{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 6 1 {CSTYLE "" -1 -1 "Cour ier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output " -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title " -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 } 3 1 0 0 12 12 1 0 1 0 2 2 19 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 18 "" 0 "" {TEXT -1 47 " Clebsch, ses 27 droites, les points de Eckardt" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 171 "Le programme suivant a \351t \351 d\351velopp\351 afin de tracer les diff\351rents \351l\351ments e xplicit\351s dans le paragraphe correspondant du site de Robert Ferr \351ol sur la surface de Clebsch" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 83 " I. Plans de Sylvester, points de Eckardt, droites diagonales, dr oites de Schlafli" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 104 "D\351termina tion des \351l\351ments de base utiles pour un syst\350me de coordonn \351es explicit\351 au paragraphe suivant" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 1084 "restart:\n# =========== passage \351quations de d roites en param\351trique [x(t),y(t),z(t)]\nparametrage:= proc(L)\n \+ local n,i,j,k,tamp, uu,vv,ww; global t: \n tamp:=NULL: t:='t': n:=nop s(L):\n for i from 1 to n do\n uu:=convert(L[i],list): vv:=uu: \n for j from 1 to 3 do\n if lhs(uu[j])=rhs(uu[j]) th en\n if lhs(uu[j])=x then vv[1]:=t: \n \+ elif lhs(uu[j])=y then vv[2]:=t:\n \+ else vv[3]:=t :\n fi;\n w w:=subs(uu[j]=NULL,uu);\n for k from 1 to 2 do\n \+ if lhs(ww[k])=x then vv[1]:= subs(y=t,z=t,rhs(w w[k])):\n elif lhs(ww[k])=y then v v[2]:= subs(x=t,z=t,rhs(ww[k])):\n \+ else vv[3]:= subs(x=t,y=t,rhs(ww[k])):\n fi; \n od:\n fi;\n od:\ntamp:=tamp,vv: \nod:\n[tamp];\nend:\n# ====== PS[1..5] les 5 plans de Sylvester ===== =====\n PS:=[seq([ x[i]=0 ,convert(subsop(i=NULL,[seq(x[j], j= 1..5 )] ),`+`)=0],i=1..5)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 219 "# ===== DE[ i] les 10 \"droites de Sylvester\"\nDE:='DE':\nfor i from 1 to 4 do\n \+ for j from i+1 to 5 do\n DE[i,j]:=[ x[i]=0 , x[j] =0 ,convert( subsop(i=NULL,j=NULL,[seq(x[j], j= 1..5 )]),`+`)=0];\nod: od:\n#print( DE); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 336 "# ====== Pts_eck les 10 \+ points de Eckardt ==========\npt:='pt':\nfor i from 1 to 3 do\n for j from i+1 to 4 do\n for k from j+1 to 5 do\n pt[i,j,k]:=[x [i]=0,op(2,DE[i,j]),op(2,DE[i,k]),\n subs(x[i]=0,op(2,DE[i,j]),op(2, DE[i,k]),add(x[l],l=1..5))=0]:\nod;od:od:\nPts_eck:=convert(pt,set): p t:='pt':\n#nops(Pts_eck); print(Pts_eck);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 396 "# ====== droites diagonales ==========\n# ***** DD[i ,j] i=1..5, j=1..3 \ntamp:=NULL: DD:=NULL:\ndep:=\{seq(x[j], j= 1..5 ) \}:\nfor i from 1 to 5 do\n reste:=subs(dep[i]=NULL,dep);\n tamp:= dep[i]: un:= reste[1]:\n reste:=subs(reste[1]=NULL,reste);\n for j from 1 to 3 do\n deux:=reste[j]:\n reste1:=subs(deux=NULL,res te):\n DD:=DD,[tamp,un+reste[j],convert(reste1,`+`)]\n od:\nod: \nDD:=[DD]:" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 756 "# == ==== droites de Schlafli ==========\n# ***** Sch1[i,j], Sch2[i,j], 1 < = i < j <= 4\nSch1:=NULL: Sch2:=NULL:\nfip:=(1+sqrt(5))/2: fim:=(1-sqr t(5))/2:\nfor i from 1 to 3 do\n for j from i+1 to 4 do\n \+ reste:=subs(x[i]=NULL,x[j]=NULL,[x[1],x[2],x[3],x[4]]):\n Sch 1:=Sch1,[x[i]+fip*x[j]+reste[1],fip*x[i]+x[j]+reste[2],-fip*(x[i]+x[j] )+x[5]]:\n Sch2:=Sch2,[x[i]+fip*x[j]+reste[2],fip*x[i]+x[j]+r este[1],-fip*(x[i]+x[j])+x[5]]:\n od:\nod:\nSch1:=collect([Sch1] ,[seq(x[i],i=1..5)]): \nSch2:=collect([Sch2],[seq(x[i],i=1..5)]):\n# = ========= pour r\351tablir un double-six correct =================\n A :=Sch1: B:=Sch2:\n Sch1:=[A[1],A[3],A[4],A[6],B[2],B[5]]:\n Sch2:=[B[1 ],B[3],B[4],B[6],A[2],A[5]]:\n#======================================= =\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "penta:=[add(x[i]^3, i= 1..5) ,add(x[i], i= 1..5 )]:" }{TEXT -1 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 " Warning, the name changecoords has been redefined\n" }}{PARA 7 "" 1 " " {TEXT -1 43 "Warning, the name arrow has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace hav e been redefined and unprotected\n" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 27 " II. Recherc he de solutions" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 18 " quelques exem ples" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1125 "#tr:= [x[1] = X, x [2] = Y, x[3] = Z, x[4] = T+X+2*Y+3*Z] ;#10 Eck\n#tr:= [x[1] = X, x[2] = Y, x[3] = Z, x[4] = T+X-2*Y+2*Z] ;#10 Eck\n#tr:= [x[1] = X-2*Y+Z, x [2] = X+Y-2*Z, x[3] = Y+Z-2*X, x[4] = T+X] ;#10 Eck\n#tr:= [x[1] = X, \+ x[2] = Y, x[3] = Z, x[4] =-T+X+2*Y+3*Z] ;#10 Eck\n#tr:= [x[1] = X, x[2 ] = Y, x[3] = Z, x[4] =-T-X-Y-Z] ;#4 eck 24 dr\ntr:= [x[1]=(-3*X+Y+Z+T )/4,x[2]=(X-3*Y+Z+T)/4,x[3]=(X+Y-3*Z+T)/4,x[4] =(X+Y+Z-T)/2] ;#Ferreol 7 Eck 27 dr\n#tr:=[x[1] = X+Y, x[2] = Y+Z, x[3] = Z+X, x[4] = T-1*(X+ Y+Z)];# forme \340 7 pts concise\n#tr:=[x[1] = -3^(1/2)*Y+X+1/4*Z, x[2 ] = 3^(1/2)*Y+X+1/4*Z, x[3] = -2*X+1/4*Z, x[4] = 3/4*Z+T];# mienne \+ \340 7 termes\n#tr:= [x[1]=(-9*X+3*Y+3*Z+T)/4,x[2]=(3*X-9*Y+3*Z+T)/4, \n# x[3]=(3*X+3*Y-9*Z+T)/4,x[4]=(3*X+3*Y+3*Z-T)/2];#hunt\n#tr:=[x [1]=-X+Y+Z,x[2] =-Y+Z+T,x[3]=X-Z+T,x[4]=T-(X+Y+Z)];#10 eck ,peu dissym \351trique\n#tr:=[x[1] = -2*X+Y, x[2] = -2*Y+Z, x[3] = -2*Z+X, x[4] = \+ T+Z];#10 eck ,peu dissym\351trique\n#tr:=[x[1]=-X+2*Y+T,x[2] =-Y+2*Z+T ,x[3]=2*X-Z+T,x[4]=X+Y];#10 eck\n#tr:=[57/220*T+91/110*X-57/220*Y-57/2 20*Z, 171/440*T-57/220*X+269/440*Y-171/440*Z, 171/440*T-57/220*X-171/4 40*Y+269/440*Z]:" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# trG7&/&%\"xG6#\"\"\",**(\"\"$F*\"\"%!\"\"%\"XGF*F/*&F.F/%\"YGF*F**&F.F /%\"ZGF*F**&F.F/%\"TGF*F*/&F(6#\"\"#,**&F.F/F0F*F**(F-F*F.F/F2F*F/*&F. F/F4F*F**&F.F/F6F*F*/&F(6#F-,**&F.F/F0F*F**&F.F/F2F*F**(F-F*F.F/F4F*F/ *&F.F/F6F*F*/&F(6#F.,**&F:F/F0F*F**&F:F/F2F*F**&F:F/F4F*F**&F:F/F6F*F/ " }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 439 "#============= essai \+ de coordonn\351es =====================\nmat:='mat':\ntr:=[x[1] = -2*X +Y, x[2] = -2*Y+Z, x[3] = -2*Z+X, x[4] = T+Z];;\nliste:=map(rhs,tr):\n liste:=map(u ->[coeff(u,X),coeff(u,Y),coeff(u,Z),coeff(u,T)],liste) : \nmat:=matrix(4,4,liste):\nposs:=linalg[det](mat):\nif poss=0 then pri ntf(\"%s\\n\", \"Incorrect : Changement de variables non bijectif \"): \n else printf(\"%s\\n\", \"Correct : Changement de variable s bijectif \"): fi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#trG7&/&%\"xG 6#\"\"\",&*&\"\"#F*%\"XGF*!\"\"%\"YGF*/&F(6#F-,&*&F-F*F0F*F/%\"ZGF*/&F (6#\"\"$,&*&F-F*F6F*F/F.F*/&F(6#\"\"%,&%\"TGF*F6F*" }}{PARA 6 "" 1 "" {TEXT -1 43 "Correct : Changement de variables bijectif " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1798 "# ------------------------------- ------------------\n# calculs des \351quations ou coordonn\351es cart \351siennes\neq3:=subs(op(tr),penta[1]): eq4:=subs(op(tr),penta[2]):\n solx5:=solve(eq4,\{x[5]\}): # x5=-x1-.. -x4\npass_dir:= op(tr),op(solx 5) :\nSH:=subs(solx5,eq3):\npts:=subs(pass_dir,Pts_eck):\nptsnew:=[seq (solve(\{op(pts[i])\},\{X,Y,Z,T\}),i=1..nops(pts))]:\nprint(\"nombre d e Eckardt ( dist. finie ou non) = \",nops(pts)):\ntamp:=NULL:\nfor i f rom 1 to nops(ptsnew) do\n if not(has(ptsnew[i],'T=0')) then tamp :=tamp,ptsnew[i] fi;\nod:\nptsreels:=[tamp]:\nprint(\"nombre de Eckard t \340 dist. finie = \",nops(ptsreels)); \nif nops(pts)=10 then\nveri f:= [seq(has(ptsnew[i],'T=0'),i=1..nops(ptsnew))]:\n#print(verif);\nif has(verif,true)then \n printf(\"%a ne marche pas,%a points de \+ Eckardt \340 distance finie \\n\",tr,nops(ptsreels))\n else \+ \n printf(\"%a, marche : 10 pts de Eckardt \340 distance fi nie\\n\",tr): \n fi:\nelse printf(\"%a ne marche pas\\n\", tr)\nfi:\nS:= subs(X=x,Y=y,Z=z,T=1,SH);\neqE:=subs(X=x,Y=y,Z=z,T=1,pts reels):\nEck:=\{seq(solve(\{op(eqE[i])\},\{x,y,z\}),i=1..nops(eqE))\}: \nEckardt:=map(u -> subs(op(u),[x,y,z]),Eck):\n#### print(DD);\nPs:=su bs(X=x,Y=y,Z=z,T=1,subs(pass_dir,PS)):\nDd1:=subs(X=x,Y=y,Z=z,T=1,subs (pass_dir,DD)):\nSc1:=subs(X=x,Y=y,Z=z,T=1,subs(pass_dir,Sch1)):\nSc2: =subs(X=x,Y=y,Z=z,T=1,subs(pass_dir,Sch2)):\nDD1:=parametrage([seq(sol ve(\{op(Dd1[i])\},\{x,y,z\}),i=1..nops(Dd1))]):\nSC1:=parametrage([seq (solve(\{op(Sc1[i])\},\{x,y,z\}),i=1..nops(Sc1))]):\nSC2:=parametrage( [seq(solve(\{op(Sc2[i])\},\{x,y,z\}),i=1..nops(Sc1))]):\nS:=expand(S): \nprintf(\"Surface = %a\\n eq. d\351velopp\351e = %a\\n\",SH,S);\nprin tf(\"Plans de Sylvester : %a\\n\",Ps);\nprintf(\"Eckardt (%a) = %a \\n Dr. diagonales (%a) :\\n%a\\nDr. de Sclafli (%a) :\\n%a\\n%a\\n\" ,nop s(Eckardt),Eckardt,nops(DD1),DD1,nops(SC1)+nops(SC2),SC1,SC2):" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$QKnombre~de~Eckardt~(~dist.~finie~ou~n on)~=~6\"\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$QDnombre~de~Eckardt~| [y~dist.~finie~~=~6\"\"\"(" }}{PARA 6 "" 1 "" {TEXT -1 182 "[x[1] = -3 /4*X+1/4*Y+1/4*Z+1/4*T, x[2] = 1/4*X-3/4*Y+1/4*Z+1/4*T, x[3] = 1/4*X+1 /4*Y-3/4*Z+1/4*T, x[4] = 1/2*X+1/2*Y+1/2*Z-1/2*T] ne marche pas,7 poi nts de Eckardt \340 distance finie " }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"SG,,*$),**(\"\"$\"\"\"\"\"%!\"\"%\"xGF+F-*&F,F-%\"yGF+F+*&F,F-%\" zGF+F+#F+F,F+F*F+F+*$),**&F,F-F.F+F+*(F*F+F,F-F0F+F-*&F,F-F2F+F+F3F+F* F+F+*$),**&F,F-F.F+F+*&F,F-F0F+F+*(F*F+F,F-F2F+F-F3F+F*F+F+*$),**&\"\" #F-F.F+F+*&FDF-F0F+F+*&FDF-F2F+F+#F+FDF-F*F+F+*$),**&F,F-F.F+F-*&F,F-F 0F+F-*&F,F-F2F+F-#F+F,F-F*F+F+" }}{PARA 6 "" 1 "" {TEXT -1 151 "Surfac e = (-3/4*X+1/4*Y+1/4*Z+1/4*T)^3+(1/4*X-3/4*Y+1/4*Z+1/4*T)^3+(1/4*X+1/ 4*Y-3/4*Z+1/4*T)^3+(1/2*X+1/2*Y+1/2*Z-1/2*T)^3+(-1/4*X-1/4*Y-1/4*Z-1/4 *T)^3" }}{PARA 6 "" 1 "" {TEXT -1 211 " eq. d\351velopp\351e = -3/16*x *y*z+9/32*y+9/32*x+9/32*z-21/16*x*y+3/32*x^2-21/16*x*z-21/16*y*z+3/32* y^2+3/32*z^2+21/32*x^2*z+21/32*x^2*y+21/32*x*y^2+21/32*x*z^2+21/32*y^2 *z+21/32*y*z^2-9/32*y^3-9/32*x^3-3/32-9/32*z^3" }}{PARA 6 "" 1 "" {TEXT -1 304 "Plans de Sylvester : [[-3/4*x+1/4*y+1/4*z+1/4 = 0, 3/4*x -1/4*y-1/4*z-1/4 = 0], [1/4*x-3/4*y+1/4*z+1/4 = 0, 3/4*y-1/4*x-1/4*z-1 /4 = 0], [1/4*x+1/4*y-3/4*z+1/4 = 0, 3/4*z-1/4*x-1/4*y-1/4 = 0], [1/2* x+1/2*y+1/2*z-1/2 = 0, -1/2*x-1/2*y-1/2*z+1/2 = 0], [-1/4*x-1/4*y-1/4* z-1/4 = 0, 1/4*x+1/4*y+1/4*z+1/4 = 0]]" }}{PARA 6 "" 1 "" {TEXT -1 107 "Eckardt (7) = \{[0, -1, 0], [0, 1/2, 1/2], [-1, 0, 0], [1/2, 1/2, 0], [0, 0, -1], [1/2, 0, 1/2], [1, 1, 1]\} " }}{PARA 6 "" 1 "" {TEXT -1 21 "Dr. diagonales (15) :" }}{PARA 6 "" 1 "" {TEXT -1 210 "[[1, 2-t , t], [t, 3*t-1, 0], [t, 0, 3*t-1], [2-t, 1, t], [3*t-1, t, 0], [0, t, 3*t-1], [t, 2-t, 1], [3*t-1, 0, t], [0, 3*t-1, t], [t, -t+1, 0], [-t+ 1, 0, t], [0, -t+1, t], [t, -t, -1], [-t, -1, t], [-1, -t, t]]" }} {PARA 6 "" 1 "" {TEXT -1 21 "Dr. de Sclafli (12) :" }}{PARA 6 "" 1 "" {TEXT -1 421 "[[3/5*5^(1/2)*t+1/10*5^(1/2)+t+1/2, -1/5*5^(1/2)*t+3/10* 5^(1/2)+1/2, t], [t, 1/2+1/5*5^(1/2)*t-3/10*5^(1/2), t+1/2-3/5*5^(1/2) *t-1/10*5^(1/2)], [t, 3/5*5^(1/2)*t+1/10*5^(1/2)+t+1/2, -1/5*5^(1/2)*t +3/10*5^(1/2)+1/2], [1/2+1/5*5^(1/2)*t-3/10*5^(1/2), t+1/2-3/5*5^(1/2) *t-1/10*5^(1/2), t], [-1/5*5^(1/2)*t+3/10*5^(1/2)+1/2, t, 3/5*5^(1/2)* t+1/10*5^(1/2)+t+1/2], [7/2-3*t+5^(1/2)*t-3/2*5^(1/2), 3/2+5^(1/2)*t-1 /2*5^(1/2), t]]" }}{PARA 6 "" 1 "" {TEXT -1 441 "[[-1/5*5^(1/2)*t+3/10 *5^(1/2)+1/2, 3/5*5^(1/2)*t+1/10*5^(1/2)+t+1/2, t], [3/2+5^(1/2)*t-1/2 *5^(1/2), 7/2-3*t+5^(1/2)*t-3/2*5^(1/2), t], [t, -1/5*5^(1/2)*t+3/10*5 ^(1/2)+1/2, 3/5*5^(1/2)*t+1/10*5^(1/2)+t+1/2], [t, -3/4*t+3/4-1/4*5^(1 /2)*t-1/4*5^(1/2), -5/4*t+1/4-3/4*5^(1/2)*t+1/4*5^(1/2)], [3/5*5^(1/2) *t+1/10*5^(1/2)+t+1/2, t, -1/5*5^(1/2)*t+3/10*5^(1/2)+1/2], [-3/4*t+3/ 4-1/4*5^(1/2)*t-1/4*5^(1/2), -5/4*t+1/4-3/4*5^(1/2)*t+1/4*5^(1/2), t]] " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 39 " V\351rification \351ventuelle du double-six " }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Les droites du double-six sont mi ses bout \340 bout et les indices du double-six sont :" }}{PARA 0 "" 0 "" {TEXT -1 37 "[1,2,3,4, 5, 6 ]\n[7,8,9,10,11,12]" }}{PARA 0 " " 0 "" {TEXT -1 135 "La v\351rification calcule les coordonn\351es des points d'intersection et les indices des droites correspondantes \340 ce point sous la forme :" }}{PARA 0 "" 0 "" {TEXT -1 47 "[ [x,y,z], \+ \{indice droite 1,indice droite 2\} ] " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "# lesdroites de Schlaef li sont SC1 et SC2:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 488 "#### rech erche du num\351ro d'ordre dans l'ensemble \"droites\" #####\nnumero:= proc(dr)\n local j:\n for j from 1 while (j<= nops(droites)) and evalb(droites[j]<>dr) do od:\n j;\nend:\n#### Num\351ros d'ordr e d'une partie de l'ensemble \"droites\" ######\nordre_partie:= proc(p artie,affichage::\{0,1\})\n local ordre,i:\n ordre:=[seq(0,i=1..no ps(partie))]:\n for i from 1 to 6 do\n ordre[i]:=numero(partie[i ]);\n od:\n if affichage = 1 then\n printf(\"Num\351ros des \+ droites %a\",ordre);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 " for \+ i from 1 to nops(ordre) do print(partie[i],\"___\",droites[ordre[i]]) \+ od;\n fi;\n ordre;\nend:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 664 " # ### 0 pas d'affichage, 1 affichage des points\nptscom:=proc(tot,affich age::\{0,1\})\n local i,j,n,sol,pts ,w:\n n:=nops(tot):pts:=NULL: \n for i from 1 to n-1 do\n for j from i+1 to n do\n sol:= [solve(\{op(expand(tot[i]-subs(t=w,tot[j])))\}, \{t,w\})]:\n \+ \n if sol<>[] then \n pts:=pts,[radnormal(subs( op(sol),tot[i]),'rationalized'),\{i,j\}]\n fi;\n od;\n od: \n pts:=[pts]:\n if affichage =1 then \n printf(\" Nombre de droites = %d\\n\",nops(tot));\n printf(\"Nombre de points d'int ersection = %a %s\",nops(pts),\n \"--- [ point,[n\260 dr1, \+ n\260 dr2] dans l'ens. donn\351]\");\n print(pts);\n fi;\n pt s;\nend:" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "# ====== faire effectuer l'instruction suivante d\351sir\351e ============" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "#### points communs de toutes les d roites\npts_dble_six:=ptscom([op(SC1),op(SC2)],1):" }{TEXT -1 0 "" }} {PARA 6 "" 1 "" {TEXT -1 23 " Nombre de droites = 12" }}{PARA 6 "" 1 " " {TEXT -1 85 "Nombre de points d'intersection = 30 --- [ point,[n \260 dr1, n\260 dr2] dans l'ens. donn\351]" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7@7$7%,&*(\"\"&\"\"\"\"#A!\"\"F(#F)\"\"#F)#\"#8F*F)F&,& #\"\"%\"#6F)*&F3F+F(F,F+<$F)\"\"(7$7%,&#F6F-F+*(\"\"$F)F-F+F(F,F+,&#F< F-F)*&F-F+F(F,F),&*$F(F,F+F)F+<$F)\"\")7$7%,&*&\"\"'F+F(F,F+#F)FHF+,&# F-FF),&F)F+FAF),&#F6F-F+*(F " 0 "" {MPLTEXT 1 0 0 "" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 701 "# =============== trac\351s ===============\nwith(plots):\naa:=2.5;\ninter:=map( u->u[1],ptscom([ op(SC1),op(SC2)],0)):\ng_pts:=pointplot3d(inter,symbol=circle,symbolsi ze=15,color=black):\ndx:=-aa: fx:=aa: dy:=-aa: fy:=aa: dz:=-aa: fz:=aa : dt:=-4: ft:=4:\ng_surf:=implicitplot3d(S,x=dx..fx,y=dy..fy,z=dz..fz, grid=[20,20,20],style=patchnogrid):\ng_diag:=spacecurve(\{op(DD1)\},t= dt..ft,numpoints=2,color=yellow,thickness=3):\ng_sc1:=spacecurve(\{op( SC1)\},t=dt..ft,numpoints=2,color=blue,thickness=3):\ng_sc2:=spacecurv e(\{op(SC2)\},t=dt..ft,numpoints=2,color=red,thickness=3):\nplotsetup( inline):\ndisplay([g_surf,g_diag,g_sc1,g_sc2],scaling=constrained,ligh tmodel=light2,view=[dx..fx,dy..fy,dz..fz],orientation=[45,80]);\n" } {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#aaG$\"#D!\"\"" }} {PARA 13 "" 1 "" {GLPLOT3D 486 486 486 {PLOTDATA 3 "6C-%+ISOSURFACEG6$ X0%)anythingG6\"6\"[gl'!%\"!!%[[hr\"5\"5\"5\"%C004000000000000C0040000 00000000C004000000000000C0519DC000000000C004000000000000C0040000000000 00C001E50D79435E51C05005912404545AC004000000000000C004000000000000BFFF 9435E50D7944C04CF1D15D586B30C004000000000000C004000000000000BFFB5E50D7 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