{VERSION 3 0 "DEC ALPHA UNIX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {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 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "sys:=\{x*y=a^2,ln(x) ^2+ln(y)^2=5/2*ln(a)^2\}:\ninc:=\{x,y\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "S1:=solve(sys,inc);" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#>%#S1G<$/%\"yG-%$expG6#,$-%'RootOfG6#,**$)%#_ZG\"\"#\"\"\"\"\"\"*$)- %#lnG6#*$)%\"aGF3F4F3F4!\"#*$)-F96#F=F3F4!\"&*&F8F5-F-6#,*F6F3*&F8F5F2 F5F>F0F5F?FCF5F3#F5F3/%\"xG-F)6#,$FEFI" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "S2:=map(simplify,S1,ln,symbolic);" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>%#S2G<$/%\"yG-%$expG6#,$-%'RootOfG6#,(*$)%#_ZG\"\"# \"\"\"\"\"\"*$)-%#lnG6#%\"aGF3F4!#8*&F8F5-F-6#,(F6\"\"$*&F8F5F2F5!\"%F 0F5F5\"\"%#F5F3/%\"xG-F)6#,$F>FE" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "X:=\{allvalues(RootOf(3*ln(a)^2-4*ln(a)*_Z+_Z^2))\}; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG<$-%#lnG6#%\"aG,$F&\"\"$" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "for i in X do S[i]:=allvalu es(subs(RootOf(3*ln(a)^2-4*ln(a)*_Z+_Z^2)=i,S2))\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"SG6#-%#lnG6#%\"aG6$<$/%\"xG-%$expG6#,$F'#\"\" \"\"\"#/%\"yG-F06#,$F'#\"\"$F5<$F-/F7-F06#,$F'#!\"$F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"SG6#,$-%#lnG6#%\"aG\"\"$6$<$/%\"xG-%$expG6#,$ F(#F,\"\"#/%\"yG-F26#,$F(#\"\"\"F6<$F//F8-F26#,$F(#!\"\"F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "S3:=\{seq(S[i],i=X)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#S3G<&<$/%\"xG*$-%%sqrtG6#%\"aG\"\"\"/%\"yG*$ )F-#\"\"$\"\"#F.<$F'/F0*&F.F.*$)F-#\"\"$F5F.!\"\"<$/F(F1/F0F)<$F?/F0*& F.F.*$-F+6#F-F.F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "select (proc(s,sys) evalb(convert(simplify(eval(subs(s,sys)),ln,symbolic),`an d`)) end,S3,sys);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$<$/%\"xG*$-%%sq rtG6#%\"aG\"\"\"/%\"yG*$)F+#\"\"$\"\"#F,<$/F&F//F.F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "S4:=\{allvalues(S2)\};" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>%#S4G<*<$/%\"xG-%$expG6#,$-%#lnG6#%\"aG#\"\"\"\"\"#/ %\"yG-F*6#,$F-#\"\"$F3<$F'/F5-F*6#,$F-#!\"$F3<$/F(F6/F5F)<$FC/F5-F*6#, $F-#!\"\"F3<$FCF4<$F " 0 "" {MPLTEXT 1 0 93 "select(proc(s,sys) evalb(convert(simplify(eval(subs(s ,sys)),ln,symbolic),`and`)) end,S4,sys);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$<$/%\"xG*$-%%sqrtG6#%\"aG\"\"\"/%\"yG*$)F+#\"\"$\"\"#F,<$/F&F/ /F.F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "9 0 0 " 0 }{VIEWOPTS 1 1 0 1 1 1803 }