// xcas version=0.7.4 fontsize=20 font=0
// fltk 7Fl_Tile 23 74 920 73 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 74 920 72 20 0
Les donnees sont les longueurs AB, BC, etc, FA et les angles (AF,AB), (AB,BC) , etc.£On se place dans le plan ACE dont on prend un repere d'origine A, i dirige vers C£1/ calcul de AC, CE, AE
,
// fltk N4xcas10Log_OutputE 23 146 920 1 20 0

]
,
// fltk 7Fl_Tile 23 149 920 68 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 149 920 30 20 0
AC:=sqrt(L1^2+L2^2-2*L1*L2*cos(phi2))
,
// fltk N4xcas10Log_OutputE 23 179 920 1 20 0

,
// fltk N4xcas8EquationE 23 180 920 37 20 0
sqrt(L1^2+L2^2-2*L1*L2*cos(phi2))
]
,
// fltk 7Fl_Tile 23 219 920 68 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 219 920 30 20 0
CE:=sqrt(L3^2+L4^2-2*L3*L4*cos(phi4))
,
// fltk N4xcas10Log_OutputE 23 249 920 1 20 0

,
// fltk N4xcas8EquationE 23 250 920 37 20 0
sqrt(L3^2+L4^2-2*L3*L4*cos(phi4))
]
,
// fltk 7Fl_Tile 23 289 920 68 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 289 920 30 20 0
EA:=sqrt(L5^2+L6^2-2*L5*L6*cos(phi6))
,
// fltk N4xcas10Log_OutputE 23 319 920 1 20 0

,
// fltk N4xcas8EquationE 23 320 920 37 20 0
sqrt(L5^2+L6^2-2*L5*L6*cos(phi6))
]
,
// fltk 7Fl_Tile 23 359 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 359 920 30 20 0
On en deduit les angles, par exemple alpha, par EC^2=(AC-AE)^2 et developpement
,
// fltk N4xcas10Log_OutputE 23 389 920 1 20 0

]
,
// fltk 7Fl_Tile 23 392 920 125 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 392 920 30 20 0
alpha:=acos((AC^2+EA^2-CE^2)/(2*AC*EA))
,
// fltk N4xcas10Log_OutputE 23 422 920 24 20 0
Evaluation time: 0.93£
,
// fltk N4xcas8EquationE 23 446 920 71 20 0
acos((L1^2+L2^2-2*L1*L2*cos(phi2)+L5^2+L6^2-2*L5*L6*cos(phi6)-L3^2-L4^2+2*L3*L4*cos(phi4))/(2*sqrt(L1^2+L2^2-2*L1*L2*cos(phi2))*sqrt(L5^2+L6^2-2*L5*L6*cos(phi6))))
]
,
// fltk 7Fl_Tile 23 519 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 519 920 30 20 0
par exemple pour le cyclohexane, les L sont tous egaux a 1, et les phij a phi
,
// fltk N4xcas10Log_OutputE 23 549 920 1 20 0

]
,
// fltk 7Fl_Tile 23 552 920 78 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 552 920 30 20 0
simplify(subst(alpha,[L1,L2,L3,L4,L5,L6,phi2,phi4,phi6],[1$6,phi$3]))
,
// fltk N4xcas10Log_OutputE 23 582 920 1 20 0

,
// fltk N4xcas8EquationE 23 583 920 47 20 0
1/3*pi
]
,
// fltk 7Fl_Tile 23 632 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 632 920 30 20 0
dans le triangle ABC, on connait AB, BC et (AB,BC)=phi2, d'ou BH et AH
,
// fltk N4xcas10Log_OutputE 23 662 920 1 20 0

]
,
// fltk 7Fl_Tile 23 665 920 92 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 665 920 30 20 0
AH:=L1*(L1-L2*cos(phi2))/AC
,
// fltk N4xcas10Log_OutputE 23 695 920 1 20 0

,
// fltk N4xcas8EquationE 23 696 920 61 20 0
(L1*(L1-L2*cos(phi2)))/(sqrt(L1^2+L2^2-2*L1*L2*cos(phi2)))
]
,
// fltk 7Fl_Tile 23 759 920 92 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 759 920 30 20 0
BH:=L1*L2*sin(phi2)/AC
,
// fltk N4xcas10Log_OutputE 23 789 920 1 20 0

,
// fltk N4xcas8EquationE 23 790 920 61 20 0
(L1*L2*sin(phi2))/(sqrt(L1^2+L2^2-2*L1*L2*cos(phi2)))
]
,
// fltk 7Fl_Tile 23 853 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 853 920 30 20 0
cas du cyclohexane
,
// fltk N4xcas10Log_OutputE 23 883 920 1 20 0

]
,
// fltk 7Fl_Tile 23 886 920 78 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 886 920 30 20 0
alpha1:=pi/2-phi/2; alpha:=pi/3;
,
// fltk N4xcas10Log_OutputE 23 916 920 1 20 0

,
// fltk N4xcas8EquationE 23 917 920 47 20 0
pi/2-phi/2,pi/3
]
,
// fltk 7Fl_Tile 23 966 920 118 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 966 920 30 20 0
B1:=point(L*cos(alpha1),L*sin(alpha1)*(1-u^2)/(1+u^2),L*sin(alpha1)*2*u/(1+u^2)):; coordinates(B1)
,
// fltk N4xcas10Log_OutputE 23 996 920 1 20 0

,
// fltk N4xcas8EquationE 23 997 920 87 20 0
"Done",[L*cos(pi/2-phi/2),(L*sin(pi/2-phi/2)*(1-u^2))/(1+u^2),(L*sin(pi/2-phi/2)*2*u)/(1+u^2)]
]
,
// fltk 7Fl_Tile 23 1086 920 152 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 1086 920 30 20 0
F1:=subst(rotation(line(x=0,y=0),alpha,B1),u,1/v):; coordinates(F1)
,
// fltk N4xcas10Log_OutputE 23 1116 920 1 20 0

,
// fltk N4xcas8EquationE 23 1117 920 121 20 0
"Done",[-sqrt(3)*L*1/2*1/(1+(1/v)^2)*sin(pi/2-phi/2)*(1-(1/v)^2)+(L*cos(pi/2-phi/2))/2,L*1/2*1/(1+(1/v)^2)*sin(pi/2-phi/2)*(1-(1/v)^2)+(sqrt(3)*L*cos(pi/2-phi/2))/2,2*L*1/v*1/(1+(1/v)^2)*sin(pi/2-phi/2)]
]
,
// fltk 7Fl_Tile 23 1240 920 232 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 1240 920 30 20 0
D1:=subst(rotation(line(x=2*abscissa(B1),y=0),-alpha,B1),u,1/v):; coordinates(D1)
,
// fltk N4xcas10Log_OutputE 23 1270 920 1 20 0

,
// fltk N4xcas8EquationE 23 1271 920 201 20 0
"Done",[sqrt(3)*L*1/2*1/(1+(1/v)^2)*sin(pi/2-phi/2)*(1-(1/v)^2)+(L*cos(pi/2-phi/2)-2*L*cos(pi/2-phi/2))/2+2*L*cos(pi/2-phi/2),L*1/2*1/(1+(1/v)^2)*sin(pi/2-phi/2)*(1-(1/v)^2)-(sqrt(3)*(L*cos(pi/2-phi/2)-2*L*cos(pi/2-phi/2)))/2,2*L*1/v*1/(1+(1/v)^2)*sin(pi/2-phi/2)]
]
,
// fltk 7Fl_Tile 23 1474 920 204 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 1474 920 30 20 0
eq0:=numer(scalarProduct(coordinates(B1),coordinates(F1))/L^2-cos(phi))
,
// fltk N4xcas10Log_OutputE 23 1504 920 1 20 0

,
// fltk N4xcas8EquationE 23 1505 920 173 20 0
cos(pi/2-phi/2)^2*v^2*u^2+cos(pi/2-phi/2)^2*v^2+cos(pi/2-phi/2)^2*u^2+cos(pi/2-phi/2)^2-2*cos(pi/2-phi/2)*sqrt(3)*v^2*sin(pi/2-phi/2)*u^2+2*cos(pi/2-phi/2)*sqrt(3)*sin(pi/2-phi/2)-v^2*sin(pi/2-phi/2)^2*u^2+v^2*sin(pi/2-phi/2)^2-2*v^2*u^2*cos(phi)-2*v^2*cos(phi)+8*v*sin(pi/2-phi/2)^2*u+sin(pi/2-phi/2)^2*u^2-sin(pi/2-phi/2)^2-2*u^2*cos(phi)-2*cos(phi)
]
,
// fltk 7Fl_Tile 23 1680 920 114 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 1680 920 30 20 0
eq1:=texpand(tlin(eq0))
,
// fltk N4xcas10Log_OutputE 23 1710 920 1 20 0

,
// fltk N4xcas8EquationE 23 1711 920 83 20 0
u^2+4*u*v+v^2+u^2*v^2*(-(cos(phi)))+(-4*u*v)*(-(cos(phi)))-cos(phi)+(-(sqrt(3)))*(-(sin(phi)))+sqrt(3)*u^2*v^2*(-(sin(phi)))+(-2*v^2)*cos(phi)+(-2*u^2)*cos(phi)+(-2*u^2*v^2)*cos(phi)-2*cos(phi)
]
,
// fltk 7Fl_Tile 23 1796 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 1796 920 30 20 0
On exprime tout en fonction de T=tan(phi/2)
,
// fltk N4xcas10Log_OutputE 23 1826 920 1 20 0

]
,
// fltk 7Fl_Tile 23 1829 920 64 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 1829 920 30 20 0
eq:=subst(numer(halftan(eq1)),tan(phi/2),T)
,
// fltk N4xcas10Log_OutputE 23 1859 920 1 20 0

,
// fltk N4xcas8EquationE 23 1860 920 33 20 0
3*u^2*v^2*T^2+(-2*u^2)*v^2*T*sqrt(3)+(-3*u^2)*v^2+3*u^2*T^2-u^2+8*u*v+3*v^2*T^2-v^2+3*T^2+2*T*sqrt(3)-3
]
,
// fltk 7Fl_Tile 23 1895 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 1895 920 30 20 0
L'equation est symetrique en u,v, en effet:
,
// fltk N4xcas10Log_OutputE 23 1925 920 1 20 0

]
,
// fltk 7Fl_Tile 23 1928 920 64 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 1928 920 30 20 0
coeffs(eq,[u,v])
,
// fltk N4xcas10Log_OutputE 23 1958 920 1 20 0

,
// fltk N4xcas8EquationE 23 1959 920 33 20 0
[3*T^2-2*T*sqrt(3)-3,3*T^2-1,8,3*T^2-1,3*T^2+2*T*sqrt(3)-3]
]
,
// fltk 7Fl_Tile 23 1994 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 1994 920 30 20 0
resolution pour u=v:
,
// fltk N4xcas10Log_OutputE 23 2024 920 1 20 0

]
,
// fltk 7Fl_Tile 23 2027 920 64 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 2027 920 30 20 0
equu:=normal(subst(eq,v,u))
,
// fltk N4xcas10Log_OutputE 23 2057 920 1 20 0

,
// fltk N4xcas8EquationE 23 2058 920 33 20 0
3*T^2*u^4+6*T^2*u^2+3*T^2+(-2*sqrt(3))*T*u^4+2*sqrt(3)*T-3*u^4+6*u^2-3
]
,
// fltk 7Fl_Tile 23 2093 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 2093 920 30 20 0
cette equation est bicarree:
,
// fltk N4xcas10Log_OutputE 23 2123 920 1 20 0

]
,
// fltk 7Fl_Tile 23 2126 920 64 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 2126 920 30 20 0
equ2:=subst(equu,u,sqrt(U))
,
// fltk N4xcas10Log_OutputE 23 2156 920 1 20 0

,
// fltk N4xcas8EquationE 23 2157 920 33 20 0
3*T^2*U^2+6*T^2*U+3*T^2+(-2*sqrt(3))*T*U^2+2*sqrt(3)*T-3*U^2+6*U-3
]
,
// fltk 7Fl_Tile 23 2192 920 98 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 2192 920 30 20 0
solu2:=normal(solve(equ2,U))
,
// fltk N4xcas10Log_OutputE 23 2222 920 1 20 0

,
// fltk N4xcas8EquationE 23 2223 920 67 20 0
[(-3*T^2-(-4*sqrt(3))*abs(T)-3)/(3*T^2+(-2*sqrt(3))*T-3),(-3*T^2-4*sqrt(3)*abs(T)-3)/(3*T^2+(-2*sqrt(3))*T-3)]
]
,
// fltk 7Fl_Tile 23 2292 920 102 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 2292 920 30 20 0
soluu:=sqrt(solu2)
,
// fltk N4xcas10Log_OutputE 23 2322 920 1 20 0

,
// fltk N4xcas8EquationE 23 2323 920 71 20 0
[sqrt((-3*T^2-(-4*sqrt(3))*abs(T)-3)/(3*T^2+(-2*sqrt(3))*T-3)),sqrt((-3*T^2-4*sqrt(3)*abs(T)-3)/(3*T^2+(-2*sqrt(3))*T-3))]
]
,
// fltk 7Fl_Tile 23 2396 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 2396 920 30 20 0
Puis on pose T=tan(109/180*pi/2)
,
// fltk N4xcas10Log_OutputE 23 2426 920 1 20 0

]
,
// fltk 7Fl_Tile 23 2429 920 54 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 2429 920 30 20 0
Tf:=tan(109./180*pi/2); [u1,u2]:=subst(soluu,T=Tf)
,
// fltk N4xcas10Log_OutputE 23 2459 920 1 20 0

,
// fltk N4xcas8EquationE 23 2460 920 23 20 0
1.4019482944763,[3.9521371121531e-17+0.64545428819918*i,3.0812363914163]
]
,
// fltk 7Fl_Tile 23 2485 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 2485 920 30 20 0
Ce qui nous donne une unique solution reelle u, dont on déduit B, F, D. 
,
// fltk N4xcas10Log_OutputE 23 2515 920 1 20 0

]
,
// fltk 7Fl_Tile 23 2518 920 54 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 2518 920 30 20 0
evalf(109/180*pi)
,
// fltk N4xcas10Log_OutputE 23 2548 920 1 20 0

,
// fltk N4xcas8EquationE 23 2549 920 23 20 0
1.9024088846738
]
,
// fltk 7Fl_Tile 23 2574 920 31 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 2574 920 30 20 0

,
// fltk N4xcas10Log_OutputE 23 2604 920 1 20 0

]
,
// fltk 7Fl_Tile 23 2607 920 461 20 0
[
// fltk N4xcas6FigureE 23 2607 920 461 20 0 landscape=0 history=0.40326 geo=0.51304  mouse_param=0.083696
// fltk N4xcas12History_PackE 25 2013 351 1055 20 0
[
// fltk 7Fl_Tile 47 2013 329 58 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2013 329 30 20 0
A:=point(0,0,0)
,
// fltk N4xcas10Log_OutputE 47 2043 329 1 20 0

,
// fltk N4xcas10Gen_OutputE 47 2044 329 27 20 0
pnt(pnt[point[0,0,0],0,"A"])
]
,
// fltk 7Fl_Tile 47 2073 329 101 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2073 329 51 20 0
B:=evalf(subst(B1,[£L,u,phi],[1,u2,evalf(109/180*pi)]))
,
// fltk N4xcas10Log_OutputE 47 2124 329 1 20 0

,
// fltk 9Fl_Scroll 47 2125 329 49 20 0
[
// fltk N4xcas10Gen_OutputE 47 2125 671 27 20 0
pnt(pnt[point[0.81411551835632,-0.47002981367447,0.34101011279515],0.0,"B"])
,
// fltk 12Fl_Scrollbar 47 290 313 20 20 0
[]
,
// fltk 12Fl_Scrollbar 360 263 16 33 20 0
[]
]
]
,
// fltk 7Fl_Tile 47 2176 329 80 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2176 329 30 20 0
C:=point(2*abscissa(B),0,0)
,
// fltk N4xcas10Log_OutputE 47 2206 329 1 20 0

,
// fltk 9Fl_Scroll 47 2207 329 49 20 0
[
// fltk N4xcas10Gen_OutputE 47 2207 351 27 20 0
pnt(pnt[point[1.6282310367126,0,0],0,"C"])
,
// fltk 12Fl_Scrollbar 47 269 313 20 20 0
[]
,
// fltk 12Fl_Scrollbar 360 242 16 33 20 0
[]
]
]
,
// fltk 7Fl_Tile 47 2258 329 80 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2258 329 30 20 0
E:=point(abscissa(B),abscissa(B)*sqrt(3),0)
,
// fltk N4xcas10Log_OutputE 47 2288 329 1 20 0

,
// fltk 9Fl_Scroll 47 2289 329 49 20 0
[
// fltk N4xcas10Gen_OutputE 47 2289 495 27 20 0
pnt(pnt[point[0.81411551835632,1.4100894410234,0],0,"E"])
,
// fltk 12Fl_Scrollbar 47 269 313 20 20 0
[]
,
// fltk 12Fl_Scrollbar 360 242 16 33 20 0
[]
]
]
,
// fltk 7Fl_Tile 47 2340 329 101 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2340 329 51 20 0
F:=evalf(subst(F1,£[L,v,phi],[1,u2,evalf(109/180*pi)]))
,
// fltk N4xcas10Log_OutputE 47 2391 329 1 20 0

,
// fltk 9Fl_Scroll 47 2392 329 49 20 0
[
// fltk N4xcas10Gen_OutputE 47 2392 690 27 20 0
pnt(pnt[point[2.2204460492503e-16,0.94005962734895,0.34101011279515],0.0,"F"])
,
// fltk 12Fl_Scrollbar 47 290 313 20 20 0
[]
,
// fltk 12Fl_Scrollbar 360 263 16 33 20 0
[]
]
]
,
// fltk 7Fl_Tile 47 2443 329 101 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2443 329 51 20 0
D:=evalf(subst(D1,£[L,v,phi],[1,u2,evalf(109/180*pi)]))
,
// fltk N4xcas10Log_OutputE 47 2494 329 1 20 0

,
// fltk 9Fl_Scroll 47 2495 329 49 20 0
[
// fltk N4xcas10Gen_OutputE 47 2495 656 27 20 0
pnt(pnt[point[1.6282310367126,0.94005962734895,0.34101011279515],0.0,"D"])
,
// fltk 12Fl_Scrollbar 47 290 313 20 20 0
[]
,
// fltk 12Fl_Scrollbar 360 263 16 33 20 0
[]
]
]
,
// fltk 7Fl_Tile 47 2546 329 80 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2546 329 30 20 0
triangle(A,C,E,display=jaune+rempli)
,
// fltk N4xcas10Log_OutputE 47 2576 329 1 20 0

,
// fltk 9Fl_Scroll 47 2577 329 49 20 0
[
// fltk N4xcas10Gen_OutputE 47 2577 1042 27 20 0
pnt(pnt[group[point[0,0,0],point[1.6282310367126,0,0],point[0.81411551835632,1.4100894410234,0],point[0,0,0]],1073741827])
,
// fltk 12Fl_Scrollbar 47 102 329 20 20 0
[]
,
// fltk 12Fl_Scrollbar 376 73 16 29 20 0
[]
]
]
,
// fltk 7Fl_Tile 47 2628 329 80 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2628 329 30 20 0
triangle(A,B,C)
,
// fltk N4xcas10Log_OutputE 47 2658 329 1 20 0

,
// fltk 9Fl_Scroll 47 2659 329 49 20 0
[
// fltk N4xcas10Gen_OutputE 47 2659 1113 27 20 0
pnt(pnt[group[point[0,0,0],point[0.81411551835632,-0.47002981367447,0.34101011279515],point[1.6282310367126,0,0],point[0,0,0]],0])
,
// fltk 12Fl_Scrollbar 47 228 329 20 20 0
[]
,
// fltk 12Fl_Scrollbar 376 199 16 29 20 0
[]
]
]
,
// fltk 7Fl_Tile 47 2710 329 80 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2710 329 30 20 0
triangle(C,E,D)
,
// fltk N4xcas10Log_OutputE 47 2740 329 1 20 0

,
// fltk 9Fl_Scroll 47 2741 329 49 20 0
[
// fltk N4xcas10Gen_OutputE 47 2741 1512 27 20 0
pnt(pnt[group[point[1.6282310367126,0,0],point[0.81411551835632,1.4100894410234,0],point[1.6282310367126,0.94005962734895,0.34101011279515],point[1.6282310367126,0,0]],0])
,
// fltk 12Fl_Scrollbar 47 310 329 20 20 0
[]
,
// fltk 12Fl_Scrollbar 376 281 16 29 20 0
[]
]
]
,
// fltk 7Fl_Tile 47 2792 329 80 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2792 329 30 20 0
triangle(A,E,F)
,
// fltk N4xcas10Log_OutputE 47 2822 329 1 20 0

,
// fltk 9Fl_Scroll 47 2823 329 49 20 0
[
// fltk N4xcas10Gen_OutputE 47 2823 1278 27 20 0
pnt(pnt[group[point[0,0,0],point[0.81411551835632,1.4100894410234,0],point[2.2204460492503e-16,0.94005962734895,0.34101011279515],point[0,0,0]],0])
,
// fltk 12Fl_Scrollbar 47 129 329 20 20 0
[]
,
// fltk 12Fl_Scrollbar 376 100 16 29 20 0
[]
]
]
,
// fltk 7Fl_Tile 47 2874 329 77 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2874 329 27 20 0
H:=point(point[0.28401534470392,0.77608329163015,-0.56305417894304])
,
// fltk N4xcas10Log_OutputE 47 2901 329 1 20 0

,
// fltk 9Fl_Scroll 47 2902 329 49 20 0
[
// fltk N4xcas10Gen_OutputE 47 2902 657 27 20 0
pnt(pnt[point[0.28401534470392,0.77608329163015,-0.56305417894304],0,"H"])
,
// fltk 12Fl_Scrollbar 47 208 329 20 20 0
[]
,
// fltk 12Fl_Scrollbar 376 179 16 29 20 0
[]
]
]
,
// fltk 7Fl_Tile 47 2953 329 80 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 2953 329 30 20 0
triangle(A,E,H,color=red)
,
// fltk N4xcas10Log_OutputE 47 2983 329 1 20 0

,
// fltk 9Fl_Scroll 47 2984 329 49 20 0
[
// fltk N4xcas10Gen_OutputE 47 2984 1258 27 20 0
pnt(pnt[group[point[0,0,0],point[0.81411551835632,1.4100894410234,0],point[0.28401534470392,0.77608329163015,-0.56305417894304],point[0,0,0]],1])
,
// fltk 12Fl_Scrollbar 47 290 329 20 20 0
[]
,
// fltk 12Fl_Scrollbar 376 261 16 29 20 0
[]
]
]
,
// fltk 7Fl_Tile 47 3035 329 31 20 0
[
// fltk N4xcas19Multiline_Input_tabE 47 3035 329 30 20 0

,
// fltk N4xcas10Log_OutputE 47 3065 329 1 20 0

]
]
// fltk N4xcas5Geo3dE 394 2633 472 435 20 0
-0.45025,2.0785,-0.45025,2.0785,[pnt(pnt[point[0,0,0],0,"A"]),pnt(pnt[point[0.814115518356319218466,-0.470029813674472616199,0.341010112795151898939],0.000000000000000000000,"B"]),pnt(pnt[point[1.62823103671263843693,0,0],0,"C"]),pnt(pnt[point[0.814115518356319218466,1.41008944102341784860,0],0,"E"]),pnt(pnt[point[-0.338813178901720135627e-20,0.940059627348945232397,0.341010112795151898939],0.000000000000000000000,"F"]),pnt(pnt[point[1.62823103671263843693,0.940059627348945232397,0.341010112795151898939],0.000000000000000000000,"D"]),pnt(pnt[group[point[0,0,0],point[1.62823103671263843693,0,0],point[0.814115518356319218466,1.41008944102341784860,0],point[0,0,0]],1073741827]),pnt(pnt[group[point[0,0,0],point[0.814115518356319218466,-0.470029813674472616199,0.341010112795151898939],point[1.62823103671263843693,0,0],point[0,0,0]],0]),pnt(pnt[group[point[1.62823103671263843693,0,0],point[0.814115518356319218466,1.41008944102341784860,0],point[1.62823103671263843693,0.940059627348945232397,0.341010112795151898939],point[1.62823103671263843693,0,0]],0]),pnt(pnt[group[point[0,0,0],point[0.814115518356319218466,1.41008944102341784860,0],point[-0.338813178901720135627e-20,0.940059627348945232397,0.341010112795151898939],point[0,0,0]],0]),pnt(pnt[point[0.28401534470392,0.77608329163015,-0.56305417894304],0,"H"]),pnt(pnt[group[point[0,0,0],point[0.81411551835632,1.4100894410234,0],point[0.28401534470392,0.77608329163015,-0.56305417894304],point[0,0,0]],1])],-0.956,1.5728,0.012778,-0.075631,-0.68204,-0.72727,0.2,0.2,0,2097152,1,1.8,0,1,65,[[0,0,1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,-1,0,0,180,1,0,0,1],[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,180,1,0,0,0],[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,180,1,0,0,0],[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,180,1,0,0,0],[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,180,1,0,0,0],[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,180,1,0,0,0],[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,180,1,0,0,0],[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,180,1,0,0,0]],24,18,256,0,100,0,0,1,0.1

,
// fltk N4xcas10Log_OutputE 23 3068 920 1 20 0

]
,
// fltk 7Fl_Tile 23 3070 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 3070 920 30 20 0
verification des contraintes sur la solution u=v
,
// fltk N4xcas10Log_OutputE 23 3100 920 1 20 0

]
,
// fltk 7Fl_Tile 23 3103 920 113 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 3103 920 69 20 0
distance(A,B), angle(A,F,B), distance(B,C), angle(B,A,C), £distance(C,D), angle(C,B,D),distance(D,E), angle(D,C,E), £distance(E,F), angle(E,D,F), distance(F,A), angle(F,E,A)
,
// fltk N4xcas10Log_OutputE 23 3172 920 1 20 0

,
// fltk N4xcas8EquationE 23 3173 920 43 20 0
1.0,1.9024088846738,1.0,1.9024088846738,1.0,1.9024088846738,1.0,1.9024088846738,1.0,1.9024088846738,1.0,1.9024088846738
]
,
// fltk 7Fl_Tile 23 3218 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 3218 920 30 20 0
2eme solution simple: on prend u=v et w s'obtient en resolvant eq
,
// fltk N4xcas10Log_OutputE 23 3248 920 1 20 0

]
,
// fltk 7Fl_Tile 23 3251 920 54 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 3251 920 30 20 0
v2:=solve(subst(eq,[u,T],[u2,Tf]),v)
,
// fltk N4xcas10Log_OutputE 23 3281 920 1 20 0

,
// fltk N4xcas8EquationE 23 3282 920 23 20 0
[3.0812363914163,-1.2836777080753]
]
,
// fltk 7Fl_Tile 23 3307 920 92 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 3307 920 48 20 0
Fv:=evalf(subst(F1,[L,v,phi],[1,v2[1],evalf(109/180*pi)])); distance(E,Fv); £angle(E,D,Fv), distance(Fv,A), angle(Fv,E,A)
,
// fltk N4xcas10Log_OutputE 23 3355 920 1 20 0

,
// fltk N4xcas8EquationE 23 3356 920 43 20 0
pnt(pnt[point[0.28401534470392,0.77608329163015,-0.56305417894304],0.0,"Fv"]),1.0,1.9024088846738,1.0,1.9024088846738
]
,
// fltk 7Fl_Tile 23 3401 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 3401 920 30 20 0
Si u different de v, alors P(u,w)=0 et P(v,w)=0 entraine v=w car P(x,w)=0 est de degré 2 en x, donc on a toutes les solutions
,
// fltk N4xcas10Log_OutputE 23 3431 920 1 20 0

]
,
// fltk 7Fl_Tile 23 3434 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 3434 920 30 20 0
Attention, ici la resolution par la methode d'elimination par les resultants echoue!
,
// fltk N4xcas10Log_OutputE 23 3464 920 1 20 0

]
,
// fltk 7Fl_Tile 23 3467 920 84 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 3467 920 30 20 0
P:=unapply(eq,u,v)
,
// fltk N4xcas10Log_OutputE 23 3497 920 1 20 0

,
// fltk N4xcas8EquationE 23 3498 920 53 20 0
 (u,v)->3*u^2*v^2*T^2+(-2*u^2)*v^2*T*sqrt(3)+(-3*u^2)*v^2+3*u^2*T^2-u^2+8*u*v+3*v^2*T^2-v^2+3*T^2+2*T*sqrt(3)-3
]
,
// fltk 7Fl_Tile 23 3553 920 64 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 3553 920 30 20 0
P(u,v)
,
// fltk N4xcas10Log_OutputE 23 3583 920 1 20 0

,
// fltk N4xcas8EquationE 23 3584 920 33 20 0
3*u^2*v^2*T^2+(-2*u^2)*v^2*T*sqrt(3)+(-3*u^2)*v^2+3*u^2*T^2-u^2+8*u*v+3*v^2*T^2-v^2+3*T^2+2*T*sqrt(3)-3
]
,
// fltk 7Fl_Tile 23 3619 920 264 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 3619 920 30 20 0
R:=resultant(P(u,v),P(u,w),u)
,
// fltk N4xcas10Log_OutputE 23 3649 920 1 20 0

,
// fltk N4xcas8EquationE 23 3650 920 233 20 0
576*v^4*T^4*w^2+576*v^4*T^4+(-384*sqrt(3))*v^4*T^3*w^2-768*v^4*T^2*w^2-384*v^4*T^2+128*sqrt(3)*v^4*T*w^2+192*v^4*w^2+64*v^4-1152*v^3*T^4*w^3-1152*v^3*T^4*w+768*sqrt(3)*v^3*T^3*w^3+1536*v^3*T^2*w^3+2304*v^3*T^2*w+(-256*sqrt(3))*v^3*T*w^3-384*v^3*w^3-640*v^3*w+576*v^2*T^4*w^4+1152*v^2*T^4*w^2+576*v^2*T^4+(-384*sqrt(3))*v^2*T^3*w^4+384*sqrt(3)*v^2*T^3-768*v^2*T^2*w^4-3840*v^2*T^2*w^2-768*v^2*T^2+128*sqrt(3)*v^2*T*w^4+(-128*sqrt(3))*v^2*T+192*v^2*w^4+1152*v^2*w^2+192*v^2-1152*v*T^4*w^3-1152*v*T^4*w+(-768*sqrt(3))*v*T^3*w+2304*v*T^2*w^3+1536*v*T^2*w+256*sqrt(3)*v*T*w-640*v*w^3-384*v*w+576*T^4*w^4+576*T^4*w^2+384*sqrt(3)*T^3*w^2-384*T^2*w^4-768*T^2*w^2+(-128*sqrt(3))*T*w^2+64*w^4+192*w^2
]
,
// fltk 7Fl_Tile 23 3885 920 31 20 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 3885 920 30 20 0
Et le resultant de R avec P(v,w) est nul car P(v,w) divise R 
,
// fltk N4xcas10Log_OutputE 23 3915 920 1 20 0

]
,
// fltk 7Fl_Tile 23 3918 920 84 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 3918 920 30 20 0
G:=gcd(R,P(v,w))
,
// fltk N4xcas10Log_OutputE 23 3948 920 1 20 0

,
// fltk N4xcas8EquationE 23 3949 920 53 20 0
3*v^2*T^2*w^2+3*v^2*T^2+(-2*sqrt(3))*v^2*T*w^2-3*v^2*w^2-v^2+8*v*w+3*T^2*w^2+3*T^2+2*sqrt(3)*T-w^2-3
]
,
// fltk 7Fl_Tile 23 4004 920 54 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 4004 920 30 20 0
normal(G-P(v,w))
,
// fltk N4xcas10Log_OutputE 23 4034 920 1 20 0

,
// fltk N4xcas8EquationE 23 4035 920 23 20 0
0
]
,
// fltk 7Fl_Tile 23 4060 920 64 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 4060 920 30 20 0
Gcof:=factor(R/G)
,
// fltk N4xcas10Log_OutputE 23 4090 920 1 20 0

,
// fltk N4xcas8EquationE 23 4091 920 33 20 0
64*(3*T^2-1)*(v-w)^2
]
,
// fltk 7Fl_Tile 23 4126 920 31 20 0
[
// fltk N4xcas19Multiline_Input_tabE 23 4126 920 30 20 0

,
// fltk N4xcas10Log_OutputE 23 4156 920 1 20 0

]