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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 257 40 "TP 8  -  PROC\311DURES \+
R\311CURSIVES - CORRIG\311" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 11 "Fa
ctorielle" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "Phi:=pr
oc(n) n*Phi(n-1) end: Phi(0):=1: 'Phi(10)'=Phi(10);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#/-%$PhiG6#\"#5\"(+)GO" }}}{EXCHG {PARA 259 "" 0 "" 
{TEXT 258 18 "Suite de Fibonacci" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "F:=proc(n) option remember; \+
F(n-1)+F(n-2) end: F(0):=1: F(1):=1:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 124 "sans option remember, l'ordinateur refait plusieurs fois le m
\352me calcul, mais avec, la m\351moire se remplit plus rapidement...
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
7 "Maximum" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "maximum:=proc
(L,n)\nif n=1 then L[1] else max(L[n],maximum(L,n-1)) fi\nend:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "L:=[1,4,5,1,9]:maximum(L,nop
s(L)),maximum(L,4);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$
\"\"*\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Tri par insertion" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 142 "insertion:=proc(x,L)\nlo
cal LL,k:\nLL:=NULL:   for k to nops(L) while x > L[k] do LL:= LL,L[k]
 od :\nLL:=LL,x,seq(L[q],q=k..nops(L)): \n[LL]\nend: " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "tri:=proc(L,n)\nlocal M,LL,k:\nif n
=1 then [L[1]]\nelse insertion(L[n],tri(L,n-1)) fi:\nend:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "tri([4,3,2,1],4);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#7&\"\"\"\"\"#\"\"$\"\"%" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 0 "" }{TEXT 260 34 
"Ensemble des parties d'un ensemble" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 81 "ajout:= proc(x,E)\nlocal A,R;\nR:=NULL; for
 A in E do R:=R,A union \{x\} od: \{R\}\nend:" }}}{EXCHG {PARA 259 "" 
0 "" {TEXT 261 72 "(\"ajoute\" l'\351l\351ment x \340 chacun des ensem
bles constituant l'ensemble E  )" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 116 "P:=proc(E)\nlocal Q,R,x;\nif E=\{\} then \{\{
\}\}\nelse\nx:=E[1] :  \nQ:=P(E minus \{x\});R:= Q union ajout(x,Q):\n
R      fi:\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "P(\{pap
a,maman,la_bonne,moi\});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<2<\"<#%&m
amanG<#%$moiG<$%%papaGF(<$F*F&<&%)la_bonneGF*F&F(<#F-<%F*F&F(<#F*<$F&F
(<$F-F&<$F-F(<%F-F*F(<%F-F*F&<$F-F*<%F-F&F(" }}}{PARA 11 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 259 "" 0 "" {TEXT 262 20 "Fonction d'Acke
rmann" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 " f
 := proc(a,b,n)\n         if n = 1 then a+b\n         else if b = 1 th
en a else f(a,f(a,b-1,n),n-1) fi\n         fi\n     end:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f(a,5,2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$%\"aG\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
9 "f(a,b,2);" }}{PARA 8 "" 1 "" {TEXT -1 42 "Error, (in f) too many le
vels of recursion" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Maple ne sai
t pas que a+...+a (b fois) = ab !" }}{PARA 0 "" 0 "" {TEXT -1 143 "En \+
fait, f(a, b, 2) = ab,   f(a, b, 3) = a^b      f(a,b,4)=a^(a^(......^a
)..) (avec \"b\" a) (notation : a^^b)  ;  nous allons le lui apprendre
 :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "g:= proc(a,b)\nif b=0
 then 1 else a^g(a,b-1) fi end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 7 "g(a,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#)%\"aG)F$)F$)F$F$" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 198 "f := proc(a,b,n)\n       \+
  if n = 1 then a+b   elif n = 2 then a*b\n         elif n = 3 then a^
b  elif n = 4 then g(a,b)\n         else if b = 1 then a else f(a,f(a,
b-1,n),n-1) fi\n         fi\n     end:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "f(3,3,4);f(3,3,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#\".()\\[(fDw" }}{PARA 8 "" 1 "" {TEXT -1 43 "Error, (in g) too many l
evels of recursion\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "f(3,3,5) \+
est \351gal \340 3^^(3^^3)=3^^(3^(3^3)), donc \351gal \340 3^(3...^3).
.)  avec 3^(3^3)=" }{XPPEDIT 18 0 "7625597484987;" "6#\".()\\[(fDw" }
{TEXT -1 30 "  \"trois\"  dans l'expression !" }}{PARA 0 "" 0 "" 
{TEXT -1 97 "D'une fa\347on g\351n\351rale, f(a,b,5)  est \351gal \340
 a^^(a^^(......^^a)..) (avec \"b\" a) (notation :  a^^^b)" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "g
\351n\351rateur de permutations :" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 189 "permute:=proc(L)\nlocal n,k,LL:\nn:=nops(L):\nif n=1
 then L else for k to n do LL[k]:=permute(subsop(k=NULL,L)) od: \nseq(
seq([L[k],op(LL[k][q])],q=1..(n-1)!),k=1..n)  fi\nend:\npermute([1,2,3
]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6(7%\"\"\"\"\"#\"\"$7%F$F&F%7%F%F
$F&7%F%F&F$7%F&F$F%7%F&F%F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Ve
rsion d'Etienne Roberlin , PCSI 2008" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 249 "permute:=proc(L)\nlocal n, LL, L1, M, q, k;\nn:= nop
s(L):\nif n=1 then [L] else\nLL:=subsop(n=NULL,L): L1:=permute(LL):M:=
NULL:\nfor k to n do M:=M,seq([seq(L1[p][q],q=1..k-1),L[n],seq(L1[p][q
],q=k..n-1)],p=1..nops(L1)) od: \n[M] fi\nend:\npermute([1,2,3]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7(7%\"\"$\"\"#\"\"\"7%F%F'F&7%F&F%F'7%
F'F%F&7%F&F'F%7%F'F&F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
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