{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 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 } {CSTYLE "_cstyle1" -1 204 "Times" 0 1 0 0 0 0 0 0 0 2 2 2 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 "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 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 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 }{PSTYLE "_pstyle1 " -1 201 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "_pstyle2" -1 202 1 {CSTYLE "" -1 -1 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "_pstyle3" -1 203 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "01." }{TEXT 204 0 "" }}} {EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 20 "zeta:=exp(2*Pi*I/8);" } {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%zetaG,&*&\"\"#! \"\"F'#\"\"\"F'F**&^#F)F*F'F)F*" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "02." }{TEXT 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 25 "a:=sum((k+1)*x^k,k=0..7);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"aG,2\"\"\"F&*&\"\"#F&%\"xGF&F&*&\"\"$F&)F)F(F&F&* &\"\"%F&)F)F+F&F&*&\"\"&F&)F)F.F&F&*&\"\"'F&)F)F1F&F&*&\"\"(F&)F)F4F&F &*&\"\")F&)F)F7F&F&" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "03." } {TEXT 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 21 "alist:=[ coeffs(a,x)];" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% &alistG7*\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "04." }{TEXT 204 0 "" }}}{EXCHG {PARA 202 "> \+ " 0 "" {MPLTEXT 1 0 21 "DFT1:=proc(list,zeta)" }{MPLTEXT 1 0 0 "" } {MPLTEXT 1 0 9 "\nlocal n;" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 15 "\nn:= nops(list);" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 58 "\n[seq(evalf(sum(lis t[j+1]*zeta^(j*k),j=0..n-1)),k=0..n-1)]" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 10 "\nend proc:" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 16 "\nDFT:=proc(list)" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 34 "\nDFT1(list,exp(2*Pi*I/nops(list)))" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 10 "\nend proc:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "05." }{TEXT 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 22 "phi:=DFT1(alist,zeta);" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 17 "\nphi:=DFT(alist);" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 44 "\nphi :=[seq(evalf(subs(x=zeta^k,a)),k=0..7)];" }{MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$phiG7*$\"#O\"\"!^$$!+(*******R!\"*$!+GU&o l*F,^$$!+&)******RF,$!+\")******RF,^$$!+v******RF,$!+PU&ol\"F,^$$!+l** ****RF,$F(F(^$$!+g******RF,$\"+HU&ol\"F,^$$!+c******RF,$\"+U******RF,^ $$!+%)******RF,$\"+)3aol*F," }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$phiG 7*$\"#O\"\"!^$$!+(*******R!\"*$!+GU&ol*F,^$$!+&)******RF,$!+\")******R F,^$$!+v******RF,$!+PU&ol\"F,^$$!+l******RF,$F(F(^$$!+g******RF,$\"+HU &ol\"F,^$$!+c******RF,$\"+U******RF,^$$!+%)******RF,$\"+)3aol*F," }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%$phiG7*$\"#O\"\"!^$$!+(*******R!\"*$ !+GU&ol*F,^$$!+&)******RF,$!+\")******RF,^$$!+v******RF,$!+PU&ol\"F,^$ $!+l******RF,$F(F(^$$!+g******RF,$\"+HU&ol\"F,^$$!+c******RF,$\"+U**** **RF,^$$!+%)******RF,$\"+)3aol*F," }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "06." }{TEXT 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 22 "IDFT1:=proc(list,zeta)" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 15 "\nl ocal a,n,eq; " }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 15 "\nn:=nops(list);" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 70 "\neq:=\{seq(list[k+1]=evalf(sum(a [j+1]*zeta^(j*k),j=0..n-1)),k=0..n-1)\};" }{MPLTEXT 1 0 0 "" } {MPLTEXT 1 0 29 "\nsolve(eq,\{seq(a[k],k=1..n)\})" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 10 "\nend proc:" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 1 "\n " }{MPLTEXT 1 0 17 "\nIDFT:=proc(list)" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 35 "\nIDFT1(list,exp(2*Pi*I/nops(list)))" }{MPLTEXT 1 0 0 "" } {MPLTEXT 1 0 10 "\nend proc:" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 17 "\nIDFT1(phi,zeta);" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 11 "\nIDFT(phi);" }{MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<*/&%\"aG6#\"\"$^$$\"+++++I!\"*$\"+3++]K!#>/&F&6#\"\"(^$$\"+++++qF, $\"+e*****\\#!#?/&F&6#\"\"%^$$\"+++++SF,$\"+(R<%>%*F9/&F&6#\"\"&^$$\"+ ++++]F,$\"+()****\\iF9/&F&6#\"\"'^$$\"+++++gF,$\"+)o3(4/&F&6#\"\"(^$$\"+++++qF,$\"+e*****\\#!#?/&F&6#\"\"&^$$\"+++++]F, $\"+()****\\iFC/&F&6#\"\"%^$$\"+++++SF,$\"+(R<%>%*FC/&F&6#\"\"#^$$\"++ +++?F,$!+%p3(4FF9/&F&6#\"\"$^$$\"+++++IF,$\"+3++]KF9/&F&6#\"\"\"^$$\"+ ++++5F,$!+-++DTF9" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "07." } {TEXT 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 19 "b:=sum(x ^k,k=0..7);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\" bG,2\"\"\"F&%\"xGF&*$)F'\"\"#F&F&*$)F'\"\"$F&F&*$)F'\"\"%F&F&*$)F'\"\" &F&F&*$)F'\"\"'F&F&*$)F'\"\"(F&F&" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "08." }{TEXT 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 21 "blist:=[coeffs(b,x)];" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&blistG7*\"\"\"F&F&F&F&F&F&F&" }}}{EXCHG {PARA 201 " " 0 "" {TEXT 204 3 "09." }{TEXT 204 0 "" }}}{EXCHG {PARA 202 "> " 0 " " {MPLTEXT 1 0 33 "alist:=[op(alist),seq(0,k=1..8)];" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alistG72\"\"\"\"\"#\"\"$\"\"% \"\"&\"\"'\"\"(\"\")\"\"!F.F.F.F.F.F.F." }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "10." }{TEXT 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 33 "blist:=[op(blist),seq(0,k=1..8)];" }{MPLTEXT 1 0 0 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&blistG72\"\"\"F&F&F&F&F&F&F&\" \"!F'F'F'F'F'F'F'" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "11." } {TEXT 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 16 "phi:=DFT (alist);" }{MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$phiG 72$\"#O\"\"!^$$!+.72P\")!\"*$\"+Y(pO^#!\")^$$!+y******RF,$!+bU&ol*F,^$ $\"+yb3!Q$F,$\"+J)GI[(F,^$$!+$)******RF,$!+<+++SF,^$$\"+X'onF%F,$\"+;K *3M$F,^$$!+'*******RF,$!+yU&ol\"F,^$$\"+Qp@![%F,$\"*p=c%**F,^$$!+5+++S F,$!+R/<,L!#<^$$\"+ap@![%F,$!*1=c%**F,^$$!+M+++SF,$\"+=U&ol\"F,^$$\"+, (onF%F,$!+gJ*3M$F,^$$!+r+++SF,$\"+t******RF,^$$\"+#p&3!Q$F,$!+1)GI[(F, ^$$!+g,++SF,$\"+\"Gaol*F,^$$!+752P\")F,$!+p(pO^#F/" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "12." }{TEXT 204 0 "" }}}{EXCHG {PARA 202 "> \+ " 0 "" {MPLTEXT 1 0 16 "psi:=DFT(blist);" }{MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$psiG72$\"\")\"\"!^$$\"+f********!#5$\"+$ \\Rt-&!\"*^$$\"#>F,$!#8F,^$$\"+y********F,$\"+ldg'\\\"F/^$$\"+0eM5?!#= $!#@F,^$$\"+*)********F,$\"+4ky\"o'F,^$$\"\"$F,$!#MF,^$$\"+++++5F/$\"+ 5P7*)>F,^$$!\"\"F/$!+%\\4h7%F=^$$\"+-+++5F/$!+UO7*)>F,^$$!#QF,$!#RF,^$ $\"+0+++5F/$!+Zjy\"o'F,^$$!*\\MF$y!#<$!\"%F/^$$\"+6+++5F/$!+jdg'\\\"F/ ^$$!$$>F,$F,F,^$$\"+L+++5F/$!+A&Rt-&F/" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "13." }{TEXT 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 42 "prod:=[seq(phi[k]*psi[k],k=1..nops(psi))];" } {MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%prodG72$\"$)G\" \"!^$$!+Iy2X8!\"($!+1A6x:!\")^$$!+\\5R:?!#<$!+6B![J\"F3^$$!+=&e!>y!\"* $\"+Q%oTD\"F/^$$!+A$QTk\"F3$\"+,r;'e$!#>^$$\"+_^XW?F9$\"+t'Q&)>'F9^$$! +WXILo!#=$\"+qVH58F3^$$\"+ziQ#G%F9$\"+VCt&)=F9^$$\"+u)*****RFJ$\"+0QW] ;F3^$$\"+BjQ#G%F9$!+aBt&)=F9^$$\"+eJ'F9^$$\"+TQ4LZF3$!+YP4L:F3^$$!+2$e!>yF9$!+h%oTD\"F/^$$\"+Pdo&o)F 3$!+vGxB=!#;^$$!+]y2X8F,$\"+ " 0 "" {MPLTEXT 1 0 16 "inv:=IDFT(prod);" }{MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$invG<2/&%\"aG6#\"#;^$$\"+4P;6x!#>$!+!H')pL#!#=/&F (6#\"\"$^$$\"+'*******f!\"*$!+6bgI>F1/&F(6#\"\"%^$$\"+++++5!\")$\"+8`f kTF1/&F(6#\"\"(^$$\"+++++GFC$\"+rx&*=`F1/&F(6#\"#7^$$\"+++++EFC$!+<\") ohHF1/&F(6#\"\")^$$\"+++++OFC$\"+q)**=q%F1/&F(6#\"#:^$$\"+/+++!)F9$!+f 4a:EF1/&F(6#\"\"#^$$\"+'*******HF9$!+y:]r:F1/&F(6#\"\"*^$$\"+++++NFC$ \"+&zRHp\"F1/&F(6#\"#9^$$\"+,+++:FC$!+N$F1/&F(6#\"\"\"^$$\"+%)********!#5$!+-v%[B#F1/&F(6#\"\"'^$$\"++ +++@FC$\"+x-%>7&F1/&F(6#\"\"&^$$\"+++++:FC$\"+c`B`^F1/&F(6#\"#6^$$\"++ +++IFC$!+9)=n-#F1/&F(6#\"#5^$$\"+++++LFC$\"+x$>d@\"F1" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 204 3 "15." }{TEXT 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 20 "coeffs(expand(a*b));" }{MPLTEXT 1 0 0 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "61\"\"\"\"\"$\"\")\"#:\"#@\"#E\"#I\" #L\"#N\"\"'\"#5F&F'\"#G\"#O" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 203 "" 0 "" {TEXT -1 0 "" }}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }