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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "restart:\nCA:=[[1,0,
0],[0,3,-50],[0,50,3]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#CAG7%7%
\"\"\"\"\"!F(7%F(\"\"$!#]7%F(\"#]F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "q:=[[1,2,3],[4,5,5],[1,2,1]];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"qG7%7%\"\"\"\"\"#\"\"$7%\"\"%\"\"&F,7%F'F(F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "with(linalg):\nA:=evalm(inve
rse(q) &* CA &* q );" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new defi
nition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definitio
n for trace" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%#
!$'e\"\"$#!$:)F,#!$5(F,7%#\"$\\(F,#\"$#)*F,#\"$A*F,7%!$,\"!$F\"!$D\"" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvectors(A);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%7%,&\"\"$\"\"\"%\"IG\"#]F&<#-%'vectorG
6#7%,&#!#V\"#`F&F'#\"#=F1F&,&#!#@F1F&F'#!\"'F17%,&F%F&F'!#]F&<#-F+6#7%
,&F/F&F'#!#=F1F&,&F5F&F'#\"\"'F17%F&F&<#-F+6#7%!\"&F&F%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "P:=transpose([ [18/53,0,-6/53],[-43
/53,1,-21/53],[-5,1,3]]);\nevalm( inverse(P) &* A &* P );\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"PG-%'matrixG6#7%7%#\"#=\"#`#!#VF,!\"&7%
\"\"!\"\"\"F27%#!\"'F,#!#@F,\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-
%'matrixG6#7%7%\"\"$!#]\"\"!7%\"#]F(F*7%F*F*\"\"\"" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 58 "BD:=evalm(\n    [[3,-50,0],\n    [50, 3,0],
\n    [0, 0,1]] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#BDG-%'matrixG
6#7%7%\"\"$!#]\"\"!7%\"#]F*F,7%F,F,\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 216 "expBDt := evalm(\n                 [[ exp(3*t)*cos
(50*t),-exp(3*t)*sin(50*t), 0],\n                  [ exp(3*t)*sin(50*t
), exp(3*t)*cos(50*t), 0],\n                  [      0 ,              \+
   0,           exp(1*t) ]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'ex
pBDtG-%'matrixG6#7%7%*&-%$expG6#,$%\"tG\"\"$\"\"\"-%$cosG6#,$F/\"#]F1,
$*&F+\"\"\"-%$sinGF4F1!\"\"\"\"!7%F8F*F=7%F=F=-F,6#F/" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "phi:= evalm( P &* expBDt &* inverse
(P) );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$phiG-%'matrixG6#7%7%,(*&-
%$expG6#,$%\"tG\"\"$\"\"\"-%$cosG6#,$F0\"#]F2#\"#6\"\"'*&F,\"\"\"-%$si
nGF5F2!\"%-F-6#F0#!\"&F:,(F+#\"\"&F1F;#!#6\"\"#F@#FCF1,(F+#FFFIF;#!#HF
:F@#FCFI7%,(F;FFF+#!\"\"F:F@#F2F:,(F;#\"#8FIF+#FIF1F@#F2F1,(F;#\"#PF:F
+#FSFIF@#F2FI7%,(F+FgnF;!\"#F@Fhn,(F+FSF;FOF@F2,(F+FgnF;FOF@#F1FI" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "map(diff,phi,t);\nsimplify(e
valm(map(diff,phi,t)-evalm(A&*phi)));" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#-%'matrixG6#7%7%,(*&-%$expG6#,$%\"tG\"\"$\"\"\"-%$cosG6#,$F.\"#]F0#
!$*Q\"\"#*&F*\"\"\"-%$sinGF3F0#!$6$F/-F+6#F.#!\"&\"\"',(F)!$q#F9#!$*fF
CF?#FBF/,(F)#!%09FCF9#!$z#F8F?#FBF87%,(F9#\"#qF/F)#\"$*\\F8F?#F0FC,(F9
#!#$)FCF)\"$F$F?#F0F/,(F9#\"#()F8F)#\"%T=FCF?#F0F87%,(F)#!$.#F8F9\"#>F
?Fjn,(F)!$G\"F9#\"#&)F8F?F0,(F)#!$`#F8F9#\"#NF8F?#F/F8" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"!F(F(F'F'" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 2 "?C" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
34 "readlib(C):\nx11:=phi[1,1];\nC(phi);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$x11G,(*&-%$expG6#,$%\"tG\"\"$\"\"\"-%$cosG6#,$F+\"#]F-#\"#6\"
\"'*&F'\"\"\"-%$sinGF0F-!\"%-F(6#F+#!\"&F5" }}{PARA 6 "" 1 "" {TEXT 
-1 76 "      phi[0][0] = 11.0/6.0*exp(3.0*t)*cos(50.0*t)-4.0*exp(3.0*t
)*sin(50.0*t)" }}{PARA 6 "" 1 "" {TEXT -1 16 "-5.0/6.0*exp(t);" }}
{PARA 6 "" 1 "" {TEXT -1 79 "      phi[0][1] = 5.0/3.0*exp(3.0*t)*cos(
50.0*t)-11.0/2.0*exp(3.0*t)*sin(50.0*t" }}{PARA 6 "" 1 "" {TEXT -1 17 
")-5.0/3.0*exp(t);" }}{PARA 6 "" 1 "" {TEXT -1 79 "      phi[0][2] = 5
.0/2.0*exp(3.0*t)*cos(50.0*t)-29.0/6.0*exp(3.0*t)*sin(50.0*t" }}{PARA 
6 "" 1 "" {TEXT -1 17 ")-5.0/2.0*exp(t);" }}{PARA 6 "" 1 "" {TEXT -1 
79 "      phi[1][0] = 5.0*exp(3.0*t)*sin(50.0*t)-exp(3.0*t)*cos(50.0*t
)/6.0+exp(t)/" }}{PARA 6 "" 1 "" {TEXT -1 4 "6.0;" }}{PARA 6 "" 1 "" 
{TEXT -1 79 "      phi[1][1] = 13.0/2.0*exp(3.0*t)*sin(50.0*t)+2.0/3.0
*exp(3.0*t)*cos(50.0*t" }}{PARA 6 "" 1 "" {TEXT -1 13 ")+exp(t)/3.0;" 
}}{PARA 6 "" 1 "" {TEXT -1 77 "      phi[1][2] = 37.0/6.0*exp(3.0*t)*s
in(50.0*t)-exp(3.0*t)*cos(50.0*t)/2.0+" }}{PARA 6 "" 1 "" {TEXT -1 11 
"exp(t)/2.0;" }}{PARA 6 "" 1 "" {TEXT -1 79 "      phi[2][0] = -exp(3.
0*t)*cos(50.0*t)/2.0-2.0*exp(3.0*t)*sin(50.0*t)+exp(t)" }}{PARA 6 "" 
1 "" {TEXT -1 5 "/2.0;" }}{PARA 6 "" 1 "" {TEXT -1 79 "      phi[2][1]
 = -exp(3.0*t)*cos(50.0*t)-5.0/2.0*exp(3.0*t)*sin(50.0*t)+exp(t)" }}
{PARA 6 "" 1 "" {TEXT -1 1 ";" }}{PARA 6 "" 1 "" {TEXT -1 77 "      ph
i[2][2] = -exp(3.0*t)*cos(50.0*t)/2.0-5.0/2.0*exp(3.0*t)*sin(50.0*t)+
" }}{PARA 6 "" 1 "" {TEXT -1 15 "3.0/2.0*exp(t);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "4 0 0" 16 }{VIEWOPTS 1 1 0 1 1 
1803 }