$*(1-ptmp);
+   endfor
+   $
+enddef;
+
 %%%%%%%%%%%%%%% COULEURS %%%%%%%%%%%%%%%%%%%
 cmykcolor Rouge,Vert,Bleu,Marron,Lime,Orange,Rose,Pourpre,Violet,Cyan,Magenta,Jaune,Olive,Noir,Grisfonce,Gris,Grisclair,Blanc,Beige,Marine,Moutarde,Vertfonce;