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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "read \"mobius.mpl\";" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "read \"MobiusonCircles.mpl\";" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=15:" }}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 18 "Generator formulas" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 126 "amatrix:=k->\n   evalf(Matrix([[1,-1],[1,1]])
^(-1) . Matrix([[sqrt(k),0],[0,1/sqrt(k)]]) . \n          Matrix([[1,-
1],[1,1]]) ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "bmatrix:=
(k,t0)->\n  evalf(Matrix([[1,-t0*I],[1,t0*I]])^(-1) . Matrix([[sqrt(k)
,0],[0,1/sqrt(k)]]) \n        . Matrix([[1,-t0*I],[1,t0*I]])):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Id:=IdentityMatrix(2):" }}}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "Multipliers of a and b, and the he
ight of fixed points of b on imaginary axis" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "multa:=evalf(6.0): multb:=evalf(2.09): t0:=evalf(0.2)
: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "a:=amatrix(multa): b:
=bmatrix(multb,t0): A:=a^(-1): B:=b^(-1):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 95 "CA:=IsometricCircle(a): CB:=IsometricCircle(b):\nCa
:=IsometricCircle(A): Cb:=IsometricCircle(B):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 16 "gens:=[a,b,A,B]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "cirs:=[Ca,Cb,CA,CB]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "pts:=map(Hcenter,cirs):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 924 "forward:=proc(v::list,m::Matrix,n)\n   global wlist,
gens,cirs,pts,eps;\n   local i,j,k,circle;\n   if nops(v) = 0 then    \+
# If v is the empty word, then four branches\n      for i from 4 to 1 \+
by -1 do\n          forward( [i], gens[i] , n)\n      end do;\n   else
  # If level greater than 0, start three branches\n      for i from 1 \+
to -1 by -1 do\n          j:=v[-1];                      # Check last \+
tag in v\n          k:= (j + i -1 mod 4) +1;       # Do modular increm
ent\n          circle:=CircleMap(m,cirs[k]):  # Compute Schottky circl
e\n          if evalf(Hradius(circle)) > eps and nops(v) < n then \n  \+
           forward([op(v),k], m.gens[k], n);    \n                    \+
   # Append next tag and go forward \n                       # if the \+
circle is large enough.\n          else         # Otherwise add circle
 to plot list\n             wlist:=[op(wlist),mobius(m,pts[k])];  \n  \+
        end if:\n      end do;\n   end if;\nend proc:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eps:=.04:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 32 "wlist:=[]: forward([],Id,10000):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "nops(wlist);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 66 "complexplot([op(wlist),wlist[1]],color=black,scalin
g=CONSTRAINED);" }}}}{MARK "0 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 
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