{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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "pt:=(f,g,h,u,v,w)-> \+ 1/(g*w)-1/(h*v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ptGR6(%\"fG%\"g G%\"hG%\"uG%\"vG%\"wG6\"6$%)operatorG%&arrowGF-,&*&\"\"\"F3*&9%F39)F3! \"\"F3*&F3F3*&9&F39(F3F7F7F-F-F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Intersections of tripolars of U,F" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "cr:= (x,y,z)->r*y*z+s*z*x+t*x*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#crGR6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF*,(*(% \"rG\"\"\"9%F19&F1F1*(%\"sGF1F3F19$F1F1*(%\"tGF1F6F1F2F1F1F*F*F*" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "equation of C(R)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "factor(subs(\{r=-f*(s/g+t/h), u = -f/(g/ v+h/w) \},cr(pt(f,g,h,u,v,w),pt(g,h,f,v,w,u),pt(h,f,g,w,u,v))));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,**,%\"sG\"\"\")%\"hG\"\"#F(%\"gGF (%\"wGF(%\"vGF(F+*(F'F()F*\"\"$F()F.F+F(F(*(%\"tGF()F,F1F()F-F+F(F(*.F +F(F4F()F,F+F(F-F(F*F(F.F(F(F(*,%\"fGF(F8F(F)F(F2F(F6F(!\"\"F1" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "when is pt on cr (for R on T(F), U on C(F))" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "con:= factor(s ubs(\{r=-f*(s/g+t/h), u = -f/(g/v+h/w) \}, (u*g*(s/v-t/w)-v*f*(t/w-r/u ))));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$conG*&*&%\"fG\"\"\",**,%\" sGF()%\"hG\"\"#F(%\"gGF(%\"wGF(%\"vGF(F.*(F+F()F-\"\"$F()F1F.F(F(*(%\" tGF()F/F4F()F0F.F(F(*.F.F(F7F()F/F.F(F0F(F-F(F1F(F(F(F(**,&*&F/F(F0F(F (*&F-F(F1F(F(F(F0F(F/F(F-F(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "when is T(U) a nodal tangent -(third intersection u(s/v-t/w) is F) ; condition same as above." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 112 "So nodal tangents meet T(F) on C(R) - they're \+ also the C(F)-polars of these points as pivotal conic is dual ...." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "con2:= factor(subs(\{ \}, ( u*g*(s/v-t/w)-v*f*(t/w-r/u))));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%con2G,$*&,***)%\"uG\"\"#\"\"\"% \"gGF,%\"sGF,%\"wGF,!\"\"**F)F,F-F,%\"tGF,%\"vGF,F,**)F3F+F,%\"fGF,F2F ,F*F,F,**F5F,F6F,%\"rGF,F/F,F0F,*(F3F,F/F,F*F,F0F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "this is (SUM(rf/u^2) = 0 when .....U on C(F) .... .... independent of status of R." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "7 2 0" 112 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }