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{MPLTEXT 1 0 93 "V:=matrix(5,5,[32,-4,10,-8,-11,-4,37,-1,1,-12,10,-1,7
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "for i to n do  A[i,i]:=1+rho^2 end \+
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "for i from 0 to 30 do om2[i]:=1+2*a
dd(lambda(k)*s[k]/s[0]*cos(Pi*i*k/30.),k=1..99) end do:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "seq(evalf(om2[k]),k=0..30); listplo
t([seq([i*Pi/30,om2[i]],i=0..30)]);#lag smoothing (identical)" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6A$\"+:.j07!\")$\"+9GM/5F%$\"+Wb6^n!\"*$
\"+!y\"f[PF*$\"+@q-hEF*$\"+%>:2J#F*$\"+=Z5j;F*$\"+G\\[L6F*$\"+O@\")eh!
#5$\"+U`I>bF7$\"+%)\\?uTF7$\"+:;p+TF7$\"+cD7TLF7$\"+fCE%4$F7$\"+b[u+AF
7$\"+y]i))=F7$\"+<g!)*e\"F7$\"+\\Pqw8F7$\"+o\\D28F7$\"+3\"G.9\"F7$\"+K
<ic6F7$\"+aXXn()!#6$\"+QS#\\s&FR$\"+eI<<YFR$\"+4!*3/_FR$\"+VFn&)zFR$\"
*XjxR*F7$\"+Z*p-;\"F7$\"+!fGGM\"F7$\"+(Q26Y\"F7$\"+<s%>a\"F7" }}{PARA 
13 "" 1 "" {GLPLOT2D 495 230 230 {PLOTDATA 2 "6#-%'CURVESG6#7A7$$\"\"!
F)$\"+:.j07!\")7$$\"+^v>Z5!#5$\"+9GM/5F,7$$\"+.^R%4#F0$\"+Wb6^n!\"*7$$
\"+aEfTJF0$\"+!y\"f[PF87$$\"+/-z)=%F0$\"+@q-hEF87$$\"+ex)fB&F0$\"+%>:2
J#F87$$\"+3`=$G'F0$\"+=Z5j;F87$$\"+eGQItF0$\"+G\\[L6F87$$\"+7/ex$)F0$
\"+O@\")ehF07$$\"+izxC%*F0$\"+U`I>bF07$$F/F8$\"+%)\\?uTF07$$\"+2t\">:
\"F8$\"+:;p+TF07$$\"+iqjc7F8$\"+cD7TLF07$$\"+<oNh8F8$\"+fCE%4$F07$$\"+
sl2m9F8$\"+b[u+AF07$$\"+Fjzq:F8$\"+y]i))=F07$$\"+#3;bn\"F8$\"+<g!)*e\"
F07$$\"+PeB!y\"F8$\"+\\Pqw8F07$$\"+#fb\\)=F8$\"+o\\D28F07$$\"+Z`n*)>F8
$\"+3\"G.9\"F07$$F5F8$\"+K<ic6F07$$\"+e[6*>#F8$\"+aXXn()!#67$$\"+8Y$QI
#F8$\"+QS#\\s&F`r7$$\"+oVb3CF8$\"+eI<<YF`r7$$\"+BTF8DF8$\"+4!*3/_F`r7$
$\"+yQ*zh#F8$\"+VFn&)zF`r7$$\"+MOrAFF8$\"*XjxR*F07$$\"+*QLu#GF8$\"+Z*p
-;\"F07$$\"+WJ:KHF8$\"+!fGGM\"F07$$\"+**G(o.$F8$\"+(Q26Y\"F07$$F;F8$\"
+<s%>a\"F0" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "C
urve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q5" }{MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 131 "f:=(41-68*cos(beta)+38*cos(2*beta)-13*co
s(3*beta)+2*cos(4*beta))/\n(367+276*cos(beta)+72*cos(2*beta)+60*cos(3*
beta)+25*cos(4*beta)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "c
:=evalf(Pi/int(f,beta=0..Pi));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"
cG$\"+LIsXP!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "rho:=seq
(c*evalf(int(f*cos(beta*k),beta=0..Pi)/Pi),k=1..25);" }}{PARA 12 "" 1 
"" {XPPMATH 20 "6#>%$rhoG6;$!+#*[G1()!#5$\"+g*Rxu&F($!+VuR\")GF($\"+4d
546F($!+#*G)pC$!#6$\"+-cIvT!#7$\"+w\"3-e$F4$!+SU%\\g$F4$\"+^(H.7#F4$!+
R_;85F4$\"+x#p#3Q!#8$!+Xihq'*!#9$\"+n)RjX%!#:$\"+S7W,;FB$!+Ec)eU\"FB$
\"+@)GT$zFE$!+9'\\B\\$FE$\"+X:Mi7FE$!+TqC**G!#;$!+rDY*H#!#<$\"+d([)4rF
U$!+V5&**Q&FU$\"+R$[3$HFU$!+]E&z@\"FU$\"+iK:&*R!#=" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 76 "g:=367+138*(y+1/y)+36*(y^2+1/y^2)+30*(y^3+1
/y^3)+25/2*(y^4+1/y^4): # AR part" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "sol:=solve(g,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%$solG6*^$\"\"\"\"\"#^$F'!\"#^$F*F'^$F*!\"\"^$#F'\"\"&#F(F0^$F/#F*F0^$
F3F/^$F3#F-F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "seq(evalf(
abs(%[i])),i=1..8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6*$\"+xz1OA!\"*F#
F#F#$\"+af8sW!#5F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "e
xpand((y-sol[5])*(y-sol[6])*(y-sol[7])*(y-sol[8])*1.);  # only solutio
n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*&$\"\"\"\"\"!F&)%\"yG\"\"%F&F&
*&$\"+++++S!#5F&)F)\"\"$F&F&$F-!#6F&*&$\"+++++!)F2F&)F)\"\"#F&F&*&F4F&
F)F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "h:=41-34*(y+1/y)+
19*(y^2+1/y^2)-13/2*(y^3+1/y^3)+(y^4+1/y^4):  # MA part" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sol:=solve(h,y);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$solG6*\"\"##\"\"\"F&F(F(,&F'F(*&^#F'F(\"\"$F'F(,&F
'F(*&^##!\"\"F&F(F,F'F(F)F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
22 "seq(abs(%[i]),i=1..8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6*\"\"##\"
\"\"F#F%F%F%F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "expan
d((y-sol[1])*(y-sol[3])*(y-sol[5])*(y-sol[6]));  # first solution" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"yG\"\"%\"\"\"F(*&F'F()F&\"\"$F
(!\"\"\"\"#F(*&\"\"'F()F&F-F(F(*&\"\"&F(F&F(F," }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 71 "expand((y-sol[2])*(y-sol[3])*(y-sol[5])*(y-sol
[6]));  # second solution" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"y
G\"\"%\"\"\"F(*&#\"\"&\"\"#F(*$)F&\"\"$F(F(!\"\"#F(F,F(*&F/F()F&F,F(F(
*&F,F(F&F(F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Two solutions:" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "Xn = -0.4Xn-1
 -0.08Xn-2 -0.08Xn-3 -0.04Xn-4 + En -4En-1 +6En-2 -5En-3 +2En-4  " }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "Xn = -0.4Xn-1 -0.08Xn-2 -0.08Xn-3 \+
-0.04Xn-4 + En -5/2En-1 +3En-2 -2En-3 +1/2En-4  " }{MPLTEXT 1 0 0 "" }
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