{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 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 "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 12 0 0 0 0 0 2 2 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Tim es" 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 Outpu t" -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 "Title" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 24 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }2 1 0 0 12 12 1 0 1 0 2 2 19 1 }} {SECT 0 {SECT 1 {PARA 256 "" 0 "" {TEXT -1 21 "Chapter 8\n\nFunctions \n" }}{PARA 0 "" 0 "" {TEXT 264 31 "\251 Copyright 2003 by Andr\351 He ck." }}}{SECT 1 {PARA 0 "" 0 "" {TEXT 257 2 "1." }{TEXT -1 10 " Consid er " }{XPPEDIT 18 0 "x^3-(a-1)*x^2+a^2*x-a^3=0" "6#/,**$%\"xG\"\"$\"\" \"*&,&%\"aGF(F(!\"\"F(*$F&\"\"#F(F,*&F+F.F&F(F(*$F+F'F,\"\"!" }{TEXT -1 19 " as an equation in " }{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 83 ". Solve it, make a function out of the first solution and compute the solution for " }{XPPEDIT 18 0 "a=0" "6#/%\"aG\"\"!" }{TEXT -1 9 " and for " }{XPPEDIT 18 0 "a=1" "6#/%\"aG\"\"\"" }{TEXT -1 33 ". Give an a pproximate result for " }{XPPEDIT 18 0 "a=2" "6#/%\"aG\"\"#" }{TEXT -1 2 ".\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "x^3-(a-1)*x^2+a^2*x-a^3=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,**$)%\"xG\"\"$\"\"\"F)*&,&%\"aGF)F )!\"\"F))F'\"\"#F)F-*&)F,F/F)F'F)F)*$)F,F(F)F-\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "sols := solve(%, x);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%solsG6%,**&\"\"'!\"\",,*&\"#!)\"\"\")%\"aG\"\"$F-F-* &\"#7F-)F/\"\"#F-F-*&\"#CF-F/F-F-\"\")F)*&F2F-,**&\"#[F-)F/F(F-F-*&F6F -)F/\"\"&F-F-*&F2F-F.F-F)*&\"#LF-)F/\"\"%F-F-#F-F4F-#F-F0F-*(F(F-,(*&# F4\"\"*F-*$F3F-F-F-*&FJF-F/F-F-#F-FKF)F-F*#F)F0F)*&F0F)F/F-F-#F-F0F),, *&F2F)F*FFF)*(F0F-FHF-F*FOF-*&F0F)F/F-F-#F-F0F)*(^#FEF-F0FE,&*&F(F)F*F FF-*(F(F-FHF-F*FOF-F-F-,,*&F2F)F*FFF)*(F0F-FHF-F*FOF-*&F0F)F/F-F-#F-F0 F)*(^##F)F4F-F0FEFYF-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " f := unapply(%[1], a);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#% \"aG6\"6$%)operatorG%&arrowGF(,**&#\"\"\"\"\"'F/*$),,*&\"#!)F/)9$\"\"$ F/F/*&\"#7F/)F7\"\"#F/F/*&\"#CF/F7F/F/\"\")!\"\"*&F:F/,**&\"#[F/)F7F0F /F/*&F>F/)F7\"\"&F/F/*&F:F/F6F/F@*&\"#LF/)F7\"\"%F/F/#F/F " 0 "" {MPLTEXT 1 0 5 "f(0);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\"'!\"\"!\")#\"\"\"\"\"$F)*&\"# 7F&F'#\"\"#F*F&#F)F*F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "s implify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#, &*&\"\"'!\"\",&\"$3\"\"\"\"*&\"#7F)\"#$*#F)\"\"#F)#F)\"\"$F)*&F.F)F'#F &F0F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(2.0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+o<_2;!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 258 2 "2." }{TEXT -1 116 " Define a function in Maple that is 1 on the segment [-1,1], a nd 0 otherwise. Also plot the graph of your function.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 41 "f := x -> piecewise(x<-1, 0, x<=1, 1, 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(-%* piecewiseG6'29$!\"\"\"\"!1F0\"\"\"F4F2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*PIECE WISEG6%7$\"\"!2%\"xG!\"\"7$\"\"\"1F)F,7$F'%*otherwiseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(f, -2..2, axes=frame);" }} {PARA 13 "" 1 "" {GLPLOT2D 351 351 351 {PLOTDATA 2 "6'-%'CURVESG6#7co7 $$!\"#\"\"!$F*F*7$$!3MLLL$Q6G\">!#.\"F/F+7$$!3]LL37&)=@5F/F+7$$!39+Dc^j z:5F/F+7$$!3zm;/\">//,\"F/F+7$$!3+]7y5\"3x+\"F/F+7$$!3VL3_I?,05F/F+7$$ !3(oTg-&fJ-5F/F+7$$!3w++++()>'***!#=$\"\"\"F*7$$!3_++++Y0j&*FioFjo7$$! 3E++++0\"*H\"*FioFjo7$$!35++++83&H)FioFjo7$$!3\\LLL3k(p`(FioFjo7$$!3An mmmj^NmFioFjo7$$!3)zmmmYh=(eFioFjo7$$!3+,++v#\\N)\\FioFjo7$$!3commmCC( >%FioFjo7$$!39*****\\FRXL$FioFjo7$$!3t*****\\#=/8DFioFjo7$$!3=mmm;a*el \"FioFjo7$$!3komm;Wn(o)!#>Fjo7$$!3IqLLL$eV(>!#?Fjo7$$\"3)Qjmm\"f`@')F` rFjo7$$\"3%z****\\nZ)H;FioFjo7$$\"3ckmm;$y*eCFioFjo7$$\"3f)******R^bJ$ FioFjo7$$\"3'e*****\\5a`TFioFjo7$$\"3'o****\\7RV'\\FioFjo7$$\"3Y'***** \\@fkeFioFjo7$$\"3_ILLL&4Nn'FioFjo7$$\"3A*******\\,s`(FioFjo7$$\"3%[mm ;zM)>$)FioFjo7$$\"3M*******pfa<*FioFjo7$$\"3Ckm;zy*zd*FioFjo7$$\"39HLL eg`!)**FioFjo7$$\"3Cm\"H#3Mo+5F/F+7$$\"3c**\\i5KJ.5F/F+7$$\"3*G$3-8I%f +\"F/F+7$$\"3@mmT:Gd35F/F+7$$\"3'GL3-UKQ,\"F/F+7$$\"3^*****\\-#4>5F/F+ 7$$\"3\"GL$eM7hH5F/F+7$$\"3Lmm;W/8S5F/F+7$$\"3;LLLj)o61\"F/F+7$$\"3w** **\\#G2A3\"F/F+7$$\"3Ymm\"H3XL7\"F/F+7$$\"3;LLL$)G[k6F/F+7$$\"3#)**** \\7yh]7F/F+7$$\"3xmmm')fdL8F/F+7$$\"3bmmm,FT=9F/F+7$$\"3FLL$e#pa-:F/F+ 7$$\"3!*******Rv&)z:F/F+7$$\"3ILLLGUYo;F/F+7$$\"3_mmm1^rZF/F+7$$\"\"#F*F+-%+AXESLABELSG6$Q!6\"Fay-%* AXESSTYLEG6#%&FRAMEG-%'COLOURG6&%$RGBGF*F*F*-%%VIEWG6$;F(F\\y%(DEFAULT G" 1 2 0 1 10 0 2 6 1 3 2 1.000000 45.000000 45.000000 0 0 "Curve 1" } }}}{PARA 0 "" 0 "" {TEXT -1 76 "You could also have defined the functi on in terms of the Heaviside function:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "convert(f(x), Heaviside);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%*HeavisideG6#,&\"\"\"F(%\"xGF(F(-F%6#,&F(!\"\"F)F(F -" }}}{PARA 0 "" 0 "" {TEXT -1 68 "Of course, you always make more com plicated definitions. An example:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "g := x -> max(-x^2+1,0)/(1-x^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*&-%$maxG6$,&* $)9$\"\"#\"\"\"!\"\"F5F5\"\"!F5F0F6F(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 5 "g(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%$maxG6$ \"\"!,&*$)%\"xG\"\"#\"\"\"!\"\"F-F-F-F(F." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "convert(%, piecewise);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*PIECEWISEG6%7$\"\"!1%\"xG!\"\"7$\"\"\"2F)F,7$F'1F,F) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 0 " " 0 "" {TEXT 259 2 "3." }{TEXT -1 21 " Define the function " } {XPPEDIT 18 0 "f" "6#%\"fG" }{TEXT -1 3 " : " }{XPPEDIT 18 0 "t->sum(( -1)^(n+1),n=1..8)" "6#f*6#%\"tG7\"6$%)operatorG%&arrowG6\"-%$sumG6$),$ \"\"\"!\"\",&%\"nGF0F0F0/F3;F0\"\")F*F*F*" }{XPPEDIT 18 0 "2/n" "6#*& \"\"#\"\"\"%\"nG!\"\"" }{TEXT -1 1 " " }{XPPEDIT 18 0 "sin(n*t)" "6#-% $sinG6#*&%\"nG\"\"\"%\"tGF(" }{TEXT -1 11 " . Compute " }{XPPEDIT 18 0 "f(Pi/10)" "6#-%\"fG6#*&%#PiG\"\"\"\"#5!\"\"" }{TEXT -1 5 " and " } {XPPEDIT 18 0 "f(Pi/6)" "6#-%\"fG6#*&%#PiG\"\"\"\"\"'!\"\"" }{TEXT -1 35 ". Plot the graph of your function.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "f := t-> sum((-1)^(n+1)*2/n*sin(n*t), n=1..8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"tG6\"6$%)operatorG%&arrowGF(-%$sumG6$,$** \"\"#\"\"\")!\"\",&%\"nGF2F2F2F2F6F4-%$sinG6#*&F6F29$F2F2F2/F6;F2\"\") F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f(Pi/10);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,,#\"\"#\"\"&\"\"\"*&F%F'-%$sinG6#,$*& \"#5!\"\"%#PiGF'F'F'F'*&#F&\"\"%F'-F*6#,$*&F&F/F0F'F'F'F/*&#\"#?\"#@F' -F*6#,$*(\"\"$F'F.F/F0F'F'F'F'*&#F&\"\"'F'-F*6#,$*(F%F'F&F/F0F'F'F'F/ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "convert(%, radical);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,*#\"#H\"$5#\"\"\"*(\"#JF'\"#U!\"\"\" \"&#F'\"\"#F'**F,F'\"#;F+F.F-,&F,F'*$F,F-F+F-F+**F,F'\"#CF+F.F-,&F,F'F 2F'F-F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+DqZ7E!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "f(Pi/6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&#\" $\"=\"$0\"\"\"\"*(\"\"&F'\"\")!\"\"\"\"$#F'\"\"#F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #$\"*pxFT'!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(f, - 2*Pi..2*Pi);" }}{PARA 13 "" 1 "" {GLPLOT2D 285 285 285 {PLOTDATA 2 "6& -%'CURVESG6#7_y7$$!3)****>YH&=$G'!#<$!3uoR'f8nl6\"!#K7$$!3ce)))\\SY*[i F*$\"3#oc(=ldf'z%!#@7$$!3/=xN:vq9iF*$\"3_x#z76M'*y$!#?7$$!3iwlsD'o/='F *$\"35)=K9-?ED\"!#>7$$!3ANa4O(Hi9'F*$\"3/:^_'pkO)GF?7$$!3S_J$o&>vxgF*$ \"3'>v1Jtw/&*)F?7$$!3dp3dxTF4gF*$\"3u;*[Ywkd)=!#=7$$!3]PgRy)4,*eF*$\"3 A28g)G+7=%FO7$$!3W07Azb%4x&F*$\"3m0@%G+ZLE'FO7$$!3$GVk)*RUut&F*$\"3_%* HJ[@ZsmFO7$$!3Agw]?#RRq&F*$\"3=yc2%ylN)pFO7$$!3i()3:TgVqcF*$\"3G8A\\6b g(>(FO7$$!3,:TzhG$pj&F*$\"3OUzq0:NBtFO7$$!3!)p03.l#*pbF*$\"3?spmDfkztF O7$$!3[DqOW,#H]&F*$\"3S=hU(*=?TtFO7$$!3So(*=%)[>paF*$\"3CM^#Hr>rN(FO7$ $!3K6D,C'paV&F*$\"33Ba7eI-LuFO7$$!3Da_$QOW!o`F*$\"3kjmRs@rZyFO7$$!3-$[.Leo0I&F*$\"3wm%\\rh9*z')FO7$$!3() o*[H1=JB&F*$\"3A!o)H:$zJ*)*FO7$$!3GX$QL=e))4&F*$\"3!Rq`W%H2t7F*7$$!3gA xs.$)fk\\F*$\"3g!*yVn/jh9F*7$$!3;TF,!GzM$\\F*$\"3yk8'eT%Rz9F*7$$!3tfxH c-O-\\F*$\"3IR>b(*=i([\"F*7$$!3IyFeK7Cr[F*$\"35))et:fn([\"F*7$$!3(ozn) 3A7S[F*$\"359t92C_\"[\"F*7$$!3-MyVhT)yx%F*$\"3y3`iM5sg9F*7$$!3/sy+9hk: ZF*$\"3Y9!)H?5mZ9F*7$$!3G4_VnTU$o%F*$\"3%elWKd$G^9F*7$$!3kXD'3A-7l%F*$ \"3/nG&[ZA`Y\"F*7$$!3,#))*Gu-)*=YF*$\"3gDp4f\"4:\\\"F*7$$!3O=srF$ene%F *$\"3mfP>;0tI:F*7$$!3(>*=dMWJAXF*$\"39fryO$*4Z;F*7$$!3ellUT0(yX%F*$\"3 X7/UJ@o-=F*7$$!3v)))o%3YdCVF*$\"3'fg%\\JvUO@F*7$$!3!>@6bny7>%F*$\"3%GO &=\\ra#G#F*7$$!3/U5IC-TeSF*$\"3-`:R@o#*z@F*7$$!3/t34t(z^'= Vn?F*7$$!3SmDTR-())y$F*$\"3?&46=u.VG#F*7$$!3wfUt0()>_OF*$\"3'=K0a[#fnG F*7$$!3W+k5D&3?f$F*$\"32MYx&>E(HJF*7$$!3:T&yWM==`$F*$\"3$fp?1g3yI$F*7$ $!3@w:K*zqn^$F*$\"37))z)oX7;L$F*7$$!3G6Y;aKs,NF*$\"3i/6!*>XEXLF*7$$!3M Yw+4dn'[$F*$\"3)\\j9i\"=$zM$F*7$$!3S\"o]Q;G;Z$F*$\"3Fgb?^c&)QLF*7$$!3` ^n`tI`TMF*$\"3YBp68%oGG$F*7$$!35AGA$)zV6MF*$\"3)4G)**ed2tJF*7$$!3)=4K& R!evP$F*$\"3!Q%)z[:d?)HF*7$$!3Ah8%e4yOM$F*$\"3R(fE-#*z!>FF*7$$!3cI1:_ \")z4LF*$\"3e$)>i)o'p'Q#F*7$$!3!***)f%3#=fF$F*$\"3')QF\"\\)Ql!*>F*7$$! 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These polynomials satisfy the recurrrence relation " }{XPPEDIT 18 0 "L[0](x)=1, L[1](x)=x" "6$/-&%\"LG6#\"\"!6# %\"xG\"\"\"/-&F&6#F+6#F*F*" }{TEXT -1 6 ", and " }{XPPEDIT 18 0 "L[n]( x)=(n-1)/n" "6#/-&%\"LG6#%\"nG6#%\"xG*&,&F(\"\"\"F-!\"\"F-F(F." } {TEXT -1 1 " " }{XPPEDIT 18 0 "``*(x*L[n-1](x)-L[n-2](x))+x*L[n-1](x) " "6#,&*&%!G\"\"\",&*&%\"xGF&-&%\"LG6#,&%\"nGF&F&!\"\"6#F)F&F&-&F,6#,& F/F&\"\"#F06#F)F0F&F&*&F)F&-&F,6#,&F/F&F&F06#F)F&F&" }{TEXT -1 7 " , f or " }{XPPEDIT 18 0 "n*`>`*1" "6#*(%\"nG\"\"\"%\">GF%F%F%" }{TEXT -1 11 ". \nCompute " }{XPPEDIT 18 0 "L[7](x) " "6#-&%\"LG6#\"\"(6#%\"xG" }{TEXT -1 48 " and check your answer with the Maple procedure " } {TEXT 0 9 "LegendreP" }{TEXT -1 29 ". Can your procedure compute " } {XPPEDIT 18 0 "L[50](x)" "6#-&%\"LG6#\"#]6#%\"xG" }{TEXT -1 2 "?\n" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 56 "L := proc(n::nonnegint, x::anything) Legendr e(n, x) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "Legendre : = proc(n,x)\n option remember;\n if n=0 then\n 1\n elif n=1 then \n x\n else\n expand( (n-1)/n*(x*L(n-1,x) - L(n-2,x)) + x*L(n-1 ,x) )\n end if\nend proc;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)Legen dreGf*6$%\"nG%\"xG6\"6#%)rememberGF)@'/9$\"\"!\"\"\"/F.F09%-%'expandG6 #,&*(,&F.F0F0!\"\"F0F.F9,&*&F2F0-%\"LG6$F8F2F0F0-F=6$,&F.F0\"\"#F9F2F9 F0F0F;F0F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "L(7,x);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&#\"$H%\"#;\"\"\"*$)%\"xG\"\"(F(F( F(*&#\"$$pF'F(*$)F+\"\"&F(F(!\"\"*&#\"$:$F'F(*$)F+\"\"$F(F(F(*&#\"#NF' F(F+F(F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "simplify(Legend reP(7,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&#\"$H%\"#;\"\"\"*$)% \"xG\"\"(F(F(F(*&#\"$$pF'F(*$)F+\"\"&F(F(!\"\"*&#\"$:$F'F(*$)F+\"\"$F( F(F(*&#\"#NF'F(F+F(F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "L(5 0,x);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,V*&#\"2Dn,,/pY,#\"0G`N)[P29 \"\"\"*$)%\"xG\"\"#F(F(F(*&#\"7v12OX5Bn\"e1)\"/kwi*ytma_?\"/K ))3sV=NF(*$)F+\"#7F(F(F4*&#\"4Dk)QD\"fux1\"F>F(*$)F+\"\"%F(F(F4*&#\"5v ^vx!H0**[+*F>F(*$)F+\"\"'F(F(F(*&#\";vl&fVNthqJ)))*p#F>F(*$)F+\"#9F(F( F(*&#\"=DkI-?3wSlVk&H0\"F'F(*$)F+\"#;F(F(F4*&#\"=vARR#)QmD?ZdnQyF'F(*$ )F+\"#=F(F(F(*&#\"=02S%)>[`wvjRN$p&\"/;W/'=#fv &y1LF?zyF'*z&[i#F]oF(*$)F+\"#AF(F(F(*&#\"?DH&*>M<1n]0ul\"R%>F>F(*$)F+ \"#CF(F(F4*&#\"?v(e)f-_=,_;A(\\<$eF>F(*$)F+\"#EF(F(F(*&#\"?D2;tejAz&o[ 5%pFrF]oF(*$)F+\"#GF(F(F4*&#\"@:@XoCqR0y/1F+RU\"F]oF(*$)F+\"#IF(F(F(*& #\"AD=bE>C7Ab\\90oDg=F'F(*$)F+\"#KF(F(F4*&#\"Av#>%fyrA=o`2Tk-xCF'F(*$) F+\"#MF(F(F(*&#\"@DZTo6^ery,HgRSo'F>F(*$)F+\"#OF(F(F4*&#\"@v;8C#[)zyGi y)))H!z&F>F(*$)F+\"#QF(F(F(*&#\"@b(=h()*4?![PI+aDGzF0F(*$)F+\"#SF(F(F4 *&#\"@D?*oqNFR^^dj%G(*=%F0F(*$)F+\"#UF(F(F(*&#\"?D0F\"=&*yBz#4(\\KxB)F >F(*$)F+\"#WF(F(F4*&#\"?v#4:'=_OqyQA6OoAF>F(*$)F+\"#YF(F(F(*&#\"?v^(QA H&[xD'3v.0c\"F'F(*$)F+\"#[F(F(F4#\"/>Z!eK,e\"F'F4*&#\">d@c^o;Cb>o!=9h7 F'F(*$)F+\"#]F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sort( %);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,V*&#\">d@c^o;Cb>o!=9h7\"0G`N)[ P29\"\"\"*$)%\"xG\"#]F(F(F(*&#\"?v^(QAH&[xD'3v.0c\"F'F(*$)F+\"#[F(F(! \"\"*&#\"?v#4:'=_OqyQA6OoA\"/K))3sV=NF(*$)F+\"#YF(F(F(*&#\"?D0F\"=&*yB z#4(\\KxB)F7F(*$)F+\"#WF(F(F3*&#\"@D?*oqNFR^^dj%G(*=%\"/kw%fyrA=o`2Tk-xCF'F(*$)F+\"#MF(F(F(*&#\"AD=bE>C7Ab\\90oDg=F'F(*$ )F+\"#KF(F(F3*&#\"@:@XoCqR0y/1F+RU\"\"/;W/'=#fM<1n]0ul\"R%>F7F(*$)F+\"#CF(F(F3*&#\">v&y1LF?zyF' *z&[i#FcoF(*$)F+\"#AF(F(F(*&#\"=02S%)>[`wvjRN$p&FcoF(*$)F+\"#?F(F(F3*& #\"=vARR#)QmD?ZdnQyF'F(*$)F+\"#=F(F(F(*&#\"=DkI-?3wSlVk&H0\"F'F(*$)F+ \"#;F(F(F3*&#\";vl&fVNthqJ)))*p#F7F(*$)F+\"#9F(F(F(*&#\":Ds?#*>i*ytma_ ?F7F(*$)F+\"#7F(F(F3*&#\"9&e7)f:\"GW?)y?AFDF(*$)F+\"#5F(F(F(*&#\"7v12O X5Bn\"e1)FDF(*$)F+\"\")F(F(F3*&#\"5v^vx!H0**[+*F7F(*$)F+\"\"'F(F(F(*&# \"4Dk)QD\"fux1\"F7F(*$)F+\"\"%F(F(F3*&#\"2Dn,,/pY,#F'F(*$)F+\"\"#F(F(F (#\"/>Z!eK,e\"F'F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 1 {PARA 0 "" 0 "" {TEXT 262 2 "6." }{TEXT -1 121 " Write an anon ymous function that select from aset of integers those values that are between 0 and 10. Use the procedure " }{TEXT 0 4 "rand" }{TEXT -1 82 " to generate a set of 100 integers and apply your anonymous function \+ to this set.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "die := rand(-50..50):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "\{seq(die(), k=1..100)\};" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#<]o!#]!#\\!#[!#Z!#W!#V!#U!#T!#S!#R!#O !#N!#M!#I!#H!#G!#F!#E!#C!#B!#@!#?!#=!#n>0 and n<10" "6#f*6#%\"nG7\"6$%)operatorG% &arrowG6\"32\"\"!F%2F%\"#5F*F*F*" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 29 "select(n -> n>0 and n<10, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<'\"\"\"\"\"$\"\"&\"\"'\"\")" }}}{PARA 0 "" 0 "" {TEXT -1 102 "Without an anonymous function the same operation on sets of integers can be done in the following way:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "select(has, %%, \{seq(k,k=1..9)\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<'\"\"\"\"\"$\"\"&\"\"'\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 0 "" 0 "" {TEXT 263 2 "7." }{TEXT -1 110 " Write an anon ymous function to drop from a polynomial in two unknowns (which can be created by the procedure " }{TEXT 0 8 "randpoly" }{TEXT -1 40 ") all \+ terms with negative coefficients.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "randpoly([x,y], coeffs=rand(-4..4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*%\"yG\"\"\"*(\"\"#F%%\"xGF%F$F%!\"\"*(\"\"$F%)F(F+F%)F$F'F%F%*&\" \"%F%)F$\"\"&F%F)" }}}{PARA 0 "" 0 "" {TEXT -1 40 "The requested anony mous function can be " }{XPPEDIT 18 0 "t -> lcoeff(t)" "6#f*6#%\"tG7\" 6$%)operatorG%&arrowG6\"-%'lcoeffG6#F%F*F*F*" }{XPPEDIT 18 0 "``*`>`*0 " "6#*(%!G\"\"\"%\">GF%\"\"!F%" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "select(t->lcoeff(t)>0, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"yG\"\"\"*(\"\"$F%)%\"xGF'F%)F$\"\"#F%F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }