// fltk 7Fl_Tile 32 63 1061 531 25 [ // fltk N4xcas6FigureE 32 63 1061 530 25 // fltk N4xcas12History_PackE 34 -1095 330 1688 25 [ // fltk 7Fl_Tile 62 -1095 302 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -1095 302 35 25 A:=point([2,-2,0]); , // fltk N4xcas10Log_OutputE 62 -1060 302 1 25 , // fltk N4xcas10Gen_OutputE 62 -1059 302 32 14 pnt(pnt[[2,-2,0],0,"A"]) ] , // fltk 7Fl_Tile 62 -1025 302 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -1025 302 35 25 O:=point([3,0,0]); , // fltk N4xcas10Log_OutputE 62 -990 302 1 25 , // fltk N4xcas10Gen_OutputE 62 -989 302 32 14 pnt(pnt[[3,0,0],0,"O"]) ] , // fltk 7Fl_Tile 62 -955 302 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -955 302 35 25 C:=point([1/2,5/2,0]); , // fltk N4xcas10Log_OutputE 62 -920 302 1 25 , // fltk N4xcas10Gen_OutputE 62 -919 302 32 14 pnt(pnt[[1/2,5/2,0],0,"C"]) ] , // fltk 7Fl_Tile 62 -885 302 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -885 302 35 25 B:=point([0,0,2]); , // fltk N4xcas10Log_OutputE 62 -850 302 1 25 , // fltk N4xcas10Gen_OutputE 62 -849 302 32 14 pnt(pnt[[0,0,2],0,"B"]) ] , // fltk 7Fl_Tile 62 -815 302 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -815 302 35 25 d1:=droite(A,C,affichage=hidden_name+line_width_3+rouge) , // fltk N4xcas10Log_OutputE 62 -780 302 1 25 , // fltk 9Fl_Scroll 62 -779 302 59 14 [ // fltk N4xcas10Gen_OutputE 62 -779 536 32 14 pnt(pnt[line[[2,-2,0],[1/2,5/2,0]],-2147352575,"d1"]) , // fltk 12Fl_Scrollbar 62 214 286 25 14 [] , // fltk 12Fl_Scrollbar 348 182 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 -718 302 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -718 302 35 25 d2:=droite(O,B,affichage=hidden_name+line_width_3+rouge) , // fltk N4xcas10Log_OutputE 62 -683 302 1 25 , // fltk 9Fl_Scroll 62 -682 302 59 14 [ // fltk N4xcas10Gen_OutputE 62 -682 488 32 14 pnt(pnt[line[[3,0,0],[0,0,2]],-2147352575,"d2"]) , // fltk 12Fl_Scrollbar 62 214 286 25 14 [] , // fltk 12Fl_Scrollbar 348 182 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 -621 302 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -621 302 35 25 assume(u:=[-0.28,-1.0,1.0]) , // fltk N4xcas10Log_OutputE 62 -586 302 1 25 , // fltk N4xcas10Gen_OutputE 62 -585 302 32 14 parameter(u,-1.0,1.0,-0.28) ] , // fltk 7Fl_Tile 62 -551 302 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -551 302 35 25 assume(v:=[0.28,-1.0,1.0]) , // fltk N4xcas10Log_OutputE 62 -516 302 1 25 , // fltk N4xcas10Gen_OutputE 62 -515 302 32 14 parameter(v,-1.0,1.0,0.28) ] , // fltk 7Fl_Tile 62 -481 302 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -481 302 35 25 M:=element(d2,u); , // fltk N4xcas10Log_OutputE 62 -446 302 1 25 , // fltk 9Fl_Scroll 62 -445 302 59 14 [ // fltk N4xcas10Gen_OutputE 62 -445 807 32 14 pnt(pnt[[3*u,0,2*(1-u)],[0,[pnt(pnt[line[[3,0,0],[0,0,2]],-2147352575]),u]],"M"]) , // fltk 12Fl_Scrollbar 62 214 286 25 14 [] , // fltk 12Fl_Scrollbar 348 182 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 -384 302 63 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -384 302 30 25 H:=projection(d1,M);segment(H,M); , // fltk N4xcas10Log_OutputE 62 -354 302 1 25 , // fltk N4xcas10Gen_OutputE 62 -353 302 32 14 Too large for display ] , // fltk 7Fl_Tile 62 -319 302 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -319 302 35 25 N:=element(d1,v); , // fltk N4xcas10Log_OutputE 62 -284 302 1 25 , // fltk 9Fl_Scroll 62 -283 302 59 14 [ // fltk N4xcas10Gen_OutputE 62 -283 1034 32 14 pnt(pnt[[2*v+1/2*(1-v),-2*v+5/2*(1-v),0],[0,[pnt(pnt[line[[2,-2,0],[1/2,5/2,0]],-2147352575]),v]],"N"]) , // fltk 12Fl_Scrollbar 62 214 286 25 14 [] , // fltk 12Fl_Scrollbar 348 182 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 -222 302 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -222 302 35 25 P:=affichage(parallele(A,d1,d2),hidden_name+cyan) , // fltk N4xcas10Log_OutputE 62 -187 302 1 25 , // fltk 9Fl_Scroll 62 -186 302 59 14 [ // fltk N4xcas10Gen_OutputE 62 -186 604 32 14 pnt(pnt[hyperplan([[9,3,27/2],[2,-2,0]]),-2147483642,"P"]) , // fltk 12Fl_Scrollbar 62 214 286 25 14 [] , // fltk 12Fl_Scrollbar 348 182 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 -125 302 63 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -125 302 30 25 H0:=projection(P,M);segment(H0,M); , // fltk N4xcas10Log_OutputE 62 -95 302 1 25 , // fltk N4xcas10Gen_OutputE 62 -94 302 32 14 Too large for display ] , // fltk 7Fl_Tile 62 -60 302 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -60 302 35 25 d:=affichage(projection(P,d2),hidden_name+line_width_3) , // fltk N4xcas10Log_OutputE 62 -25 302 1 25 , // fltk 9Fl_Scroll 62 -24 302 59 14 [ // fltk N4xcas10Gen_OutputE 62 -24 887 32 14 pnt(pnt[line[[303/121,-20/121,-90/121],[-60/121,-20/121,152/121]],-2147352576,"d"]) , // fltk 12Fl_Scrollbar 62 214 286 25 14 [] , // fltk 12Fl_Scrollbar 348 182 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 37 302 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 37 302 35 25 K:=inter_unique(d,d1); , // fltk N4xcas10Log_OutputE 62 72 302 1 25 , // fltk 9Fl_Scroll 62 73 302 59 14 [ // fltk N4xcas10Gen_OutputE 62 73 369 32 14 pnt(pnt[[168/121,-20/121,0],0,"K"]) , // fltk 12Fl_Scrollbar 62 107 302 25 14 [] , // fltk 12Fl_Scrollbar 364 73 16 34 14 [] ] ] , // fltk 7Fl_Tile 62 134 302 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 134 302 35 25 L:=projection(d2,K); , // fltk N4xcas10Log_OutputE 62 169 302 1 25 , // fltk 9Fl_Scroll 62 170 302 59 14 [ // fltk N4xcas10Gen_OutputE 62 170 357 32 14 pnt(pnt[[228/121,0,90/121],0,"L"]) , // fltk 12Fl_Scrollbar 62 204 302 25 14 [] , // fltk 12Fl_Scrollbar 364 170 16 34 14 [] ] ] , // fltk 7Fl_Tile 62 231 302 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 231 302 35 25 l:=longueur2(K,L); , // fltk N4xcas10Log_OutputE 62 266 302 1 25 , // fltk N4xcas10Gen_OutputE 62 267 302 32 14 100/121 ] , // fltk 7Fl_Tile 62 301 302 63 25 [ // fltk N4xcas19Multiline_Input_tabE 62 301 302 30 25 normal(longueur2(M,H0)); , // fltk N4xcas10Log_OutputE 62 331 302 1 25 , // fltk N4xcas10Gen_OutputE 62 332 302 32 14 100/121 ] , // fltk 7Fl_Tile 62 366 302 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 366 302 35 25 affichage(perpendiculaire_commune(d1,d2),magenta+line_width_3) , // fltk N4xcas10Log_OutputE 62 401 302 1 25 , // fltk 9Fl_Scroll 62 402 302 59 14 [ // fltk N4xcas10Gen_OutputE 62 402 649 32 14 pnt(pnt[line[[168/121,-20/121,0],[228/121,0,90/121]],131077]) , // fltk 12Fl_Scrollbar 62 436 302 25 14 [] , // fltk 12Fl_Scrollbar 364 402 16 34 14 [] ] ] , // fltk 7Fl_Tile 62 463 302 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 463 302 35 25 segment(M,N,affichage=vert+line_width_2) , // fltk N4xcas10Log_OutputE 62 498 302 1 25 , // fltk 9Fl_Scroll 62 499 302 59 14 [ // fltk N4xcas10Gen_OutputE 62 499 744 32 14 pnt(pnt[group[[3*u,0,2*(1-u)],[2*v+1/2*(1-v),-2*v+5/2*(1-v),0]],65538]) , // fltk 12Fl_Scrollbar 62 533 302 25 14 [] , // fltk 12Fl_Scrollbar 364 499 16 34 14 [] ] ] , // fltk 7Fl_Tile 62 560 302 31 25 [ // fltk N4xcas19Multiline_Input_tabE 62 560 302 30 25 , // fltk N4xcas10Log_OutputE 62 590 302 1 25 ] ] // fltk N4xcas5Geo3dE 382 94 591 499 25 -3.535,3.535,-3.535,3.535,[pnt(pnt[[2,-2,0],0,"A"]),pnt(pnt[[3,0,0],0,"O"]),pnt(pnt[[1/2,5/2,0],0,"C"]),pnt(pnt[[0,0,2],0,"B"]),pnt(pnt[line[[2,-2,0],[1/2,5/2,0]],-2147352575,"d1"]),pnt(pnt[line[[3,0,0],[0,0,2]],-2147352575,"d2"]),parameter(u,-1.0,1.0,-0.28),parameter(v,-1.0,1.0,0.28),pnt(pnt[[3*u,0,2*(1-u)],[0,[pnt(pnt[line[[3,0,0],[0,0,2]],-2147352575]),u]],"M"]),pnt(pnt[[2-3/2*((3*u-2)*-3/2+9)/(45/2),-2+9/2*((3*u-2)*-3/2+9)/(45/2),0],0,"H"]),pnt(pnt[group[[2-3/2*((-3*(3*u-2))/2+9)*2/45,-2+9/2*((-3*(3*u-2))/2+9)*2/45,0],[3*u,0,2*(1-u)]],0]),pnt(pnt[[2*v+1/2*(1-v),-2*v+5/2*(1-v),0],[0,[pnt(pnt[line[[2,-2,0],[1/2,5/2,0]],-2147352575]),v]],"N"]),pnt(pnt[hyperplan([[9,3,27/2],[2,-2,0]]),-2147483642,"P"]),pnt(pnt[[3*u+9*((2-3*u)*9-6+(-2*(1-u))*27/2)/(1089/4),3*((2-3*u)*9-6+(-2*(1-u))*27/2)/(1089/4),2*(1-u)+27/2*((2-3*u)*9-6+(-2*(1-u))*27/2)/(1089/4)],0,"H0"]),pnt(pnt[group[[3*u+9*((2-3*u)*9-6+(-2*(1-u))*27/2)*4/1089,3*((2-3*u)*9-6+(-2*(1-u))*27/2)*4/1089,2*(1-u)+27/2*((2-3*u)*9-6+(-2*(1-u))*27/2)*4/1089],[3*u,0,2*(1-u)]],0]),pnt(pnt[line[[303/121,-20/121,-90/121],[-60/121,-20/121,152/121]],-2147352576,"d"]),pnt(pnt[[168/121,-20/121,0],0,"K"]),pnt(pnt[[228/121,0,90/121],0,"L"]),100/121,100/121,pnt(pnt[line[[168/121,-20/121,0],[228/121,0,90/121]],131077]),pnt(pnt[group[[3*u,0,2*(1-u)],[2*v+1/2*(1-v),-2*v+5/2*(1-v),0]],65538])],-3.535,3.535,0.20192,-0.098448,-0.8061,-0.54748,0.5,0.5,0,2097152,1,2.5,0 , // fltk N4xcas10Log_OutputE 32 593 1061 1 25 ] , // fltk 7Fl_Tile 32 596 1061 75 25 [ // fltk N4xcas23Comment_Multiline_InputE 32 596 1061 74 25 Resolution analytique du probleme, on calcule d'abord la longueur au carre, puis£sa derivee par rapport a u et v qui doit s'annuler, on en deduit u et v correspondant au minimum£ainsi que la longueur minimale. , // fltk N4xcas10Log_OutputE 32 670 1061 1 25 ] , // fltk 7Fl_Tile 32 673 1061 113 25 [ // fltk N4xcas19Multiline_Input_tabE 32 673 1061 35 25 f:=normal(longueur2(M,N)) , // fltk N4xcas10Log_OutputE 32 708 1061 1 25 , // fltk N4xcas8EquationE 32 709 1061 77 25 (45*v^2)/2+(-9)*v*u-21*v+13*u^2-11*u+21/2 ] , // fltk 7Fl_Tile 32 788 1061 103 25 [ // fltk N4xcas19Multiline_Input_tabE 32 788 1061 35 25 fu:=diff(f,[u,v]); , // fltk N4xcas10Log_OutputE 32 823 1061 1 25 , // fltk N4xcas8EquationE 32 824 1061 67 25 [(-9)*v+13*2*u-11,(45*2*v)/2-9*u-21] ] , // fltk 7Fl_Tile 32 893 1061 103 25 [ // fltk N4xcas19Multiline_Input_tabE 32 893 1061 35 25 sol:=solve(fu,[u,v]); , // fltk N4xcas10Log_OutputE 32 928 1061 1 25 , // fltk N4xcas8EquationE 32 929 1061 67 25 [[76/121,215/363]] ] , // fltk 7Fl_Tile 32 998 1061 103 25 [ // fltk N4xcas19Multiline_Input_tabE 32 998 1061 35 25 normal(subst(f,[u,v],sol[0])) , // fltk N4xcas10Log_OutputE 32 1033 1061 1 25 , // fltk N4xcas8EquationE 32 1034 1061 67 25 100/121 ] , // fltk 7Fl_Tile 32 1103 1061 53 25 [ // fltk N4xcas23Comment_Multiline_InputE 32 1103 1061 52 25 On trace la fonction f=MN^2 des 2 variables u,v avec des niveaux de couleur pour representer£la valeur de f, le minimum en violet semble effectivement atteint pour u,v = [76/121,215/363] , // fltk N4xcas10Log_OutputE 32 1155 1061 1 25 ] , // fltk 7Fl_Tile 32 1158 1061 414 25 [ // fltk N4xcas19Multiline_Input_tabE 32 1158 1061 35 25 plotdensity(f,[u=-3..3,v=-3..3]) , // fltk N4xcas10Log_OutputE 32 1193 1061 24 25 Evaluation time: 0.12£ , // fltk 7Fl_Tile 32 1217 1061 355 25 [ // fltk N4xcas7Graph2dE 32 1217 983 355 25 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, // fltk 7Fl_Tile 1015 1217 78 355 25 [ // fltk N4xcas14Mouse_PositionE 1015 1217 78 28 25 [] , // fltk 8Fl_Group 1015 1245 78 85 25 [ // fltk 9Fl_Button 1015 1245 26 17 25 [] , // fltk 9Fl_Button 1041 1245 26 17 25 [] , // fltk 9Fl_Button 1067 1245 26 17 25 [] , // fltk 9Fl_Button 1015 1262 26 17 25 [] , // fltk 9Fl_Button 1041 1262 26 17 25 [] , // fltk 9Fl_Button 1067 1262 26 17 25 [] , // fltk 9Fl_Button 1015 1279 26 17 25 [] , // fltk 9Fl_Button 1041 1279 26 17 25 [] , // fltk 9Fl_Button 1067 1279 26 17 25 [] , // fltk 9Fl_Button 1015 1296 26 17 25 [] , // fltk 9Fl_Button 1041 1296 26 17 25 [] , // fltk 9Fl_Button 1067 1296 26 17 25 [] , // fltk 9Fl_Button 1015 1313 26 17 25 [] , // fltk 11Fl_Menu_Bar 1041 1313 52 17 25 [] ] , // fltk 8Fl_Group 1015 1330 78 242 25 [ ] ] ] ] , // fltk 7Fl_Tile 32 1574 1061 36 25 [ // fltk N4xcas19Multiline_Input_tabE 32 1574 1061 35 25 , // fltk N4xcas10Log_OutputE 32 1609 1061 1 25 ]