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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "with(plots): with(linalg):" }}{PARA 7 "" 1 "" {TEXT 
-1 50 "Warning, the name changecoords has been redefined\n" }}{PARA 7 
"" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have \+
been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 107 "R2:=proc(f,k);# procedure qui resout x\"+k^2*x=f\ng:
= 1/k*int(f*sin(k*(s-t)), t=0..s);\nsubs(s=t,g); end proc;" }}{PARA 7 
"" 1 "" {TEXT -1 60 "Warning, `g` is implicitly declared local to proc
edure `R2`\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#R2GR6$%\"fG%\"kG6#%
\"gG6\"F+C$>8$*&-%$intG6$*&9$\"\"\"-%$sinG6#*&9%F5,&%\"sGF5%\"tG!\"\"F
5F5/F=;\"\"!F<F5F:F>-%%subsG6$/F<F=F.F+F+F+" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 793 "C:=proc(x,y
,z);\n x0:=t-> a*cos((1+m*u)*t+r)+m*x1(t);\n E:=expand(diff(diff(x0(t)
,t),t)+(1-m*h*cos(2*(1+m*u)*t))*x0(t)+2*m*f*diff(x0(t),t)+m*v*x0(t)^3)
;\nH1:=simplify(1/m*convert(series(E,m,2), polynom)-x1(t)-diff(diff(x1
(t),t),t));\nE1:=convert(series(subs(t=2*Pi/(1+m*u),R2(H1,1)),m,2)-ser
ies(subs(t=2*Pi/(1+m*u),R2(H1,1)),m,1),polynom);\nE2:=expand(convert(s
eries(subs(t=2*Pi/(1+m*u), diff(R2(H1,1),t)),m,2)-series(subs(t=2*Pi/(
1+m*u), \ndiff(R2(H1,1),t)),m,1),polynom));\n P:=matrix(2,2,[[coeff(E1
,cos(r)), coeff(E2,cos(r))],[coeff(E1,sin(r)), coeff(E2,sin(r))]]);\n \+
S:=[solve(det(P),a)];T:=subs(h=x,f=y,v=z,S);u1:=solve(T[3],u); \nu2:=s
olve(T[5]-T[3],u);u3:=solve(diff(T[3],u));w:=subs(u=u3,T[3]);\n plot([
T[5],T[3]],u=u1-.1..u2+.1, view=[u1-.1..u2+.1,0..w],numpoints=1500,thi
ckness=2);\n end proc;\n" }}{PARA 7 "" 1 "" {TEXT -1 60 "Warning, `x0`
 is implicitly declared local to procedure `C`\n" }}{PARA 7 "" 1 "" 
{TEXT -1 59 "Warning, `E` is implicitly declared local to procedure `C
`\n" }}{PARA 7 "" 1 "" {TEXT -1 60 "Warning, `H1` is implicitly declar
ed local to procedure `C`\n" }}{PARA 7 "" 1 "" {TEXT -1 60 "Warning, `
E1` is implicitly declared local to procedure `C`\n" }}{PARA 7 "" 1 "
" {TEXT -1 60 "Warning, `E2` is implicitly declared local to procedure
 `C`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `P` is implicitly decl
ared local to procedure `C`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning,
 `S` is implicitly declared local to procedure `C`\n" }}{PARA 7 "" 1 "
" {TEXT -1 59 "Warning, `T` is implicitly declared local to procedure \+
`C`\n" }}{PARA 7 "" 1 "" {TEXT -1 60 "Warning, `u1` is implicitly decl
ared local to procedure `C`\n" }}{PARA 7 "" 1 "" {TEXT -1 60 "Warning,
 `u2` is implicitly declared local to procedure `C`\n" }}{PARA 7 "" 1 
"" {TEXT -1 60 "Warning, `u3` is implicitly declared local to procedur
e `C`\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, `w` is implicitly dec
lared local to procedure `C`\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"
CGR6%%\"xG%\"yG%\"zG6.%#x0G%\"EG%#H1G%#E1G%#E2G%\"PG%\"SG%\"TG%#u1G%#u
2G%#u3G%\"wG6\"F7C/>8$R6#%\"tGF76$%)operatorG%&arrowGF7,&*&%\"aG\"\"\"
-%$cosG6#,&*&,&FDFD*&%\"mGFD%\"uGFDFDFD9$FDFD%\"rGFDFDFD*&FLFD-%#x1G6#
FNFDFDF7F7F7>8%-%'expandG6#,*-%%diffG6$-Fen6$-F:F<F=F=FD*&,&FDFD*(FLFD
%\"hGFD-FF6#,$*&FJFDF=FD\"\"#FD!\"\"FDFinFDFD**FboFDFLFD%\"fGFDFgnFDFD
*(FLFD%\"vGFD)Fin\"\"$FDFD>8&-%)simplifyG6#,(*&-%(convertG6$-%'seriesG
6%FUFLFbo%(polynomGFDFLFcoFD-FRF<Fco-Fen6$-Fen6$FhpF=F=Fco>8'-Fbp6$,&-
Fep6%-%%subsG6$/F=,$*&%#PiGFDFJFcoFbo-%#R2G6$F[pFDFLFboFD-Fep6%FdqFLFD
FcoFgp>8(-FW6#-Fbp6$,&-Fep6%-Feq6$Fgq-Fen6$F[rF=FLFboFD-Fep6%FirFLFDFc
oFgp>8)-%'matrixG6%FboFbo7$7$-%&coeffG6$F^q-FF6#FO-Fgs6$FarFis7$-Fgs6$
F^q-%$sinGFjs-Fgs6$FarF`t>8*7#-%&solveG6$-%$detG6#F`sFC>8+-Feq6&/F]oFN
/Feo9%/Fgo9&Fet>8,-Fht6$&F^u6#FioFM>8--Fht6$,&&F^u6#\"\"&FDFjuFcoFM>8.
-Fht6#-FenFiu>8/-Feq6$/FMFevFju-%%plotG6'7$FavFju/FM;,&FguFD$FDFcoFco,
&F]vFD$FDFcoFD/%%viewG7$Fcw;\"\"!Fjv/%*numpointsG\"%+:/%*thicknessGFbo
F7F7F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
8 "" 1 "" {TEXT -1 28 "Error, invalid terms in sum\n" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "C(0.65,.1,.16);" }
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