{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 } {CSTYLE "Blue Emphasis" -1 256 "Times" 0 0 0 0 255 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Green Emphasis" -1 257 "Times" 1 12 0 128 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Maroon Emphasis" -1 258 "Times" 1 12 128 0 128 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Purple Emphasis" -1 259 "Times" 1 12 102 0 230 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Dark Red Emphasis" -1 260 "T imes" 1 12 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Red Emphasis" -1 261 "Times" 1 12 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{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 "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times " 1 18 0 0 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 3 0 3 0 2 2 0 1 } {PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 128 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 128 0 0 1 1 1 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 Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 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 }{PSTYLE "Bullet Item" -1 15 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 3 3 1 0 1 0 2 2 15 2 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times " 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 257 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 {PARA 3 "" 0 "" {TEXT -1 36 "Programming in Maple . . first st eps" }}{PARA 0 "" 0 "" {TEXT -1 37 "by Peter Stone, Nanaimo, B.C., Can ada" }}{PARA 0 "" 0 "" {TEXT -1 18 "Version: 29.3.2007" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 " " 0 "" {TEXT -1 19 "Automating commands" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 214 "Frequently, you wi ll want to repeat some particular command or sequence of commands seve ral different times with possibly slightly different values involved. \+ You can achieve this with a looping structure using the " }{TEXT 0 3 " for" }{TEXT -1 6 " and " }{TEXT 0 2 "do" }{TEXT -1 10 " commands." }} {PARA 0 "" 0 "" {TEXT -1 44 "The following loop prints a table of valu es." }}{PARA 0 "" 0 "" {TEXT -1 94 "To move to a new line when writing a sequence of commands after a prompt, type [Shift-Return]." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "fo r k from 1 to 5 do print(k, k^2) end do;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 103 "The command that is repeatedly ex ecuted is the print command, and it is enclosed in the pair of symbols " }}{PARA 257 "" 0 "" {TEXT -1 1 " " }{TEXT 0 13 "do . . end do" } {TEXT -1 2 ", " }}{PARA 0 "" 0 "" {TEXT -1 62 "which serve to bracket \+ the command or commands to be repeated." }}{PARA 0 "" 0 "" {TEXT -1 98 "To make this bracketing clearer an indented style of writing seque nces of commands can be adopted." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "for k from 1 to 7 do\n pri nt(`2 to the power of`,k,` is`,2^k)\nend do;" }}}{PARA 0 "" 0 "" {TEXT -1 61 "\nThe following loop solves a sequence of quadratic equat ions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "for j from 0 to 4 do\n solve(x^2-2*x-j=0,x);\nend d o; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"!\"\"#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$,&\"\"\"F$*$\"\"##F$F&F$,&F$F$F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&\"\"\"F$*$\"\"$#F$\"\"#F$,&F$F$F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6$,&*$\"\"&#\"\"\"\"\"#F'F'F',&F$!\"\"F'F'" }}}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Try this " }}{PARA 0 "" 0 "" {TEXT -1 48 "Write a loop to solve all equations of the form " }{XPPEDIT 18 0 " x^2-k*x-1 = 0;" "6#/,(*$%\"xG\"\"#\"\"\"*&%\"kGF(F&F(!\"\"F(F+\"\"!" } {TEXT -1 5 " for " }{XPPEDIT 18 0 "k = 0,1,2,3,4" "6'/%\"kG\"\"!\"\"\" \"\"#\"\"$\"\"%" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 28 "______ ______________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 28 "____________________________" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 4 "An s " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "for k from 0 to 4 do \n solve(x^2-k*x-1=0);\nend do ;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 46 "Factorials . . an example of a Maple procedure" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 24 "For a positive integer " }{TEXT 262 1 "n" }{TEXT -1 3 ", " } {XPPEDIT 18 0 "n!" "6#-%*factorialG6#%\"nG" }{TEXT -1 8 ", read \"" } {TEXT 263 1 "n" }{TEXT -1 29 " factorial\", is the product " } {XPPEDIT 18 0 "n*`.`*(n-1)*`.`*(n-2)*` . . . `*(3)*`.`*(2)*`.`*(1)" "6 #*8%\"nG\"\"\"%\".GF%,&F$F%F%!\"\"F%F&F%,&F$F%\"\"#F(F%%(~.~.~.~GF%\" \"$F%F&F%F*F%F&F%F%F%" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 55 " For example, 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120." }}{PARA 0 "" 0 "" {TEXT -1 21 "By definition 0! = 1." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 131 "There is a built-in Maple procedure for computing factorials, but it is straightforward exercise to write a procedure to calculate " }{XPPEDIT 18 0 "n!" "6#-%*factorialG6#%\"n G" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 52 "A simple form for a Maple procedure definition is:\n\n" } {TEXT 0 22 "procedurename := proc(" }{TEXT -1 30 " - - - input argumen ts - - - " }{TEXT 0 5 ")\n " }}{PARA 0 "" 0 "" {TEXT 0 8 " local " }{TEXT -1 80 " . . names of any variables which are to be understood only within the procedure" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 52 " - - - body of procedure - \+ - -" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 0 18 " \+ last statement " }{TEXT -1 84 "- - - the result of the last statement \+ is the output (return value) of the procedure" }}{PARA 0 "" 0 "" {TEXT 0 9 "end proc:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 194 "Once a procedure is activated in the usual way (by put ting the cursor anywhere in the Maple input for the procedure and pres sing [Enter] ), it can be used just like any built-in Maple procedure. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 "Type \+ " }{TEXT 0 14 "procedurename(" }{TEXT -1 30 " - - - input arguments - - - " }{TEXT 0 1 ")" }{TEXT -1 19 " on a command line." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 5 "Notes" }{TEXT -1 1 " :" }}{PARA 15 "" 0 "" {TEXT -1 11 "The symbol " }{TEXT 0 1 "#" }{TEXT -1 73 " indicates that a comment follows. Comments are ignored during \+ execution." }}{PARA 15 "" 0 "" {TEXT -1 11 "The symbol " }{TEXT 0 6 "e nd if" }{TEXT -1 70 " is used to indicate the end of the conditional w hich starts with the " }{TEXT 0 2 "if" }{TEXT -1 16 " directly above. " }}{PARA 15 "" 0 "" {TEXT -1 131 "The value returned by the procedure is the value of the last statement to be executed. In this procedure \+ the value of the variable " }{TEXT 261 4 "fact" }{TEXT -1 13 " is retu rned." }}{PARA 15 "" 0 "" {TEXT -1 24 "The double colon symbol " } {TEXT 0 2 "::" }{TEXT -1 40 " is a shorthand for the Maple procedure \+ " }{TEXT 0 9 "typematch" }{TEXT -1 44 " which checks the type of a Map le variable.\n" }{TEXT 0 12 "n::nonnegint" }{TEXT -1 13 " checks that \+ " }{TEXT 261 1 "n" }{TEXT -1 138 " is a non-negative integer. Using th is in connection with the procedure definition will cause an error to \+ be generated when the procedure " }{TEXT 0 11 "myFactorial" }{TEXT -1 84 " is called with an argument which does not match the type of a non -negative integer." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 366 "myFactorial := proc(n::nonnegint) # the na me of procedure, input varable n\n local fact, k; # variables \+ which are local or internal\n # to the procedur e\nfact := 1;\n if n > 1 then\n for k from 2 to n do\n \+ fact := k*fact;\n end do; \n end if;\n fact\nend proc; # the symbol 'end' indicates the end of the procedure." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,myFactorialGf*6#'%\"nG%*nonnegintG6$%%factG%\"k G6\"F-C%>8$\"\"\"@$2F19$?(8%\"\"#F1F4%%trueG>F0*&F6F1F0F1F0F-F-F-" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 105 "The foll owing loop compares values given by Maple's factorial function with th ose given by the procedure " }{TEXT 0 11 "myFactorial" }{TEXT -1 2 ". \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "for n from 0 to 20 do \n print('factorial'(n)=n!,'myFactoria l'(n)=myFactorial(n));\nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-% *factorialG6#\"\"!\"\"\"/-%,myFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"\"\"F'/-%,myFactorialGF&F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"\"#F'/-%,myFactorialGF&F' " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"\"$\"\"'/-%,myFa ctorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"\"% \"#C/-%,myFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factor ialG6#\"\"&\"$?\"/-%,myFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"\"'\"$?(/-%,myFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"\"(\"%S]/-%,myFactorialGF&F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"\")\"&?.%/-%,myFacto rialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"\"*\"'! )GO/-%,myFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factori alG6#\"#5\"(+)GO/-%,myFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6$/-%*factorialG6#\"#6\")+o\"*R/-%,myFactorialGF&F(" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$/-%*factorialG6#\"#7\"*+;+z%/-%,myFactorialGF&F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"#8\"++3-Fi/-%,myFact orialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"#9\",+ 7Hyr)/-%,myFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*facto rialG6#\"#:\".+!oVn28/-%,myFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"#;\"/+!)))*yA4#/-%,myFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"#<\"0+g4Guob$/-%,m yFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"# =\"1+!GdqtBS'/-%,myFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/ -%*factorialG6#\"#>\"3+?$)3/5X;7/-%,myFactorialGF&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%*factorialG6#\"#?\"4++kw\"3?!HV#/-%,myFactorialGF &F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Try this " } }{PARA 0 "" 0 "" {TEXT -1 27 "(a) Compare the values of " }{XPPEDIT 18 0 "n!" "6#-%*factorialG6#%\"nG" }{TEXT -1 80 " with those of the Ma ple function GAMMA(n+1). You could write a loop to do this." }}{PARA 0 "" 0 "" {TEXT -1 33 "(b) Plot a graph of the function " }{TEXT 261 8 "GAMMA(x)" }{TEXT -1 58 ", which is the Maple version of the mathema tical function " }{XPPEDIT 18 0 "GAMMA(x);" "6#-%&GAMMAG6#%\"xG" }} {PARA 0 "" 0 "" {TEXT -1 29 "_____________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 29 "__ ___________________________" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 4 "Ans " }}{PARA 0 "" 0 "" {TEXT -1 5 "(a) " }{XPPEDIT 18 0 "GAMMA(n+1)=n!" "6#/-%&GAMMAG6#,&%\" nG\"\"\"F)F)-%*factorialG6#F(" }{TEXT -1 32 " for every non-negative i nteger " }{TEXT 264 1 "n" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "for n from 0 to 20 do \n print('factorial'(n)=n!,'GAMMA'(n+1)=GAMMA(n+1));\nend do;" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "(b) The f ollowing picture shows the graph of " }{XPPEDIT 18 0 "y=GAMMA(x)" "6#/ %\"yG-%&GAMMAG6#%\"xG" }{TEXT -1 24 " over the interval from " } {XPPEDIT 18 0 "x=-4" "6#/%\"xG,$\"\"%!\"\"" }{TEXT -1 5 " and " } {XPPEDIT 18 0 "x=5" "6#/%\"xG\"\"&" }{TEXT -1 16 " approximately. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 190 "p1 := plot(GAMMA(x),x=-4.01..5,y=-5..8,discont=true):\np2 := plot s[implicitplot](\{x=-1,x=-2,x=-3,x=-4\},x=-4.01..0,y=-5..8,\n color =COLOR(RGB,.4,.4,.4),linestyle=3):\nplots[display]([p1,p2]);" }}{PARA 13 "" 1 "" {GLPLOT2D 467 467 467 {PLOTDATA 2 "6)-%'CURVESG6)7gn7$$!3z* ***********4S!#<$!3/zdY4=,0TF*7$$!3%*4FjG?y4SF*$!39-4;UK$y>%F*7$$!3:=: \"HP#f4SF*$!3_NsAy&H?G%F*7$$!3Zlv@&3z$4SF*$!3'*))fa6hy!Q%F*7$$!3EEVr$Q k\"4SF*$!3%*\\.[&)4%[[%F*7$$!3?b)\\Eq]*3SF*$!3'>1$GG)eLf%F*7$$!3T4+&Hf _(3SF*$!3q)Gy([Kq)p%F*7$$!3\"3yI=YZ&3SF*$!3OO*e+GGH\"[F*7$$!3bKQ$\\JN$ 3SF*$!3H./Tk\\(p$\\F*7$$!3'F*7$$!37%H#>ozY1SF*$!3?^j*yoh*zjF*7$$!3$*R?K!*eC1SF*$!3FM,qH \"))*3mF*7$$!3^<_+%F*$!3(HxZ+\\KU#zF*7$$!3x%)=*)R\\+0SF*$!3SMu*[!p!HE)F*7$ $!3(R^udY%y/SF*$!3M/X.kR^Y')F*7$$!3H>sSUDf/SF*$!3?FQ],IV5!*F*7$$!3RGE \"*f_Q/SF*$!3\">3*ejwDR%*F*7$$!3y4J\"o6rT+%F*$!3#ztU*Ry.F**F*7$$!3t2#o &>;'R+%F*$!3!*e/ksn_X5!#;7$$!3]<;@?*eP+%F*$!3j$zxH\\SA5\"Fht7$$!3l=a8d Q`.SF*$!3)4dCK9MG<\"Fht7$$!3Vo8&ziJL+%F*$!3]F\"HhE,WC\"Fht7$$!3vRC80d6 .SF*$!3P%z^2,q5L\"Fht7$$!3>]g'p/?H+%F*$!3\"GR%GjXn?9Fht7$$!3Z\"45491F+ %F*$!32g![&eCYL:Fht7$$!3\\B:)>([]-SF*$!3e8a!>Gxrl\"Fht7$$!3ck\"ez[%H-S F*$!3M-&y)[hp4=Fht7$$!3UK17*z)3-SF*$!33y!)ocU^))>Fht7$$!3h&)*p>Yt=+%F* $!3D\"G1s'=z#>TM$Fht7$$!3(\\r4LO]5+%F*$!3?mdq lvhgRFht7$$!3&[4mn%)G3+%F*$!3KsC$f$))z?]Fht7$$!3%HwG(>2j+SF*$!3'>]I>-T **f'Fht7$$!3HwJ)\\Z>/+%F*$!32k/l/3yE**Fht7$$!37,`*3Q=.+%F*$!3A\"Rzczx! 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The first two terms of the sequence are known as \+ the starting values and, if they are both equal to 1, the first few te rms of the sequence are: " }{XPPEDIT 18 0 "1,1,2,3,5,8,13,21,34" "6+\" \"\"F#\"\"#\"\"$\"\"&\"\")\"#8\"#@\"#M" }{TEXT -1 62 ". The terms of t his sequence are called the Fibonacci numbers." }}{PARA 0 "" 0 "" {TEXT -1 49 "The following loop prints terms of this sequence." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "prevterm := 1:\nterm := 1:\nfor k from 1 to 25 do\n newterm := \+ prevterm + term;\n print(newterm);\n prevterm := term;\n term := newterm;\nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\" \"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#@" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#M" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#b " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#*)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$W\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$L#" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"$x$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$5'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$()*" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"%(f\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%%e#" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"%\"=%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%ln" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"&Y4\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"&6x\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"&d'G " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"&oj%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"&D](" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"'$R@\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"'=k>" }}}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Try this " }}{PARA 0 "" 0 "" {TEXT -1 36 "Write a \+ procedure which returns the " }{TEXT 266 1 "n" }{TEXT -1 21 " th Fibon naci number." }}{PARA 0 "" 0 "" {TEXT -1 29 "_________________________ ____" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 " " {TEXT -1 29 "_____________________________" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 4 "Ans " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 278 "fibonacci := proc(n::posint)\n local prevterm,term,newterm,m,k; \n prevterm := 1:\n term := 1:\n m := n-2;\n if m>0 then \n \+ for k to m do\n newterm := prevterm + term;\n prevt erm := term;\n term := newterm;\n end do:\n end if;\n \+ term;\nend proc;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "for n to 20 do\n fibonacci(n) := fibonacci( n);\nend do;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 21 "There is a procedure " }{TEXT 0 9 "fibonacci" }{TEXT -1 8 " in the " }{TEXT 0 8 "combinat" }{TEXT -1 74 " package which can be accessed (without loading the package) via the name " }{TEXT 0 19 "co mbinat[fibonacci]" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "combinat[fibonacci](20);" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "combinat[fibonacci](200);\nfibonacci(200);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "Convers ion to binary " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "We define a Maple procedure to convert a non-negative int eger to binary form. " }}{PARA 0 "" 0 "" {TEXT -1 92 "The return value is a sequence which consists of the binary digits in the appropriate \+ order." }}{PARA 0 "" 0 "" {TEXT -1 30 "Giving the procedure the name \+ " }{TEXT 0 16 "`convert/BINARY`" }{TEXT -1 49 "will mean that it can b e called using the syntax " }{TEXT 0 18 "convert(..,BINARY)" }{TEXT -1 13 ". instead of " }{TEXT 0 20 "`convert/BINARY`(..)" }{TEXT -1 1 " ." }}{PARA 0 "" 0 "" {TEXT -1 19 "See the help page " }{HYPERLNK 17 " convert" 2 "convert" "" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 259 5 "Notes" }{TEXT -1 2 ": " }}{PARA 0 "" 0 "" {TEXT -1 20 "The Maple procedure " }{TEXT 0 4 "iquo" }{TEXT -1 103 " can be used to obtain both the quotient and remainder when one i nteger is divided by another integer. " }}{PARA 0 "" 0 "" {TEXT -1 12 "The command " }{TEXT 261 19 "q := iquo(q,2,'r');" }{TEXT -1 42 " comp utes the quotient and remainder when " }{TEXT 261 1 "q" }{TEXT -1 47 " is divided by 2. \nThe quotient is assigned to " }{TEXT 261 1 "q" } {TEXT -1 36 " while the remainder is assigned to " }{TEXT 261 1 "r" } {TEXT -1 20 ". See the help page " }{HYPERLNK 17 "iquo" 2 "iquo" "" } {TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 55 "The sequence of binary d igits is saved in the variable " }{TEXT 261 10 "bin_digits" }{TEXT -1 73 ", which is initially assigned the null expression sequence designa ted by " }{TEXT 261 4 "NULL" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 14 "The statement " }{TEXT 261 27 "bin_digits := r,bin_digits;" } {TEXT -1 86 " \"adds\" the new binary digit to the sequence so that it precedes the previous digits. " }}{PARA 0 "" 0 "" {TEXT -1 128 "The r eturn value of the procedure is the value given by the last statement \+ in the loop after the last time that it is executed. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 198 "`convert /BINARY` := proc(n::nonnegint)\n local q,bin_digits,r;\n q := n;\n bin_digits := NULL;\n while q<>0 do\n q := iquo(q,2,'r');\n \+ bin_digits := r,bin_digits;\n end do;\nend proc; " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%/convert/BINARYGf*6#'%\"nG%*nonnegintG6%% \"qG%+bin_digitsG%\"rG6\"F.C%>8$9$>8%%%NULLG?(F.\"\"\"F7F.0F1\"\"!C$>F 1-%%iquoG6%F1\"\"#.8&>F46$FAF4F.F.F." }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 14 "The procedure " }{TEXT 0 16 "`convert /BINARY`" }{TEXT -1 42 " can be compared with the Maple procedure " } {TEXT 0 16 "`convert/binary`" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 88 "Similar syntax can be used for both procedures, but the o utput from the Maple procedure " }{TEXT 0 16 "`convert/binary`" } {TEXT -1 42 " \"looks like\" an integer in decimal form. " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "conve rt(193,BINARY);\nconvert(193,binary);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6*\"\"\"F#\"\"!F$F$F$F$F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"),++6 " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "A := array(1..32,1..3):\nfor n to 32 do\n A[n,1]:= n;\n A[n,2] :=[convert(n,BINARY)];\n A[n,3] := convert(n,binary); \nend do:\nevalm(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrix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pprint76\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Try this " }}{PARA 0 "" 0 "" {TEXT -1 25 " (a) Modify the procedure " }{TEXT 0 16 "`convert/BINARY`" }{TEXT -1 32 " in order to define a procedure " }{TEXT 0 15 "`convert/OCTAL`" } {TEXT -1 239 " which computes the octal (base 8) digits of a non-negat ive integer. The return value should be a sequence which consists of t he octal digits of the input parameter in the appropriate order. Compa re your procedure with the Maple procedure " }{TEXT 0 15 "`convert/oct al`" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 22 "(b) Write a proce dure " }{TEXT 0 21 "`convert/HEXADECIMAL`" }{TEXT -1 345 " which compu tes the hexadecimal (base 16) digits of a non-negative integer. The re turn value should be a sequence which consists of the hexadecimal digi ts of the input parameter in the appropriate order. Use the symbols: 0 , 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, for the hexadecimal dig its. Compare your procedure with the Maple procedure " }{TEXT 0 21 "`c onvert/hexadecimal`" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 29 "__ ___________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{PARA 0 "" 0 "" {TEXT -1 29 "_____________________________" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 5 "" 0 " " {TEXT -1 4 "Ans " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "(a) All we need to do is divide repeatedly by 8 instead o f 2. " }}{PARA 0 "" 0 "" {TEXT -1 83 "It is appropriate to rename the \+ variable which holds the sequence of octal digits. " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 206 "`convert/ OCTAL` := proc(n::nonnegint)\n local q,octal_digits,r;\n q := n;\n octal_digits := NULL;\n while q<>0 do\n q := iquo(q,8,'r'); \n octal_digits := r,octal_digits;\n end do;\nend proc; " }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "The proc edure " }{TEXT 0 15 "`convert/OCTAL`" }{TEXT -1 41 "can be compared wi th the Maple procedure " }{TEXT 0 15 "`convert/octal`" }{TEXT -1 2 ". \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "convert(2045,OCTAL);\nconvert(2045,octal);" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "A := arra y(1..32,1..3):\nfor n to 32 do\n A[n,1]:= n;\n A[n,2] :=[convert(n ,OCTAL)];\n A[n,3] := convert(n,octal);\nend do:\nevalm(A);" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 66 "(b) We ne ed to divide repeatedly by 16 and collect the remainders." }}{PARA 0 " " 0 "" {TEXT -1 116 "When a remainder is greater than 9 we must switch to the appropriate letter for the corresponding hexadecimal digit." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 379 "`convert/HEXADECIMAL` := proc(n::nonnegint)\n local q,hex_dig its,r;\n q := n;\n hex_digits := NULL;\n while q<>0 do\n q \+ := iquo(q,16,'r');\n if r=10 then r := A\n elif r=11 then r \+ := B\n elif r=12 then r := C\n elif r=13 then r := D\n \+ elif r=14 then r := E\n elif r=15 then r := F end if;\n hex_ digits := r,hex_digits;\n end do;\nend proc; " }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "The procedure " }{TEXT 0 21 "`convert/HEXADECIMAL`" }{TEXT -1 41 "can be compared with the Ma ple procedure " }{TEXT 0 21 "`convert/hexadecimal`" }{TEXT -1 2 ". " } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "convert(12345678,HEXADECIMAL);\nconvert(12345678,hexadecimal);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "A := array(1..32,1..3):\nfor n to 32 do\n A[n,1]:= n;\n A [n,2] :=[convert(n,HEXADECIMAL)];\n A[n,3] := convert(n,hexadecimal) ;\nend do:\nevalm(A);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}} }{SECT 1 {PARA 4 "" 0 "" {TEXT -1 36 "Plotting graphs of several funct ions" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 101 " The following procedure plots several graphs on the same set of axes. \nThe loop constructs a sequence " }{TEXT 261 5 "polys" }{TEXT -1 85 " of polynomials which are then taken as the members of a list of expre ssions to plot." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 170 "polyplot := proc(n::posint)\n local k,polys ,x;\n polys := NULL;\n for k from 1 to n do\n polys := polys, x^k;\n end do;\n plot([polys],x=-4..4,-8..8);\nend proc; " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%)polyplotGf*6#'%\"nG%'posintG6%%\"kG %&polysG%\"xG6\"F.C%>8%%%NULLG?(8$\"\"\"F59$%%trueG>F16$F1)8&F4-%%plot G6%7#F1/F;;!\"%\"\"%;!\")\"\")F.F.F." }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 24 "We can draw the graphs " }{XPPEDIT 18 0 "y = x,y = x^2,y = x^3,y = x^4;" "6&/%\"yG%\"xG/F$*$F%\"\"#/F$*$F %\"\"$/F$*$F%\"\"%" }{TEXT -1 42 " on the same set of axes with the co mmand:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "polyplot(4);" }}{PARA 13 "" 1 "" {GLPLOT2D 487 487 487 {PLOTDATA 2 "6(-%'CURVESG6$7S7$$!\"%\"\"!F(7$$!3ommmmFiDQ!#1DBF.FH7$$!3kmmmw))yr@F.FK7$$!3;+++S(R#**>F.FN7$$ !30++++@)f#=F.FQ7$$!3-+++gi,f;F.FT7$$!3qmmm\"G&R2:F.FW7$$!3XLLLtK5F8F. 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" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 179 "sine_plot : = proc(n::posint)\n local k,curves,x;\n curves := NULL;\n for k \+ from 1 to n do\n curves := curves,sin(k*x);\n end do;\n plot( [curves],x=0..2*Pi);\nend proc; " }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #>%*sine_plotGf*6#'%\"nG%'posintG6%%\"kG%'curvesG%\"xG6\"F.C%>8%%%NULL G?(8$\"\"\"F59$%%trueG>F16$F1-%$sinG6#*&F4F58&F5-%%plotG6$7#F1/F>;\"\" !,$*&\"\"#F5%#PiGF5F5F.F.F." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "sine_plot(5);" }}{PARA 13 " " 1 "" {GLPLOT2D 596 318 318 {PLOTDATA 2 "6)-%'CURVESG6$7en7$$\"\"!F)F (7$$\"3i]cC&eb&p8!#=$\"3+9&o'z\"y_O\"F-7$$\"3YqR*pd)>hDF-$\"3K!y=V&*)G LDF-7$$\"3Zs[E^dK,RF-$\"3R]F<<.6.QF-7$$\"3ab^NehL]_F-$\"3I,*y(H4U7]F-7 $$\"35*QhW&\\$Hf'F-$\"3%=pD*eceDhF-7$$\"3zS11.fpPyF-$\"3w>82*oU&fqF-7$ $\"3upr'fwtl7*F-$\"3@)*QjP!>8\"zF-7$$\"3!QRa&4L&f/\"!#<$\"3[[%3w7ESl)F -7$$\"3YjXwg<#)y6FQ$\"3Pi.Z,bcT#*F-7$$\"36qGW%H$\\:8FQ$\"3!e$pSF\"oen* 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