{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 "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 Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1388 " # ========= hyperbolo \357des ===============\n graf_hyp:= proc(a,b,c,pmUN,maxX,maxY,maxZ,m axk)\n local n,hyp,plan,m,cercle,cercle1,cercle1XY,cer_paraXY,cer_ para,t,u,R;\n if not(member(pmUN, \{1,-1\}) and a>0 and b>0 and c> 0 and a>= b) then\n print( \"V\351rifiez : le 4-i\350me param \350tre dans \{1,-1\} et a>0, b>0, c>0,\na>=b ?\"); break fi;\n n: =6;\n hyp:=x^2/a^2+y^2/b^2-z^2/c^2+pmUN;\n m:=c/b*sqrt( (a^2- b^2)/(a^2+c^2)): t:=arctan(m):\n plan:=z-m*y-k:\n cercle:=ma p(u ->collect(normal(u),[x,y,z]),[subs(z=m*y+k,hyp),plan]):\n\ncercle1 :=simplify(subs(x=X,y=Y*cos(t)-Z*sin(t),z=Y*sin(t)+Z*cos(t),cercle)): \n\ncercle1XY:=collect(simplify(subs(Z=solve(cercle1[2],Z),cercle1[1]) ),[X,Y]):\n cercle1XY:=collect(cercle1XY/coeff(cercle1XY,X^2),[X, Y]):\n R:=sqrt((coeff(cercle1XY,X)^2+coeff(cercle1XY,Y)^2)/4-subs (X=0,Y=0,cercle1XY)):\n cer_paraXY:=[ coeff(cercle1XY,X)/2+R*cos( u),\ncoeff(cercle1XY,Y)/2+R*sin(u),solve(cercle1[2],Z)]:\n cer_pa ra:= [cer_paraXY[1], cer_paraXY[2]*cos(t)+cer_paraXY[3]*sin(t),\n \+ -cer_paraXY[2]*sin(t)+cer_paraXY[3]*cos(t)]:\ndisplay3 d([implicitplot3d(hyp,x=-maxX..maxX,y=-maxY..maxY,z=-maxZ..maxZ\n,grid =[20,20,20],style=PATCHNOGRID),\n seq(spacecurve((subs(k =i*maxk/n,cer_para)),u=0..2*Pi,\ncolor=red),i=-n..n) ],\n\nscaling=con strained,view=[-maxX..maxX,-maxY..maxY,-maxZ..maxZ],orientation=[\n30, 70]);\n end:\n\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2839 " \+ # ========= ellipso\357de ===============\n graf_ell:= proc(a,b,c,max X,maxY,maxZ,maxk)# c < a < b\n local n,hyp,plan,m,cercle,cercle1,c ercle1XY,cer_paraXY,cer_para,t,u,R;\n if not(a>0 and b>0 and c>0 \+ and a>= c and b>=c) then\n print( \"V\351rifiez : a>0, b>0, c>0 , b >= a >= c ?\"); break fi;\n n:=4;\n hyp:=x^2/a^2+y^2/b^2+ z^2/c^2-1;\n m:=c/b*sqrt( (b^2-a^2)/(a^2-c^2)): t:=arctan(m):\n \+ plan:=z-m*y-k:\n cercle:=map(u ->collect(normal(u),[x,y,z]),[ subs(z=m*y+k,hyp),plan]):\n\ncercle1:=simplify(subs(x=X,y=Y*cos(t)-Z*s in(t),z=Y*sin(t)+Z*cos(t),cercle)):\n\ncercle1XY:=collect(simplify(sub s(Z=solve(cercle1[2],Z),cercle1[1])),[X,Y]):\n cercle1XY:=collect (cercle1XY/coeff(cercle1XY,X^2),[X,Y]):\n R:=sqrt(\n(coeff(cercle 1XY,X)^2+coeff(cercle1XY,Y)^2)/4-subs(X=0,Y=0,cercle1XY)):\n cer_ paraXY:=[ coeff(cercle1XY,X)/2+R*cos(u),\ncoeff(cercle1XY,Y)/2+R*sin(u ),solve(cercle1[2],Z)]:\n cer_para:= [cer_paraXY[1], cer_paraXY[2 ]*cos(t)+cer_paraXY[3]*sin(t),\n -cer_paraXY[2]*si n(t)+cer_paraXY[3]*cos(t)]:\n with(plots):\n display3d([implicitp lot3d(hyp,x=-maxX..maxX,y=-maxY..maxY,z=-maxZ..maxZ\n,grid=[20,20,20], style=PATCHNOGRID),\n seq(spacecurve((subs(k=i*maxk/n,ce r_para)),u=0..2*Pi,\ncolor=red),i=-n..n) ],\n\nscaling=constrained,vie w=[-maxX..maxX,-maxY..maxY,-maxZ..maxZ],orientation=[\n10,70]);\n end :\n # ========= parabolo\357de elliptique ===============\n graf_par a:=proc(a,b,maxX,maxY,maxZ,maxk)\n local t,n,para,section,sectionXY,c er_para,cer_paraXY,sol,R,cercle1XY,plan;\n if not(a>0 and b>0 a nd a>=b) then\n print( \"V\351rifiez : a>0, b>0, a >= b ?\"); \+ break fi;\n n:=4;\n para:=z-x^2/a^2-y^2/b^2;\n plan:=z- tan(t)*y-k:\n section:=[subs(z=tan(t)*y+k,para),plan]:\n\nsection XY:=simplify(subs(x=X,y=Y*cos(t)-Z*sin(t),z=Y*sin(t)+Z*cos(t),section \n)):\n\ncercle1XY:=collect(simplify(subs(Z=solve(sectionXY[2],Z),sect ionXY[1])),[X,Y\n]):\n sol:=[solve(coeff(cercle1XY,X,2)-coeff(cer cle1XY,Y,2),t)];\n\n cercle1XY:=evalf(subs(t=sol[1],cercle1XY)); \n cercle1XY:=collect(cercle1XY/coeff(cercle1XY,X,2),[X,Y]);\n \+ R:=sqrt(\n(coeff(cercle1XY,X)^2+coeff(cercle1XY,Y)^2)/4-subs(X=0,Y= 0,cercle1XY)):\n t:=sol[1];\n cer_paraXY:=[\ncoeff(cercle1XY ,X)/2+R*cos(u),coeff(cercle1XY,Y)/2+R*sin(u),solve(sectionXY[\n2],Z)]: \n cer_para:= simplify(evalf([cer_paraXY[1],\ncer_paraXY[2]*cos(t )+cer_paraXY[3]*sin(t),\n -cer_paraXY[2]*sin(t)+ce r_paraXY[3]*cos(t)])):\n\n with(plots):\n display3d([implici tplot3d(para,x=-maxX..maxX,y=-maxY..maxY,\n z=-maxZ. .maxZ ,grid=[20,20,20],style=PATCHNOGRID),\n seq(spacecurv e((subs(k=i*maxk/n,cer_para)),u=0..2*Pi,\n color=red ,thickness=2),i=-n..n) ],\n\nscaling=constrained,view=[-maxX..maxX,-ma xY..maxY,0..maxZ],orientation=[-100\n,70]);\nend:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 311 "#---------------- applications --------- ------------------------\n typ:='jpeg'; # ainsi, on peut changer tout \+ en gif ... ou autre\n\n graf_ell(2,3,1,2,3,1,0.7);\n plotsetup(inline) ;\n\n graf_hyp(3,2,2,1,24,16,16,6);\n plotsetup(inline);\n\n graf_hyp (3,2,4,-1,8,8,10,4);\n plotsetup(inline);\n\n graf_para(3,2,11,7,12,4 );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$typG%%jpegG" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "60-%+ISOSURFACEG6$X0%)anything G6\"6\"[gl'!%\"!!%[[hr\"5\"5\"5\"%C000000000000000C008000000000000BFF0 0000000000004000000000000000C000000000000000C008000000000000BFECA1AF28 6BCA1B3FFCCF11BA811050C000000000000000C008000000000000BFE9435E50D79436 3FF9F8E8992CAD08C000000000000000C008000000000000BFE5E50D79435E513FF77D 849C02D62AC000000000000000C008000000000000BFE286BCA1AF286C3FF55CE5C303 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