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{SECT 0 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 8 "restart;" }
{MPLTEXT 1 202 0 "" }}{PARA 201 "> " 0 "" {TEXT 203 10 "Exercice 1" }
{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 204 10 "Question
 a" }{TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 14 "e
ns:=proc(E,f)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nlocal n,i,s;
" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 20 "\nn:=nops(E);s:=NULL;" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\nfor i from 1 to n do " }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 31 "\n if f[i]=1 then s:=s,E[i]; f
i;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "
" }{MPLTEXT 1 202 5 "\n\{s\};" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 
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1 202 33 "ens([a,b,c,d,e,f],[1,1,0,0,0,1]);" }{MPLTEXT 1 202 0 "" }}
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{PARA 200 "> " 0 "" {MPLTEXT 1 202 15 "ens2:=proc(E,l)" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 11 "\nlocal n,s;" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 12 "\nn:=nops(l);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 
202 26 "\ns:=\{seq(E[l[k]],k=1..n)\};" }{MPLTEXT 1 202 0 "" }{MPLTEXT 
1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" 
{MPLTEXT 1 202 30 "ens2([a,b,c,d,e,f],[1,3,4,5]);" }{MPLTEXT 1 202 0 "
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{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 204 10 "Question
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ns3:=proc(E,l,k)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\nlocal i,n
,s;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 20 "\nn:=nops(l);s:=NULL;" }
{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 56 "\nfor i from 1 to n do if l[i]
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 {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 204 10 "Questio
n d" }{TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 24 "
colle:=(d,z)->[d,op(z)]:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> \+
" 0 "" {MPLTEXT 1 202 23 "colle(a,[u_1,u_2,u_3]);" }{MPLTEXT 1 202 0 "
" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#7&I\"aG6\"I$u_1GF%I$u_2GF%I$u_3GF
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{TEXT 207 10 "Exercice 2" }{TEXT 205 0 "" }}}{EXCHG {PARA 202 "" 0 "" 
{TEXT 204 10 "Question a" }{TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "
" {MPLTEXT 1 202 34 "parties:=proc(n) options remember;" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 24 "\nlocal gauche,droite,p; " }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 26 "\nif n=0 then p:=\{[]\} else " }{TEXT 
208 28 "on construit les parties de " }{TEXT 209 2 "E " }{TEXT 208 32 
"\340 n \351l\351ments \340 partir de celles " }{TEXT 209 37 "E'= E pr
iv\351 du premier \351l\351ment not\351 0" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 43 "\n       gauche:=map2(colle,0,parties(n-1));" }
{TEXT 208 1 " " }{TEXT 209 6 "gauche" }{TEXT 208 21 " contient toutes \+
les " }{TEXT 209 10 "parties E'" }{TEXT 208 28 " vues comme des partie
s de E" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 44 "\n       droite:=map2
(colle,1,parties(n-1)); " }{TEXT 209 6 "droite" }{TEXT 208 20 " contie
nt toutes les" }{TEXT 209 14 " parties de E'" }{TEXT 208 13 " aux quel
les " }{TEXT 209 21 "on ajoute l'\351l\351ment 0" }{MPLTEXT 1 202 0 ""
 }{MPLTEXT 1 202 36 "\n       p:=\{op(gauche),op(droite)\}; " }{TEXT 
208 3 "on " }{TEXT 209 8 "fusionne" }{TEXT 208 30 " ces deux ensembles
 de parties" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nfi;" }{MPLTEXT 
1 202 0 "" }{MPLTEXT 1 202 13 "\nend:        " }{MPLTEXT 1 202 0 "" }}
}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 11 "parties(3);" }{MPLTEXT 
1 202 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#<*7%\"\"\"\"\"!F%7%F%F%F
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{TEXT 204 10 "Question b" }{TEXT 205 0 "" }}{PARA 205 "> " 0 "" 
{MPLTEXT 1 0 31 "map2(ens,[a,b,c,d],parties(4));" }{MPLTEXT 1 0 0 "" }
}{PARA 203 "" 1 "" {XPPMATH 20 "6#<2<$I\"aG6\"I\"dGF&<$F%I\"cGF&<#F%<%
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{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 204 "" 0 "" {TEXT 207 10 "Exercice
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 a" }{TEXT 205 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 40 "c
ombinaison:=proc(n,k) options remember;" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 27 "\nlocal gauche,droite,combi;" }{MPLTEXT 1 202 0 "" 
}{MPLTEXT 1 202 50 "\nif is(n<0) or is(k<0) or is(k>n) then combi:=\{
\}; " }{TEXT 208 28 "dans ce cas le probl\350me n'a " }{TEXT 209 15 "p
as de solution" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 34 "\nelif n=0 or
 k=0 then combi:=\{[]\};" }{MPLTEXT 1 202 2 "  " }{TEXT 208 20 "dans c
e cas seule l'" }{TEXT 209 13 "ensemble vide" }{TEXT 208 9 " convient"
 }{TEXT 209 0 "" }{MPLTEXT 1 202 2 "\n " }{TEXT 208 94 "taiter le cas \+
n=k est inutile car on le cas k>n ou n<0 ou k<0 suffit \340 compenser \+
cette absence" }{TEXT 208 14 "\nOn consid\350re " }{TEXT 209 37 " E'=E
 priv\351 du dernier element not\351 n" }{MPLTEXT 1 202 0 "" }
{MPLTEXT 1 202 34 "\nelse gauche:=combinaison(n-1,k); " }{TEXT 209 6 "
gauche" }{TEXT 208 13 " contient les" }{TEXT 209 32 " combinaisons \34
0 k \351l\351ments de E'" }{TEXT 208 34 ", vues comme des combinaisons
 de E" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 35 "\n     droite:=combina
ison(n-1,k-1);" }{MPLTEXT 1 210 1 " " }{TEXT 209 7 "droite " }{TEXT 
208 13 "contient les " }{TEXT 209 33 "combianisons \340 k-1 \351l\351m
ents de E'" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 36 "\n     droite:=ma
p2(colle,n,droite); " }{TEXT 208 3 "on " }{TEXT 209 6 "ajoute" }{TEXT 
208 21 " aux combinaisons de " }{TEXT 209 19 "droite, l'\351l\351m\351
nt n" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 38 "\n     combi:=\{op(gauc
he),op(droite)\}; " }{TEXT 208 3 "on " }{TEXT 209 8 "fusionne" }{TEXT 
208 47 " les ensembles de combinaisons droite et gauche" }{MPLTEXT 1 
202 0 "" }{MPLTEXT 1 202 4 "\nfi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 
202 7 "\ncombi;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }
{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 17 "c
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{PARA 202 "" 0 "" {TEXT 204 10 "Question b" }{TEXT 205 0 "" }}}{EXCHG 
{PARA 200 "> " 0 "" {MPLTEXT 1 202 40 "map2(ens2,[a,b,c,d,e],combinais
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