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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra
ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "F:=vector([2*x-x*y*z,x^2-3*y+z,x*y-x*z+2]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"FG-%'vectorG6#7%,&*&\"\"#\"\"\"%\"xGF,F,
*(F-F,%\"yGF,%\"zGF,!\"\",(*$)F-F+F,F,*&\"\"$F,F/F,F1F0F,,(*&F-F,F/F,F
,*&F-F,F0F,F1F+F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 87 "First find the fixed points.  The last two lines s
how how you can extract each of these" }}{PARA 0 "" 0 "" {TEXT -1 47 "
(unfortunately, the are not ordered correctly)." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 25 "_EnvAllSolutions := true:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 51 "Fsol:=evalf(solve(\{F[1]=x,F[2]=y,F[3]=z\},\{x
,y,z\}));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%FsolG6$<%/%\"xG$\"\"!F
*/%\"zG$\"\"#F*/%\"yG$\"+++++]!#5<%/F0$\"+f&[/r(F3/F($\"+:i(oL\"!\"*/F
,$\"+59%pH\"F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Fsol[1];" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"xG$\"\"!F'/%\"zG$\"\"#F'/%\"yG
$\"+++++]!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Fsol[1][2];
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"zG$\"\"#\"\"!" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "Now compu
te the Jacobian, and linearize F about each.  (We don't actually need \+
to compute" }}{PARA 0 "" 0 "" {TEXT -1 45 "the linearization, just the
 Jacobian matrix)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Jf:=jacobian(F,[x,y,z]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#JfG-%'matrixG6#7%7%,&\"\"#\"\"\"*&%\"yGF,
%\"zGF,!\"\",$*&%\"xGF,F/F,F0,$*&F3F,F.F,F07%,$*&F+F,F3F,F,!\"$F,7%,&F
.F,F/F0F3,$F3F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 46 "Now evaluate the Jacobian at each fixed point:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 29 "Jf1:=subs(Fsol[1],evalm(Jf));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%$Jf1G-%'matrixG6#7%7%$\"+++++5!\"*$!\"!\"\"!F-7%$F/F/!\"$\"\"\"7%$!
+++++:F,F1F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Jf2:=subs(F
sol[2],evalm(Jf));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Jf2G-%'matrix
G6#7%7%$\"*(********!\"*$!+B,&Qt\"F,$!+H:zI5F,7%$\"+ICvtEF,!\"$\"\"\"7
%$!+Tb'*e_!#5$\"+:i(oL\"F,$!+:i(oL\"F," }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "Now compute the eigenvalu
es of each Jacobian matrix" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eig
envalues(Jf1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$!\"$\"\"!$F%F%$\"\"
\"F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eigenvalues(Jf2);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6%^$$!+\\5!>Z\"!#5$\"+Sd=I7!\"*^$F$$!+
Sd=I7F)$!+3g\\UIF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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