{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 }{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 "" 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 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 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 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT -1 39 "Lecture Note 8, Problem 2 0, Section 4.6" }}{PARA 0 "" 0 "" {TEXT -1 82 "We want to use Maple in order to solve the above problem, this time requiring that" }}{PARA 0 "" 0 "" {TEXT -1 66 "all the values x_1, x_2, x_3 should be strictly positive integers." }}{PARA 0 "" 0 "" {TEXT -1 73 "The program below \+ computes the number of assignments to the x_i such that" }}{PARA 0 "" 0 "" {TEXT -1 71 "the sum is strictly less than 11 and those such that the sum equals 11." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "x := array(1..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%&ar rayG6$;\"\"\"\"\"$7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "re s1 := 0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%res1G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "res2 := 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "for x[1] from 1 to 11 by 1 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "for x[2] from 1 to 11 by 1 do" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 29 "for x[3] from 1 to 11 by 1 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "addi := x[1] + x[2] + x[3];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "if (addi < 11) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "print(x[1],x[2],x[3]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "res 1 := res1 + 1;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 19 "if (addi = 11) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "print(x[1],x[2], x[3]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "res2 := res2+1;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 " fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "print(`The number of different sums below 11 is`, res1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "print(`The numbe r of different sums equal to 11 is` , res2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"F#F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"F# \"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"F#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"F#\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6% \"\"\"F#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"F#\"\"'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"F#\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"F#\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\" F#\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 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"6%\"\"$\"\"'\"\"#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6%\"\"$\"\"(\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6% \"\"%\"\"\"F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"\"\"\"#" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"\"F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"% \"\"\"\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"\"\"\"'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"#F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\" \"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"#F#" }}{PARA 11 " " 1 "" {XPPMATH 20 "6%\"\"%\"\"#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"$\"\"# " }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"$F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%F# \"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%F#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%F#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" \"%\"\"&\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"&\"\"#" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"'\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"\"F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"& \"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"\"\"\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"\"\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"\"F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"& \"\"#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"#F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"#\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\" &\"\"$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"$\"\"#" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"%\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" \"&\"\"%\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&F#\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'\"\"\"F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" \"'\"\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'\"\"\"\"\"%" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'\"\"#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'\"\"#F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'\" \"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'\"\"$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'\"\"$\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'\"\"%\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" \"(\"\"\"F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"(\"\"\"\"\"#" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"(\"\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"(\"\"#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" \"(\"\"#F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"(\"\"$\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\")\"\"\"F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\")\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" \")\"\"#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"*\"\"\"F$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$%IThe~number~of~different~sums~below~1 1~isG\"$?\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%LThe~number~of~differe nt~sums~equal~to~11~isG\"#X" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 14 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }