{VERSION 3 0 "DEC ALPHA UNIX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 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 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 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 0 255 "sys:=\{x[a],x[d],y[ a],y[h],y[c],x[b]-x[c],x[h]-x[e],(x[b]-x[a])*(y[e]-y[a])-(y[b]-y[a])*( x[e]-x[a]),\n(x[c]-x[d])*(y[e]-y[d])-(y[c]-y[d])*(x[e]-x[d]),(x[b]-x[a ])^2+(y[b]-y[a])^2-4,(x[d]-x[c])^2+(y[d]-y[c])^2-9,y[e]-1,1-t*x[b],(x[ a]-x[c])^2+(y[a]-y[c])^2-u\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "var:=t,u,x[a],x[d],y[a],y[c],y[h],y[e],x[b],y[b],y[d],x[h],x[e], x[c];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$varG60%\"tG%\"uG&%\"xG6#% \"aG&F)6#%\"dG&%\"yGF*&F06#%\"cG&F06#%\"hG&F06#%\"eG&F)6#%\"bG&F0F;&F0 F-&F)F5&F)F8&F)F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gb:=Gr oebner[gbasis](sys,plex(var));\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>% #gbG70,,*$)&%\"xG6#%\"cG\"\"'\"\"\"!#A*$)F)\"\"%F.\"$j\"*$)F)\"\"#F.!$ a%\"$&Q\"\"\"*$)F)\"\")F.F9,*&F*6#%\"eG\"#5*$)F)\"\"&F.F9*$)F)\"\"$F.! \"*F)FD,*&F*6#%\"hGFAFBF9FEFHF)FD,,&%\"yG6#%\"dGFAF'F9F0!#=F4\"#'*!$N \"F9,,&FO6#%\"bGFAF'!\"\"F0\"#8F4!#T\"#?F9,&&F*FWF9F)FY,&&FOF?F9FYF9&F OFK&FOF+&FO6#%\"aG&F*FP&F*F^o,&%\"uGF9F4FY,,*$)F)\"\"(F.F9%\"tGF8FBF/F EF3F)F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "G:=array(1..nop s(gb),1..nops([var]),sparse):\nfor i to nops(gb) do\n for j to nops([ var]) do\n if has(gb[i],var[j]) then G[i,j]:=1 fi\n od\nod:\nprin t(G);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7070\"\"!F(F(F(F( F(F(F(F(F(F(F(F(\"\"\"70F(F(F(F(F(F(F(F(F(F(F(F(F)F)70F(F(F(F(F(F(F(F( F(F(F(F)F(F)70F(F(F(F(F(F(F(F(F(F(F)F(F(F)70F(F(F(F(F(F(F(F(F(F)F(F(F( F)70F(F(F(F(F(F(F(F(F)F(F(F(F(F)70F(F(F(F(F(F(F(F)F(F(F(F(F(F(70F(F(F( F(F(F(F)F(F(F(F(F(F(F(70F(F(F(F(F(F)F(F(F(F(F(F(F(F(70F(F(F(F(F)F(F(F( F(F(F(F(F(F(70F(F(F(F)F(F(F(F(F(F(F(F(F(F(70F(F(F)F(F(F(F(F(F(F(F(F(F( F(70F(F)F(F(F(F(F(F(F(F(F(F(F(F)70F)F(F(F(F(F(F(F(F(F(F(F(F(F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "equ1:=subs(x[c]=z,gb[1]);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%equ1G,,*$)%\"zG\"\"'\"\"\"!#A*$)F( \"\"%F*\"$j\"*$)F(\"\"#F*!$a%\"$&Q\"\"\"*$)F(\"\")F*F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "equ2:=subs(z=w^(1/2),equ1):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(equ2,w);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%'RootOfG6#,,*$)%#_ZG\"\"$\"\"\"!#A*$)F)\"\"#F+ \"$j\"F)!$a%\"$&Q\"\"\"*$)F)\"\"%F+F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "[allvalues(%)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "fsol:=[fsolve(gb[1],x[c])];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%fsolG7&$!+aN;t=!\"*$!+Cd=J7F($\"+Cd=J7F($\"+aN;t=F( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "fsol:=select(proc(x) x> 0 end,fsol); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%fsolG7$$\"+Cd=J7! \"*$\"+aN;t=F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "for i to nops(fsol) do\n Fsol[i]:=fsolve(select(has,\{op(subs(x[c]=fsol[i],gb ))\},\{var\}),\{var\} minus \{x[c]\})\nunion \{x[c]=fsol[i]\}\nod;" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>&%%FsolG6#\"\"\"<0/&%\"xG6#%\"aG\"\"! /&F+6#%\"dGF./&F+6#%\"eG$\"+5UX6y!#5/&F+6#%\"bG$\"+Cd=J7!\"*/%\"tG$\"+ D9DA\")F9/&%\"yGF1$\"+SKsNFF@/&FGF<$\"+7(Ghd\"F@/&F+6#%\"hGF7/%\"uG$\" +(G=e^\"F@/&FGF5$F'F./&FGF,F./&FGFPF./&FG6#%\"cGF./&F+FinF>" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%%FsolG6#\"\"#<0/&%\"xG6#%\"aG\"\"!/&F+6#% \"dGF./&%\"yG6#%\"eG$\"\"\"F./&F5F1$!+!RVLM#!\"*/&F56#%\"bG$\"++?)*3q! #5/%\"tG$\"+@@cQ`FE/&F5F,F./%\"uG$\"++/&F+FA$\"+aN;t=F>/&F+6#%\" hG$\"+x'=Dn#F>/&F+F6FX/&F5FVF./&F56#%\"cGF./&F+FjnFR" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 771 "for i to 2 do\n text:=plots[textplot](s ubs(Fsol[i],\{\n [x[a]-.1,y[a]-.1,\"A\"],\n \+ [x[b],y[b]+.2,\"B\"],\n [x[c]+.1,y[c]-.1,\"C\"],\n \+ [x[d]-.1,y[d],\"D\"],\n [x[e],y[e]+.2,\"E\"],\n \+ [x[h],y[h]-.1,\"H\"]\})):\npicture:=plot(subs(Fsol[i],[\n \+ [[x[a],y[a]],[x[c],y[c]]],\n [[x[a],y[a]],[x[d],y[d]]],\n [[x[a], y[a]],[x[b],y[b]]],\n [[x[c],y[c]],[x[d],y[d]]],\n [[x[e],y[e]],[x [h],y[h]]],\n [[x[c],y[c]],[x[b],y[b]]],\n [[x[a],y[a]],[x[h],y[h] ]],\n [[x[h],y[h]],[x[c],y[c]]],\n [[x[a],y[a]],[x[e],y[e]]],\n \+ [[x[b],y[b]],[x[e],y[e]]],\n [[x[c],y[c]],[x[e],y[e]]],\n [[x[e],y [e]],[x[d],y[d]]]]),\n thickness=[1,1,3,3,3,1,1,1,1,1,1,1],\n colo r=black):\n figure[i]:=plots[display](\{text,picture\},axes=none)\n\no d:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "for i to 2 do\n figu re[i]\nod;" }}{PARA 13 "" 1 "" {INLPLOT "67-%%TEXTG6$7$$!\"\"F(F'%\"AG -F$6$7$$\"+Cd=J8!\"*F'%\"CG-F$6$7$$\"+5UX6y!#5$\"#7F(%\"EG-F$6$7$$\"+C d=J7F/$\"+7(Ghx\"F/%\"BG-F$6$7$F'$\"+SKsNFF/%\"DG-F$6$7$F4F'%\"HG-%'CU RVESG6%7$7$\"\"!FQ7$$\"3$******Rs&=J7!#!\"*$!\"\"F+%\"CG-F$6$7$$\"+x'=Dn#F)$\"#7F+%\"EG-F $6$7$$\"+aN;t=F)$\"++?)*3!*!#5%\"BG-F$6$7$F*$!+!RVLM#F)%\"DG-F$6$7$F0F *%\"HG-F$6$7$F*F*%\"AG-%'CURVESG6%7$7$\"\"!FQ7$$\"3,+++aN;t=!# " 0 "" {MPLTEXT 1 0 216 "sys:=\{x[a],x[d],y[a],y[h],y[c],x[ b]-x[c],x[h]-x[e],(x[b]-x[a])*(y[e]-y[a])-(y[b]-y[a])*(x[e]-x[a]),\n(x [c]-x[d])*(y[e]-y[d])-(y[c]-y[d])*(x[e]-x[d]),(x[b]-x[a])^2+(y[b]-y[a] )^2-4,(x[d]-x[c])^2+(y[d]-y[c])^2-9,y[e]-1\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "var:=t,u,x[a],x[d],y[a],y[c],y[h],y[e],x[b],y[b] ,y[d],x[h],x[e],x[c]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "gb :=Groebner[gbasis](sys,plex(var));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%#gbG70,,&%\"xG6#%\"cG\"$&Q*$)F'\"\"*\"\"\"\"\"\"*$)F'\"\"(F/!#A*$)F' \"\"&F/\"$j\"*$)F'\"\"$F/!$a%,*&F(6#%\"eG\"#5F5F0F9!\"*F'F7,*&F(6#%\"h GFAF5F0F9FBF'F7,,*&F'F0&%\"yG6#%\"dGF0FAF1F0F5!#=F9\"#'*F'!$N\",(*$)F' \"\"#F/F0*$)FIFSF/F0FBF0,,*&&FJ6#%\"bGF0F'F/FAF1!\"\"F5\"#8F9!#TF'\"#? ,(*$)FXFSF/F0!\"%F0FQF0,&&F(FYF0F'Fen,&&FJF?F0FenF0&FJFE&FJF)&FJ6#%\"a G&F(FK&F(Fdo" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "16 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }