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-x[b])*x[b]+(y[p]-y[b])*y[b],\n3*x[g]-x[p]-x[a]-x[b],3*y[g]-y[p]-y[a]-
y[b]\};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$sysG<),&&%\"xG6#%\"pG\"
\"\"%\"dG!\"\",&*&,&F'F+&F(6#%\"aGF-F+F1F+F+*&,&&%\"yGF)F+&F7F2F-F+F8F
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[x[g],y[g]]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#gbG73,fn*&)&%\"xG
6#%\"gG\"\"#\"\"\")&%\"yGF+F-F.\"\")*$)F)\"\"%F.\"#C*&F/F.F4F.!#=*&)%
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}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "varlist:=[x[p],y[p],x[a],y
[a],x[b],y[b],x[g],y[g]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$varG7*
&%\"xG6#%\"pG&%\"yGF(&F'6#%\"aG&F+F-&F'6#%\"bG&F+F1&F'6#%\"gG&F+F5" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 173 "G:=array(1..nops(gb),1..no
ps(varlist),sparse):\n  for i to nops(gb) do\n    for j to nops(varlis
t) do\n      if has(gb[i],varlist[j]) then G[i,j]:=1 fi\n    od\n  od:
\n  print(G);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#737*\"\"!
F(F(F(F(F(\"\"\"F)7*F(F)F(F)F(F)F(F)7*F(F(F)F(F)F(F)F(7*F(F)F)F)F(F(F)
F)F,7*F(F(F)F(F(F(F)F)7*F(F)F(F(F(F(F)F)F.F.F.7*F)F(F(F(F(F(F(F(F,F,7*
F(F)F)F)F(F(F(F(7*F(F)F)F(F(F(F)F)F,F." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "equ:=remove(has,gb,\{p,a,b\}):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "nops(equ);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "equ:=equ[1];" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$equG,fn*&)&%\"xG6#%\"gG\"\"#\"\"\")
&%\"yGF*F,F-\"\")*$)F(\"\"%F-\"#C*&F.F-F3F-!#=*&)%\"dGF,F-)F(\"\"'F-!#
F*(F'F-F.F-F9F-\"#E*(F'F-F.F-)F:F4F-!\"#*()F:\"\"$F-)F/F4F-F(\"\"\"\"
\"**(F(F-FDF-F.F-!\"%*(F:FGFFF-F(F-!#7*(F9F-F.F-F3F-!#a*(F:F-)F(FEF-F.
F-!#O*&F:F-)F(\"\"&F-!#C*&FDF-FSF-FH*&F3F-F9F-\"#A*&F3F-FAF-!\"\"*&FPF
-FDF-FJ*$F;F-F7*$F'F-!\")*&F:F-)F(\"\"(F-\"#F*(FDF-FPF-F.F-\"#=*(F:F-F
.F-FSF-\"#a*(F:F-FPF-FFF-F\\o*(F9F-F'F-FFF-F=*&FPF-F:F-F4*&F'F-F9F-FJ*
&F9F-F.F-FJ*(F(F-F:F-F.F-\"#7*&FAF-FFF-FZ*&F9F-FFF-F4" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "degree(equ,x[g]);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "
degree(equ,y[g]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "equ:=factor(equ);" }}{PARA 12 "" 1 
"" {XPPMATH 20 "6#>%$equG,$*&,6*&)&%\"xG6#%\"gG\"\"#\"\"\")%\"dGF.F/\"
\"\"*&F0F/)&%\"yGF,F.F/F2*&F*F2F1F2\"\"%*&)F*\"\"$F/F1F/!\"'*(F*F/F1F/
F4F/F<*$)F*F8F/\"\"**&F)F/F4F/F@*$F)F/!#7F8F2*$F4F/!\"%F2,,F(F2F3F2F=!
\"$FBF.F9FGF2!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "map(p
roc(z) degree(z,\{x[g],y[g]\}) end,\n    convert(equ,list));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7%\"\"!\"\"%\"\"$" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 56 "Equ[1]:=select(proc(z) degree(z,\{x[g],y[g]\})=3 e
nd,equ);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$EquG6#\"\"\",,*&)&%\"x
G6#%\"gG\"\"#\"\"\")%\"dGF/F0F'*&F1F0)&%\"yGF-F/F0F'*(F+F'F2F'F4F0!\"$
*$F*F0F/*&)F+\"\"$F0F2F0F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
56 "Equ[2]:=select(proc(z) degree(z,\{x[g],y[g]\})=4 end,equ);" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%$EquG6#\"\"#,6*&)&%\"xG6#%\"gGF'\"
\"\")%\"dGF'F/\"\"\"*&F0F/)&%\"yGF-F'F/F2*&F+F2F1F2\"\"%*&)F+\"\"$F/F1
F/!\"'*(F+F/F1F/F4F/F<*$)F+F8F/\"\"**&F*F/F4F/F@*$F*F/!#7F8F2*$F4F/!\"
%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 196 "sys:=\{x[p]-d,\nx[a]^
2+y[a]^2-1,x[b]^2+y[b]^2-1,\n(x[p]-x[a])*x[a]+(y[p]-y[a])*y[a],(x[p]-x
[b])*x[b]+(y[p]-y[b])*y[b],\n1-t*((x[a]-x[b])^2+(y[a]-y[b])^2),\n3*x[g
]-x[p]-x[a]-x[b],3*y[g]-y[p]-y[a]-y[b]\};" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%$sysG<*,(*$)&%\"xG6#%\"aG\"\"#\"\"\"\"\"\"*$)&%\"yGF+
F-F.F/!\"\"F/,&&F*6#%\"pGF/%\"dGF4,(*$)&F*6#%\"bGF-F.F/*$)&F3F>F-F.F/F
4F/,&F/F/*&%\"tGF/,&*$),&F)F/F=F4F-F.F/*$),&F2F/FBF4F-F.F/F/F4,*&F36#%
\"gG\"\"$&F3F7F4F2F4FBF4,*&F*FOFQF6F4F)F4F=F4,&*&,&F6F/F)F4F/F)F/F/*&,
&FRF/F2F4F/F2F/F/,&*&,&F6F/F=F4F/F=F/F/*&,&FRF/FBF4F/FBF/F/" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "gb:=Groebner[gbasis](sys,lex
deg([x[p],y[p],x[a],y[a],x[b],y[b],t],[x[g],y[g]]));" }}{PARA 12 "" 1 
"" {XPPMATH 20 "6#>%#gbG74,,*&)&%\"xG6#%\"gG\"\"#\"\"\")%\"dGF-F.!\"\"
*&F/F.)&%\"yGF+F-F.F1*(F)\"\"\"F0F7F3F.\"\"$*$F(F.!\"#*&)F)F8F.F0F.F8,
(*&F0F.%\"tGF7!\"'F0F7*&F?F.F)F.\"\"',4*&)F0F8F.F?F.\"#7*$FEF.F:*&F)F.
F/F.F:F0F-*(F0F.F3F.F?F.FF*&F(F.F0F.!\"$*&F0F.F3F.FKF>!#7F)F-,*F4FK&F5
6#%\"pGF7&F56#%\"aGF7&F56#%\"bGF7,*F)FK&F*FSF7&F*FVF7F0F7,(*(F0F.FRF7F
4F7F7*(F)F.FYF7F0F.F7F)F1,0*(FRF.F)F.F/F.F1*(F/F.F4F.FYF.F7*(F0F.F(F.F
RF.F8*&F4F.F0F.F1**F0F.F4F.F)F.FYF.FK*&F4F.F)F.F8*&FRF.F)F.F:,,FHF7FLF
K*(F0F.FOF7F4F.F7FJFKF)F-,&F\\oF1*&F)F.FOF.F7,&&F*FPF7F0F1,4*&F/F.FRF.
F:*(F/F.F?F.FRF.FF*(F4F.FYF.F0F.F8**F0F.F4F.F?F.FYF.FM*(F0F.F)F.FRF.FK
*&F?F.F4F.FFF4FKFRF-*&F?F.FRF.FM,(F\\pF@*&FOF.F?F.FBFOF1,0FGF7FHFK*&FY
F.F/F.F:F0F7FgnFB*&F0F.)FRF-F.F-F)FK,2*&F4F.F/F.F8*&FOF.F/F.F1FgoF-F[p
F@*(F0F.FYF.FRF.F-FRF-FOF7F4FK,(*&FYF.F0F.F7*&FRF.FOF.F7F1F7,0FGF1FapF
-FHF8F0FKFgnF@*&F0F.)FYF-F.F-F)F8,0*(FOF.FYF.F0F.F7F[pF8FRF:FgoF1FioFK
FOF1F4F8,.FGF7FL!\"*FJFaqF0F-*&F0F.)FOF-F.F7F)FB" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 30 "equ:=remove(has,gb,\{p,a,b,t\}):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "nops(equ);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "eq
u:=factor(equ[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$equG,,*&)&%\"
xG6#%\"gG\"\"#\"\"\")%\"dGF,F-!\"\"*&F.F-)&%\"yGF*F,F-F0*(F(\"\"\"F/F6
F2F-\"\"$*$F'F-!\"#*&)F(F7F-F/F-F7" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 242 "sys:=
\{x[p]-d,\nx[a]^2+y[a]^2-1,x[b]^2+y[b]^2-1,\n(x[a]-x[p])^2+(y[a]-y[p])
^2+x[a]^2+y[a]^2-x[p]^2-y[p]^2,\n\n(x[b]-x[p])^2+(y[b]-y[p])^2+x[b]^2+
y[b]^2-x[p]^2-y[p]^2,\n1-t*((x[a]-x[b])^2+(y[a]-y[b])^2),\n3*x[g]-x[p]
-x[a]-x[b],3*y[g]-y[p]-y[a]-y[b]\};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6
#>%$sysG<*,(*$)&%\"xG6#%\"aG\"\"#\"\"\"\"\"\"*$)&%\"yGF+F-F.F/!\"\"F/,
&&F*6#%\"pGF/%\"dGF4,(*$)&F*6#%\"bGF-F.F/*$)&F3F>F-F.F/F4F/,&F/F/*&%\"
tGF/,&*$),&F)F/F=F4F-F.F/*$),&F2F/FBF4F-F.F/F/F4,.*$),&F=F/F6F4F-F.F/*
$),&FBF/&F3F7F4F-F.F/F;F/F@F/*$)F6F-F.F4*$)FTF-F.F4,.*$),&F)F/F6F4F-F.
F/*$),&F2F/FTF4F-F.F/F'F/F0F/FUF4FWF4,*&F36#%\"gG\"\"$FTF4F2F4FBF4,*&F
*F\\oF^oF6F4F)F4F=F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "gb:
=Groebner[gbasis](sys,lexdeg([x[p],y[p],x[a],y[a],x[b],y[b],t],[x[g],y
[g]]));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#gbG74,,*&)&%\"xG6#%\"gG
\"\"#\"\"\")%\"dGF-F.!\"\"*&F/F.)&%\"yGF+F-F.F1*(F)\"\"\"F0F7F3F.\"\"$
*$F(F.!\"#*&)F)F8F.F0F.F8,(*&F0F.%\"tGF7!\"'F0F7*&F?F.F)F.\"\"',4*&)F0
F8F.F?F.\"#7*$FEF.F:*&F)F.F/F.F:F0F-*(F0F.F3F.F?F.FF*&F(F.F0F.!\"$*&F0
F.F3F.FKF>!#7F)F-,*F4FK&F56#%\"pGF7&F56#%\"aGF7&F56#%\"bGF7,*F)FK&F*FS
F7&F*FVF7F0F7,(*(F0F.FRF7F4F7F7*(F)F.FYF7F0F.F7F)F1,0*(FRF.F)F.F/F.F1*
(F/F.F4F.FYF.F7*(F0F.F(F.FRF.F8*&F4F.F0F.F1**F0F.F4F.F)F.FYF.FK*&F4F.F
)F.F8*&FRF.F)F.F:,,FHF7FLFK*(F0F.FOF7F4F.F7FJFKF)F-,&F\\oF1*&F)F.FOF.F
7,&&F*FPF7F0F1,4*&F/F.FRF.F:*(F/F.F?F.FRF.FF*(F4F.FYF.F0F.F8**F0F.F4F.
F?F.FYF.FM*(F0F.F)F.FRF.FK*&F?F.F4F.FFF4FKFRF-*&F?F.FRF.FM,(F\\pF@*&FO
F.F?F.FBFOF1,0FGF7FHFK*&FYF.F/F.F:F0F7FgnFB*&F0F.)FRF-F.F-F)FK,2*&F4F.
F/F.F8*&FOF.F/F.F1FgoF-F[pF@*(F0F.FYF.FRF.F-FRF-FOF7F4FK,(*&FYF.F0F.F7
*&FRF.FOF.F7F1F7,0FGF1FapF-FHF8F0FKFgnF@*&F0F.)FYF-F.F-F)F8,0*(FOF.FYF
.F0F.F7F[pF8FRF:FgoF1FioFKFOF1F4F8,.FGF7FL!\"*FJFaqF0F-*&F0F.)FOF-F.F7
F)FB" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "equ:=remove(has,gb,
\{p,a,b,t\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "nops(equ);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 20 "equ:=factor(equ[1]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$equG,,*&)&%\"xG6#%\"gG\"\"#\"\"\")%\"dGF,F-!\"\"*&F.F-)&%\"yG
F*F,F-F0*(F(\"\"\"F/F6F2F-\"\"$*$F'F-!\"#*&)F(F7F-F/F-F7" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "series(subs(x[g]=t*X,y[g]=t*Y,Equ[1
]),t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+'%\"tG,(*&)%\"XG\"\"#\"\"\"
)%\"dGF)F*\"\"\"*&F+F*)%\"YGF)F*F-*$F'F*F)\"\"#,&*(F(F-F,F-F/F*!\"$*&)
F(\"\"$F*F,F*F5\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "sol
1x:=[solve(subs(y[g]=t*x[g],Equ[1]),\{x[g]\})];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&sol1xG7%<#/&%\"xG6#%\"gG\"\"!F&<#/F(,$*&,(*&)%\"dG\"
\"#\"\"\")%\"tGF5F6\"\"\"F5F9*$F3F6F9F6*&F4\"\"\",&F9F9*$F7F6F9\"\"\"!
\"\"#F9\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "sol1x:=op(s
elect(has,sol1,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sol1xG/&%\"x
G6#%\"gG,$*&,(*&)%\"dG\"\"#\"\"\")%\"tGF0F1\"\"\"F0F4*$F.F1F4F1*&F/\"
\"\",&F4F4*$F2F1F4\"\"\"!\"\"#F4\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "X1:=subs(sol1x,x[g]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#X1G,$*&,(*&)%\"dG\"\"#\"\"\")%\"tGF+F,\"\"\"F+F/*$F)F,F/F,*&F
*\"\"\",&F/F/*$F-F,F/\"\"\"!\"\"#F/\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "Y1:=subs(sol1x,t*x[g]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#Y1G,$*&*&%\"tG\"\"\",(*&)%\"dG\"\"#\"\"\")F(F.F/F)F.F)*$F,F/F
)F)F/*&F-\"\"\",&F)F)*$F0F/F)\"\"\"!\"\"#F)\"\"$" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 0 0" 126 }{VIEWOPTS 1 1 0 1 1 
1803 }