{VERSION 5 0 "IBM INTEL NT" "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 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 " Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } } {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "t:=phi->(phi-Pi/2)*2 /3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tGf*6#%$phiG6\"6$%)operator G%&arrowGF(,&*&#\"\"#\"\"$\"\"\"9$F1F1*&F0!\"\"%#PiGF1F4F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "x:=phi->(1+cos(t(phi)))*cos( t(phi)):y:=phi->(1+cos(t(phi)))*sin(t(phi)):y(phi);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,$*&,&\"\"\"F&-%$sinG6#,&*(\"\"#F&\"\"$!\"\"%$phiGF&F &*&\"\"'F.%#PiGF&F&F&F&-%$cosGF)F&F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 210 "xx:=(phi,u)->x(phi)+u*cos(phi):\nyy:=(phi,u)->y(phi) +u*sin(phi):\nsol:=solve(\{xx(phi,u)=xx(phi+Pi/2,v),yy(phi,u)=yy(phi+P i/2,v)\},\{u,v\}):\nsol2:=solve(\{xx(phi,u)=xx(phi+3*Pi/2,v),yy(phi,u) =yy(phi+3*Pi/2,v)\},\{u,v\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "uu:=combine(expand(subs(sol,u)));vv:=combine(expand(subs(sol,v) ));\nuu2:=combine(expand(subs(sol2,u)));vv2:=combine(expand(subs(sol2, v)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#uuG,&*&#\"\"&\"\"%\"\"\"-% $cosG6#,$*&\"\"$!\"\"%$phiGF*F*F*F**&#F*F)F**&F0#F*\"\"#-%$sinGF-F*F*F *" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vvG,&*&#\"\"$\"\"%\"\"\"*&F(#F *\"\"#-%$cosG6#,$*&F(!\"\"%$phiGF*F*F*F*F3*&#F*F)F*-%$sinGF0F*F3" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$uu2G,&*&\"\"$#\"\"\"\"\"#-%$sinG6#, $*&F'!\"\"%$phiGF)F)F)F)-%$cosGF-F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%$vv2G,&*&\"\"$#\"\"\"\"\"#-%$cosG6#,$*&F'!\"\"%$phiGF)F)F)F)-%$sinG F-F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "xxx:=combine(expan d(xx(phi,uu)));yyy:=combine(expand(yy(phi,uu)));\nxxx2:=combine(expand (xx(phi,uu2)));yyy2:=combine(expand(yy(phi,uu2)));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$xxxG,,*&#\"\"$\"\")\"\"\"*&-%$sinG6#,$*(\"\"#F*F(! 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