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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 21 "Leslieho r\371sov\375 mod
el" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "N
\341sleduj\355c\355 p\370\355klad popisuje model v\375voje populace na
 Nov\351m Z\351landu." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT 257 7 "\310\341st 1." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 34 "Nejprve vytvo\370\355me Leslieho matici.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 33 "L:=diag(0,0,0,0,0,0,0,0,0,0,0,0):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "a:='a':for j from 1 to 12 do L[1,j]
:=a[j] od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "b:='b':for j from 1 t
o 11 do L[j+1,j]:=b[j] od: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "prin
t(L);\n" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 47 "Spo\350\355t\341me charakteristick\375 polynom dan\351 ma
tice:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "p(lambda):=charpoly(L,lamb
da);\n" }}}{PARA 12 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 43 "Zad\341me data populace ovc\355 na Nov\351m Z\351landu." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "a:=array(1..12,[0,0.045,0
.391,0.472,0.484,0.546,0.543,0.502,0.468,0.459,0.433,0.421]):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "b:=array(1..11,[0.845,0.975,0.965,0
.950,0.926,0.895,0.850,0.786,0.691,0.561,0.370]):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 38 "for j from 1 to 12 do L[1,j]:=a[j] od:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "for j from 1 to 11 do L[j+1,j]:=b[j
] od: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "print(L);\n" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 47 "Nakresl\355me si graf charakteristick\351
ho polynomu." }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "
plot(p(lambda),lambda=-2..2,y=-2..2);\n" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 44 "A nech\341me si spo\350\355tat vlastn\355 hodnoty p\370
\355mo." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eigenvals(L);\n" }}
{PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT 258 32 " 2. Vlastnosti Leslieho matice  " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "x.0:=[1,1,1,1,1,1,1,1,1,1,1,1]; k:=0;" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "x:=x.k; k:=k+1; x.k:=evalm(L &*
 x);" }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "y.k:=[x.k[1]
/x[1],x.k[2]/x[2],x.k[3]/x[3],x.k[4]/x[4],x.k[5]/x[5],x.k[6]/x[6],x.k[
7]/x[7],x.k[8]/x[8],x.k[9]/x[9],x.k[10]/x[10],x.k[11]/x[11],x.k[12]/x[
12]];" }}{PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "normalize(x.k);" }}{PARA 12 "" 1 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "eigenvals(L);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "18 0 0" 0 }{VIEWOPTS 1 
1 0 1 1 1803 }