{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 "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 "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Plane equations n\{B0:B1:B2:0\}. p\{P0:P1 :P2:P3\}" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "n:=N0+N1*b1+N2* b2;p:=P0+P1*c1+P2*c2+P3*c3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG, (%#N0G\"\"\"*&%#N1GF'%#b1GF'F'*&%#N2GF'%#b2GF'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,*%#P0G\"\"\"*&%#P1GF'%#c1GF'F'*&%#P2GF'%#c2GF'F' *&%#P3GF'%#c3GF'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "4 Sphere eq uations" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "b:=(b1-n1)^2+(b2 -n2)^2+(b3-n3)^2-r;c:=(c1-p1)^2+(c2-p2)^2+(c3-p3)^2-s; " }{TEXT -1 0 " " }{MPLTEXT 1 0 69 "ab:=b1^2+(b2-a2)^2+(b3-a3)^2-alpha;ac:=c1^2+(c2-a2 )^2+(c3-a3)^2-beta;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG,**$),&%# b1G\"\"\"%#n1G!\"\"\"\"#F*F**$),&%#b2GF*%#n2GF,F-F*F**$),&%#b3GF*%#n3G F,F-F*F*%\"rGF," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG,**$),&%#c1G \"\"\"%#p1G!\"\"\"\"#F*F**$),&%#c2GF*%#p2GF,F-F*F**$),&%#c3GF*%#p3GF,F -F*F*%\"sGF," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#abG,**$)%#b1G\"\"# \"\"\"F**$),&%#b2GF*%#a2G!\"\"F)F*F**$),&%#b3GF*%#a3GF0F)F*F*%&alphaGF 0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#acG,**$)%#c1G\"\"#\"\"\"F**$), &%#c2GF*%#a2G!\"\"F)F*F**$),&%#c3GF*%#a3GF0F)F*F*%%betaGF0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Distance equation" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 40 "bc:=(c1-b1)^2+(c2-b2)^2+(c3-b3)^2-gamma;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#bcG,**$),&%#c1G\"\"\"%#b1G!\"\"\"\" #F*F**$),&%#c2GF*%#b2GF,F-F*F**$),&%#c3GF*%#b3GF,F-F*F*%&gammaGF," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "bab:=simplify(b-ab);cac:=sim plify(c-ac);bcbc:=simplify(bc-b-c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%$babG,:*(\"\"#\"\"\"%#b1GF(%#n1GF(!\"\"*$)F*F'F(F(*(F'F(%#b2GF(%#n2 GF(F+*$)F0F'F(F(*(F'F(%#b3GF(%#n3GF(F+*$)F5F'F(F(%\"rGF+*(F'F(F/F(%#a2 GF(F(*$)F:F'F(F+*(F'F(F4F(%#a3GF(F(*$)F>F'F(F+%&alphaGF(" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$cacG,:*(\"\"#\"\"\"%#c1GF(%#p1GF(!\"\"*$)F*F' F(F(*(F'F(%#c2GF(%#p2GF(F+*$)F0F'F(F(*(F'F(%#c3GF(%#p3GF(F+*$)F5F'F(F( %\"sGF+*(F'F(F/F(%#a2GF(F(*$)F:F'F(F+*(F'F(F4F(%#a3GF(F(*$)F>F'F(F+%%b etaGF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%bcbcG,F%\"rG\"\"\"%\"sGF' *(\"\"#F'%#b1GF'%#n1GF'F'*$)F,F*F'!\"\"*(F*F'%#b2GF'%#n2GF'F'*$)F2F*F' F/*(F*F'%#b3GF'%#n3GF'F'*$)F7F*F'F/*$)%#p1GF*F'F/*(F*F'%#c2GF'%#p2GF'F '*$)F?F*F'F/*(F*F'%#c3GF'%#p3GF'F'*$)FDF*F'F/*(F*F'%#c1GF'FF'F1F'F/*(F*F'FCF'F6F'F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "e1:=resultant(n,bab,b1);e2:=resultant(p,c ac,c1);e3:=resultant(resultant(b,bcbc,b1),p,c1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e1G,<*(\"\"#\"\"\"%#n1GF(%#N0GF(F(**F'F(F)F(%#N2GF(% #b2GF(F(*&%#N1GF()F)F'F(F(**F'F(F/F(F-F(%#n2GF(!\"\"*&F/F()F2F'F(F(**F 'F(F/F(%#b3GF(%#n3GF(F3*&F/F()F8F'F(F(*&F/F(%\"rGF(F3**F'F(F/F(F-F(%#a 2GF(F(*&F/F()F>F'F(F3**F'F(F/F(F7F(%#a3GF(F(*&F/F()FBF'F(F3*&F/F(%&alp haGF(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e2G,>*(\"\"#\"\"\"%#p1GF (%#P0GF(F(**F'F(F)F(%#P2GF(%#c2GF(F(**F'F(F)F(%#P3GF(%#c3GF(F(*&%#P1GF ()F)F'F(F(**F'F(F2F(F-F(%#p2GF(!\"\"*&F2F()F5F'F(F(**F'F(F2F(F0F(%#p3G F(F6*&F2F()F:F'F(F(*&F2F(%\"sGF(F6**F'F(F2F(F-F(%#a2GF(F(*&F2F()F@F'F( F6**F'F(F2F(F0F(%#a3GF(F(*&F2F()FDF'F(F6*&F2F(%%betaGF(F(" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#e3G,h]m**\"\"#\"\"\")%#P1GF'F()%#p2GF'F(%&ga mmaGF(F(**F'F(F)F()%#n2GF'F()%#n3GF'F(F(**\"\")F()%#P0GF'F(%#b2GF(F0F( !\"\"**F'F(F)F(%\"rGF(F-F(F8**F'F(F)F()%#n1GF'F()%#p3GF'F(F8**F'F(F)F( )%#p1GF'F(F-F(F(**F'F(F)F(FF(F(**F'F(F)F(F:F(FF(F(*(FIF(F5F (F/F(F(*(FIF(F5F(FF(FBF(F(*,FIF(F6F(F*F(F=F(F/F(F (*,FIF(F6F(F*F(F=F(F+F(F8*,FIF(F6F(F*F(F=F(F1F(F(*,FIF(F6F(F*F(F=F(FAF (F8*,FIF(F6F(F*F(F=F(F>F(F8*,FIF(F6F(F*F(F:F(FBF(F8*,FIF(F6F(F*F(F=F(F :F(F8*,FIF(F6F(F*F(F=F(FMF(F(*,FIF(F6F(F*F(FF(FBF(F(*.FIF(FYF(FenF(F*F(F=F (F/F(F(*.FIF(FYF(FenF(F*F(F=F(F+F(F8*.FIF(FYF(FenF(F*F(F=F(F1F(F(*.FIF (FYF(FenF(F*F(F=F(FAF(F8*.FIF(FYF(FenF(F*F(F=F(F>F(F8*.FIF(FYF(FenF(F* F(F:F(FBF(F8*.FIF(FYF(FenF(F*F(F=F(F:F(F8*.FIF(FYF(FenF(F*F(F=F(FMF(F( *.FIF(FYF(FenF(F*F(FF(FBF(F(*.FIF(F^oF(FRF(F*F(F =F(F/F(F(*.FIF(F^oF(FRF(F*F(F=F(F+F(F8*.FIF(F^oF(FRF(F*F(F=F(F1F(F(*.F IF(F^oF(FRF(F*F(F=F(FAF(F8*.FIF(F^oF(FRF(F*F(F=F(F>F(F8*.FIF(F^oF(FRF( F*F(F:F(FBF(F8*.FIF(F^oF(FRF(F*F(F=F(F:F(F8*.FIF(F^oF(FRF(F*F(F=F(FMF( F(*.FIF(F^oF(FRF(F*F(FF(F8*,F4F(F)F(Fgn F(F2F(FRF(F8*,FIF(F)F(FF(F8*,F4F(F)F(FjnF(F0F(FenF(F8*,FIF(F)F(F/F(FenF(F,F(F 8*,FIF(F)F(F/F(FRF(F?F(F8*,FIF(F)F(F/F(FenF(F7F(F(*,FIF(F)F(F/F(FRF(FG F(F(*,FIF(F)F(F+F(FRF(F?F(F8*,FIF(F)F(F+F(FenF(F7F(F(*,FIF(F)F(F+F(FRF (FGF(F(*,FIF(F)F(F1F(FenF(F,F(F8*,FIF(F)F(F1F(FRF(F?F(F8*,FIF(F)F(F1F( FenF(F7F(F(*,FIF(F)F(F1F(FRF(FGF(F(*,FIF(F)F(FAF(FenF(F,F(F8*,FIF(F)F( FAF(FRF(F?F(F8*,FIF(F)F(FAF(FenF(F7F(F(*,FIF(F)F(FAF(FRF(FGF(F(*,FIF(F )F(FenF(F,F(F>F(F8*,F4F(F)F(FZF(F,F(F7F(F8*,F4F(F)F(F_oF(F?F(FGF(F8*,F IF(F)F(F>F(FenF(F7F(F(*,FIF(F)F(F>F(FRF(FGF(F(*,FIF(F)F(F:F(FGF(F2F(F( *,FIF(F)F(F:F(F7F(F0F(F(*,FIF(F)F(F:F(FRF(F?F(F(*,FIF(F)F(F:F(FRF(FGF( F8*,FIF(F)F(FMF(FGF(F2F(F(*,FIF(F)F(FMF(FenF(F,F(F(*,FIF(F)F(FMF(FRF(F ?F(F(*,FIF(F6F(F*F(F=F(F-F(F8*,FIF(F)F(F-F(FRF(F?F(F8*,FIF(F)F(F-F(Fen F(F7F(F(*,FIF(F)F(FenF(F,F(F-F(F8*,FIF(F)F(FGF(F2F(F-F(F8*,FIF(F)F(F7F (F0F(F-F(F8*,FIF(F)F(F-F(FRF(FGF(F(**F'F(F)F(F+F(FAF(F(**F'F(F)F(F:F(F 1F(F8**F'F(F)F(F1F(FAF(F(**FIF(F)F(FjnF(FF(F8**F'F(F)F(FMF(FF(F8**FIF(F)F(FgnF(F1F(F(**FIF(F)F(F GF()F2FKF(F8**F'F(F)F(FF(F(**F'F(F)F(F+F(F1F(F(**FIF(F)F()F,FKF(FenF(F8**F'F(F)F(F1F( F>F(F(**F'F(F)F(FAF(F>F(F(**FIF(F)F(FZF(F+F(F(**FIF(F)F(F_oF(F>F(F(**F IF(F)F(FZF(FjnF(F(*.F4F(F)F(FGF(F2F(F7F(F0F(F(*.F4F(F)F(FGF(F2F(FenF(F ,F(F(*.F4F(F)F(FGF(F2F(FRF(F?F(F(*.F4F(F)F(FGF(F2F(FenF(F7F(F8*.F4F(F) F(F7F(F0F(FenF(F,F(F(*.F4F(F)F(F7F(F0F(FRF(F?F(F(*.F4F(F)F(F7F(F0F(FRF (FGF(F8*.F4F(F)F(FenF(F,F(FRF(F?F(F(*.F4F(F)F(FenF(F,F(FRF(FGF(F8*.F4F (F)F(FRF(F?F(FenF(F7F(F8*.F4F(F)F(FenF(F7F(FRF(FGF(F(*.FIF(FYF(FenF(F* F(F-F(FBF(F(*.FIF(FYF(FenF(F*F(F=F(F-F(F8*.FIF(F^oF(FRF(F*F(F-F(FBF(F( *.FIF(F^oF(FRF(F*F(F=F(F-F(F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "9 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }