{VERSION 4 0 "IBM INTEL NT" "4.0" } {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 "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 "Normal" -1 256 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "hf:=(x,y,z,f,g,h)->g *h*x^2-f^2*y*z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#hfGR6(%\"xG%\"yG %\"zG%\"fG%\"gG%\"hG6\"6$%)operatorG%&arrowGF-,&*(9(\"\"\"9)F4)9$\"\"# F4F4*()9'F8F49%F49&F4!\"\"F-F-F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "hf gives F-Hirst inverse of (x,y,z)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "X:=f^2/x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG*&* $)%\"fG\"\"#\"\"\"F*%\"xG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "Y:=g^2/y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"YG*&*$)%\"gG\" \"#\"\"\"F*%\"yG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "Z:= h^2/z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG*&*$)%\"hG\"\"#\"\"\"F *%\"zG!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "X,Y,Z gives F-isoc onjygate of x,y,z" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "l1:= h f(y,z,x,g,h,f)*hf(Z,X,Y,h,f,g)-hf(z,x,y,h,f,g)*hf(Y,Z,X,g,h,f);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l1G,&*&,&*(%\"hG\"\"\"%\"fGF*)%\"yG \"\"#F*F**()%\"gGF.F*%\"zGF*%\"xGF*!\"\"F*,&*&*(F+F*F1F*)F)\"\"%F*F**$ )F2F.F*F4F**&*()F)F.F*)F+F.F*F0F*F**&F3F*F-F*F4F4F*F**&,&*(F+F*F1F*F;F *F**(F>F*F3F*F-F*F4F*,&*&*(F)F*F+F*)F1F9F*F**$F,F*F4F**&*(F0F*F>F*F?F* F**&F2F*F3F*F4F4F*F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "l2: =hf(z,x,y,h,f,g)*hf(X,Y,Z,f,g,h) -hf(x,y,z,f,g,h)*hf(Z,X,Y,h,f,g);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l2G,&*&,&*(%\"fG\"\"\"%\"gGF*)%\"zG \"\"#F*F**()%\"hGF.F*%\"xGF*%\"yGF*!\"\"F*,&*&*(F+F*F1F*)F)\"\"%F*F**$ )F2F.F*F4F**&*()F)F.F*)F+F.F*F0F*F**&F3F*F-F*F4F4F*F**&,&*(F+F*F1F*F;F *F**(F>F*F3F*F-F*F4F*,&*&*(F)F*F+F*)F1F9F*F**$F,F*F4F**&*(F0F*F>F*F?F* F**&F2F*F3F*F4F4F*F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "l3: =hf(x,y,z,f,g,h)*hf(Y,Z,X,g,h,f)-hf(y,z,x,g,h,f)*hf(X,Y,Z,f,g,h);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l3G,&*&,&*(%\"gG\"\"\"%\"hGF*)%\"xG \"\"#F*F**()%\"fGF.F*%\"yGF*%\"zGF*!\"\"F*,&*&*(F+F*F1F*)F)\"\"%F*F**$ )F2F.F*F4F**&*()F)F.F*)F+F.F*F0F*F**&F3F*F-F*F4F4F*F**&,&*(F+F*F1F*F;F *F**(F>F*F3F*F-F*F4F*,&*&*(F)F*F+F*)F1F9F*F**$F,F*F4F**&*(F0F*F>F*F?F* F**&F2F*F3F*F4F4F*F4" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "l1,l2,l3 \+ are coefficients of line x,y,z and X,Y,Z" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "factor(l1*(-f*(s/g+t/h))^2/f+l2*s^2/g+l3*t^2/h);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#,$*&*(%\"fG\"\"\",2*.%\"sGF'%\"hGF')% \"gG\"\"#F')%\"zGF.F'%\"xGF'F&F'!\"\"*.F*F'F+F'F-F'F/F'%\"yGF')F&F.F'F '*,F*F')F+\"\"$F')F1F.F'F4F'F-F'F'*,F*F'F7F'F1F')F4F.F'F&F'F2*.F1F')F+ F.F'F-F'F;F'%\"tGF'F&F'F2*.F+F'F-F'F0F'F;F'F>F'F5F'F'*,F+F'F9F')F-F8F' F0F'F>F'F'*,F1F'FAF'F/F'F>F'F&F'F2F',2F)F2F3F2F6F'F:F'F " 0 "" {MPLTEXT 1 0 93 "ck:= (x,y,z)->( -f*(s/g+t/h))*x*(g^2*z^2-h^2*y^2)+s*y*(h^2*x^2-f^2*z^2)+t*z*(f^2*y^2-g ^2*x^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ckGR6%%\"xG%\"yG%\"zG6 \"6$%)operatorG%&arrowGF*,(**%\"fG\"\"\",&*&%\"sGF1%\"gG!\"\"F1*&%\"tG F1%\"hGF6F1F19$F1,&*&)F5\"\"#F1)9&F>F1F1*&)F9F>F1)9%F>F1F6F1F6*(F4F1FD F1,&*&FBF1)F:F>F1F1*&)F0F>F1F?F1F6F1F1*(F8F1F@F1,&*&FJF1FCF1F1*&F=F1FH F1F6F1F1F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Check that the Hirst inverse map w orks" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "factor(ck(hf(x,y,z, f,g,h),hf(y,z,x,g,h,f),hf(z,x,y,h,f,g)));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*&*(,(*(%\"hG\"\"\"%\"yGF(%\"fGF(F(*(%\"gGF(%\"xGF(F'F( F(*(F,F(%\"zGF(F*F(F(F(,.*()F,\"\"#F()F'F3F()F-F3F(F(*,F2F(F-F(F'F(F/F (F*F(!\"\"*(F2F()F/F3F()F*F3F(F(*,F,F(F4F(F-F(F)F(F*F(F7*,F,F(F)F(F'F( F/F(F:F(F7*(F4F()F)F3F(F:F(F(F(,2*,F:F(%\"tGF(F)F(F9F(F2F(F(*.%\"sGF(F 'F(F,F(F9F(F)F(F:F(F(*.F'F(F,F(F/F(F>F(FAF(F:F(F7*,F:F(FCF(F4F(F>F(F/F (F7*.FCF(F'F(F2F(F9F(F-F(F*F(F(*.F-F(F4F(F,F(F>F(FAF(F*F(F7*,F2F(FCF(F 4F(F5F(F/F(F7*,F2F(FAF(F)F(F4F(F5F(F(F(F(*&F'F(F,F(F7" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "cub:=f^2*t*y*z^2*g^2+s*h*g*z^2*y*f^2-h*g*z*y^2*t*f^2-f^2*s*h^2* y^2*z+s*h*g^2*z^2*x*f-x*h^2*g*y^2*t*f-g^2*s*h^2*x^2*z+g^2*t*y*h^2*x^2; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cubG,2*,)%\"fG\"\"#\"\"\"%\"tGF *%\"yGF*)%\"zGF)F*)%\"gGF)F*F**.%\"sGF*%\"hGF*F0F*F-F*F,F*F'F*F**.F3F* F0F*F.F*)F,F)F*F+F*F'F*!\"\"*,F'F*F2F*)F3F)F*F5F*F.F*F6*.F2F*F3F*F/F*F -F*%\"xGF*F(F*F**.F:F*F8F*F0F*F5F*F+F*F(F*F6*,F/F*F2F*F8F*)F:F)F*F.F*F 6*,F/F*F+F*F,F*F8F*F=F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "factor(cub-subs(z=0,cub));" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "bit:=z*(-g^2*s*h^2*x^2-h*g*y ^2*t*f^2-f^2*s*h^2*y^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$bitG*&% \"zG\"\"\",(**)%\"gG\"\"#F'%\"sGF')%\"hGF,F')%\"xGF,F'!\"\"*,F/F'F+F') %\"yGF,F'%\"tGF')%\"fGF,F'F2**F7F'F-F'F.F'F4F'F2F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 12 "" 1 "" {TEXT -1 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "20 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }