{VERSION 5 0 "IBM INTEL LINUX" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{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 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{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 26 "m:=Matrix([[1,-1],[1,1]]);" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 15 "First generator
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "amatrix:=k->\n   m^(-1) . Matri
x([[sqrt(k),0],[0,1/sqrt(k)]]) . m;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "m2:=Matrix([[1,-I],[1,I]]);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }{TEXT -1 16 "Second generator" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 66 "bmatrix:=k->\n  m2^(-1) . Matrix([[sqrt(k),0],[0,1/sq
rt(k)]]) . m2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 21 "
Choose a small circle" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "C:=Hcircle
(0,.4);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Fix generators and abb
reviate the inverses" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "a:=amatrix(
6): b:=bmatrix(6): A:=a^(-1): B:=b^(-1):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 26 "Generate a vector of words" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 61 "v:=[a,b,A,B,a^2,b^2,A^2,B^2,a.b,a.B,A.b,A.B,b.a,b.A,B.a,B.A]:
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 26 "Generate a lis
t of circles" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "circles:=[ C , op( \+
map( CircleMap, v, C ) ) ]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT -1 19 "Display the circles" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 
"display( map(PlotHcircle,circles),\n    scaling=constrained, axes=box
ed );" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }