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{SECT 0 {EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}
{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 18 "read \"mobius.mpl\";" }}}
{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 27 "read \"MobiusonCircles.mpl
\";" }}}{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 18 "read \"twogen.mpl
\";" }}}{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=15:" }}}
{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 22 "Id:=IdentityMatrix(2):" }}
}{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 36 "m:=twogen(1.91+.05*I,1.91
+.05*I,-2):" }}}{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 39 "a:=m[3]: b
:=m[4]: A:=a^(-1): B:=b^(-1):" }}}{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 
1 0 47 "CA:=IsometricCircle(a): CB:=IsometricCircle(b):" }{MPLTEXT 1 
0 48 "\nCa:=IsometricCircle(A): Cb:=IsometricCircle(B):" }}}{EXCHG 
{PARA 215 "> " 0 "" {MPLTEXT 1 0 16 "gens:=[a,b,A,B]:" }}}{EXCHG 
{PARA 215 "> " 0 "" {MPLTEXT 1 0 20 "cirs:=[Ca,Cb,CA,CB]:" }}}{EXCHG 
{PARA 215 "> " 0 "" {MPLTEXT 1 0 52 "display( map(PlotHcircle,cirs),sc
aling=constrained);" }}}{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 23 "pt
s:=map(Hcenter,cirs):" }}}{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 40 "
wlist:=Array(1..10000,datatype=complex):" }}}{EXCHG {PARA 215 "> " 0 "
" {MPLTEXT 1 0 46 "forward:=proc(tag::integer,m::Matrix, maxlev )" }
{MPLTEXT 1 0 42 "\n   global wlist,numpts,gens,cirs,pts,eps;" }
{MPLTEXT 1 0 21 "\n   local i,k,circle;" }{MPLTEXT 1 0 67 "\n   if tag
 = 0 then    # If v is the empty word, then four branches" }{MPLTEXT 
1 0 33 "\n      for i from 4 to 1 by -1 do" }{MPLTEXT 1 0 43 "\n      \+
    forward( i , gens[i] , maxlev-1)" }{MPLTEXT 1 0 14 "\n      end do
;" }{MPLTEXT 1 0 57 "\n   else  # If level greater than 0, start three
 branches" }{MPLTEXT 1 0 35 "\n      for i from 1 to -1 by -1 do " }
{MPLTEXT 1 0 71 "\n          k:= (tag + i -1 mod 4) +1;     # Do modul
ar increment of tag" }{MPLTEXT 1 0 67 "\n          circle:=CircleMap(m
,cirs[k]):  # Compute Schottky circle" }{MPLTEXT 1 0 63 "\n          i
f evalf(Hradius(circle)) > eps and maxlev > 0 then " }{MPLTEXT 1 0 54 
"\n             forward( k , m.gens[k], maxlev - 1);    " }{MPLTEXT 1 
0 57 "\n                       # Append next tag and go forward " }
{MPLTEXT 1 0 56 "\n                       # if the circle is large eno
ugh." }{MPLTEXT 1 0 59 "\n          else         # Otherwise add circl
e to plot list" }{MPLTEXT 1 0 48 "\n             wlist[numpts+1]:=mobi
us(m,pts[k]);" }{MPLTEXT 1 0 33 "\n             numpts:=numpts+1:  " }
{MPLTEXT 1 0 18 "\n          end if:" }{MPLTEXT 1 0 14 "\n      end do
;" }{MPLTEXT 1 0 11 "\n   end if;" }{MPLTEXT 1 0 10 "\nend proc:" }}}
{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 9 "eps:=.05:" }}}{EXCHG {PARA 
215 "> " 0 "" {MPLTEXT 1 0 58 "s:=time(): numpts:=0: forward(0,Id,100)
: numpts; time()-s;" }}}{EXCHG {PARA 215 "> " 0 "" {MPLTEXT 1 0 91 "co
mplexplot([op(convert(wlist[1..numpts],list)),wlist[1]],color=black,sc
aling=CONSTRAINED);" }}}{PARA 216 "" 0 "" }{PARA 217 "" 0 "" }{PARA 
218 "" 0 "" }{PARA 219 "" 0 "" }}{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
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