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Suite r\303\251currente du type: u[n+1] = f ( u[n] )(c) Alain Le Stang - "Apprendre Maple" - 2006
S\303\251lectionner Edit/Execute/Worksheet ou cliquer le bouton !!! pour ex\303\251cuter ce Maplet.
restart:with(Maplets[Elements]):with(Maplets[Examples]):with(Maplets[Tools]):nomFichier:='nomFichier': nouvGraphe:=NULL:Proc\303\251dure graphe_suite:
Cette proc\303\251dure donne pour r\303\251sultat la repr\303\251sentation graphique des termes de la suite r\303\251currente
de premier terme NiNJI3UwRzYi et d\303\251finie par : pour tout n entier naturel , u[n+1] =f ( u[n] ) .
f : fonction , u0 : premier terme, nbiter : nombre d'it\303\251rations , titre : L\303\251gende du graphique.
graphe_suite:=proc(f,u0,nbiter)
global nouvGraphe;
local a,S,k,mini,maxi,m1,m2,w,t;
a:=evalf(u0);
m1:=a:m2:=m1:
S:=[a,0],[a,evalf(f(a))];
for k to nbiter do
a:=evalf(f(a));
if a<m1 then m1:=a end if;
if a>m2 then m2:=a end if;
S:=S,[a,a],[a,f(a)];
end do;
S:=[S];
mini:=m1-(m2-m1)/10:
maxi:=m2+(m2-m1)/10;
w:=[ plot({x,f(x)},x=mini..maxi,color=[black,blue]),plot(S,x=mini..maxi,color=red)],scaling=constrained;
t:=Get('titre');
if length(t)>0 then w:=w,title=t fi;
nouvGraphe:=plots[display](w);
end proc;Proc\303\251dure termes:
Cette proc\303\251dure donne pour r\303\251sultat la liste des premiers termes [ u[0], u[1], ... , u[nbiter] ] de la suite r\303\251currente
de premier terme NiNJI3UwRzYi et d\303\251finie par : pour tout n entier naturel , u[n+1] =f ( u[n] ) .
f : fonction , u0 : premier terme, nbiter : nombre d'it\303\251rations
termes:=proc(f,u0,nbiter)
local a,k,S;
a:=evalf(u0):S:=a;
for k to nbiter do
a:=evalf(f(a)):S:=S,a
end do;
[S]
end proc;Proc\303\251dure MontreTable:
Cette proc\303\251dure lance le maplet d'exemples ShowTable permettant de visualiser la liste des valeurs despremiers termes n , u[n] de la suite r\303\251currente.
MontreTable:=proc(fonc,var,u0,nbiter)
local k,ts;
ts:=termes(unapply(fonc,var),u0,nbiter);
Maplets:-Examples:-ShowTable(
[["n=", "u[n]="], seq( [k,evalf(ts[k])], k = 1..nbiter )],
'title' = "Premiers termes", 'height'=400)
end proc;Proc\303\251dures d'enregistrement du graphique sous format .gif :Enregistrer := proc()
global nomFichier,nouvGraphe;
if assigned( nomFichier ) then
plotsetup( 'gif', 'plotoutput' = nomFichier );
print( nouvGraphe );
plotsetup( 'default' );
nomFichier:='nomFichier'
else
EnregSous();
end if;
end proc:
EnregSous := proc()
global nomFichier;
local nnomFichier;
try
nnomFichier := Maplets:-Examples:-GetFile(
'title' = "Enregistrer sous",
'filefilter' = "gif",
'approvecaption' = "Enregistrer"
);
catch:
return;
end try;
if nnomFichier[-4..-1] = ".gif" then
nomFichier := nnomFichier;
else
nomFichier := cat( nnomFichier, ".gif" );
end if;
Enregistrer();
end proc;
Proc\303\251dure de r\303\251initialisation des 2 variables globales :RAZ:=proc()
global nouvGraphe,nomFichier;
nouvGraphe:=NULL;nomFichier:='nomFichier';
end proc;Maplet:maplet3 := Maplet( Window( "Suite r\303\251currente u[n+1]=f(u[n])",
BoxColumn('vscroll'='as_needed',
["Fonction f: ", TextField['fonc'](),"de la variable: ", TextField['var'](3)],
[" Premier terme: ",TextField['u0']()],
["Nombre d'it\303\251rations: ",TextField['nbiter']()],
[" Titre du graphique: ",TextField['titre']()],
Plotter['PL1'](),
[ Button['Rep']("Graphe",Evaluate( 'PL1'= 'graphe_suite(unapply(fonc,var),u0,nbiter)')),
Button("Premiers termes", Evaluate('function' = "MontreTable",Argument(fonc),Argument(var),
Argument(u0),Argument(nbiter) ) ),
Button("Effacer", Action(SetOption('fonc' = ""), SetOption('var' = ""), SetOption('u0' = ""),
SetOption('nbiter'=""), SetOption('titre'=""), Evaluate('function' = "RAZ"), Evaluate( 'PL1' = 'plot(undefined,x=-10..10,axes=NONE)' ))),
Button("Aide", RunWindow('Aide')),
Button("Enregistrer", Evaluate('function' = "Enregistrer") ),
Button("Quitter", Shutdown())]
) ),
Window['Aide']('title' = "Description", 'layout' = 'Description', width=400, height=250),
Font['F1']('family'="Comic Sans MS", 'bold'='false', 'italic'='false', size=12),
BoxLayout['Description'](
BoxColumn('border'=true, 'inset'=0, 'spacing'=4,
BoxRow('inset'=0, 'spacing'=0,
TextBox('wrapped'=true, 'width'=80, 'height'=15, 'font'='F1',
'editable'='false', 'value'=
"Ce maplet donne la repr\303\251sentation graphique des premiers termes de la suite r\303\251currente de premier terme u0 et d\303\251finie pour tout n entier naturel par: u[n+1]=f(u[n]).\134nPour cela, cliquer le bouton ""Graphe"" apr\303\250s avoir rempli les 5 diff\303\251rents champs:\134nFonction, nom de la variable, premier terme, nombre d'it\303\251rations, titre.\134n\134nCe maplet permet \303\251galement de visualiser les valeurs des premiers termes de la suite r\303\251currente.\134nPour cela, cliquer le bouton ""Premiers termes"".\134n\134nPour sauvegarder le graphique cr\303\251\303\251 au format .gif, cliquer le bouton ""Enregistrer""."
)
),
BoxRow('inset'=0, 'spacing'=0,
Button("Fermer", 'font'='F1', CloseWindow('Aide') )
)
)
)
):
Maplets[Display](maplet3);