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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "#fonctions sur ense
mbles ou listes:\n#op, nops, minus, union, intersect, subset, select, \+
remove, member" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "#Q1\nS1:=
seq(2*k+1,k=1..6);\nE1:=\{S1\};\nL1:=[S1];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#S1G6(\"\"$\"\"&\"\"(\"\"*\"#6\"#8" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#E1G<(\"\"$\"\"&\"\"(\"\"*\"#6\"#8" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#L1G7(\"\"$\"\"&\"\"(\"\"*\"#6\"#8" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "#Q2\nmap(isprime,E1);\nmap(isprime,
L1);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$%&falseG%%tru
eG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(%%trueGF$F$%&falseGF$F$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "#Q3\nmap(isprime,S1); #appl
ique isprime \340 3, les autres valeurs sont consid\351r\351es comme a
rguments suppl\351mentaire de isprime" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "#Q4\nop(E1);
 #pour prendre les \351l\351ments d'un ensemble d'\351l\351ments, il f
aut donc appliquer op \340 tous les sous-ensembles\nflatset:=E->map(op
,E);\nflatset(\{\{1,2\},\{2,3\}\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#%#E1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(flatsetGf*6#%\"EG6\"6$%)o
peratorG%&arrowGF(-%$mapG6$%#opG9$F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#<%\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 
"#Q5\nflat_list:=L->map(op,L);\nflat_list([[1,2],[3,4]]);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%*flat_listGf*6#%\"LG6\"6$%)operatorG%&arrowGF
(-%$mapG6$%#opG9$F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&\"\"\"\"
\"#\"\"$\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "#Q6  \nele
ments:=M->seq(seq(M[i,j],j=1..nops(M[i])),i=1..nops(M)):\nelements([[1
,2],[3,4]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&\"\"\"\"\"#\"\"$\"\"%
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "#Q7\nwith(numtheory); \+
#charge la bibliot\350que numtheory contenant la fonction sum2qr\nsum2
sqr(218);\nsum2sqr(33);" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, the p
rotected name order has been redefined and unprotected\n" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#7Q%&GIgcdG%)bigomegaG%&cfracG%)cfracpolG%+cyclot
omicG%)divisorsG%)factorEQG%*factorsetG%'fermatG%)imagunitG%&indexG%/i
ntegral_basisG%)invcfracG%'invphiG%*issqrfreeG%'jacobiG%*kroneckerG%'l
ambdaG%)legendreG%)mcombineG%)mersenneG%(migcdexG%*minkowskiG%(mipolys
G%%mlogG%'mobiusG%&mrootG%&msqrtG%)nearestpG%*nthconverG%)nthdenomG%)n
thnumerG%'nthpowG%&orderG%)pdexpandG%$phiG%#piG%*pprimrootG%)primrootG
%(quadresG%+rootsunityG%*safeprimeG%&sigmaG%*sq2factorG%(sum2sqrG%$tau
G%%thueG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7$\"\"(\"#8" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
44 "map(L->[seq(flat_list(sum2sqr(i)),i=1..10)];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6,7$\"\"!\"\"\"7$F%F%7\"7$F$\"\"#7$F)F%F'F'7$F)F)7$F$\"\"
$7$F%F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 540 "#Q8 principe: s
um2sqr donne une liste de listes, en lui appliquant flatlist, puis en \+
prenant la somme des carr\351s des deux membres on retombe sur le nomb
re bon\n#on aurait seq(flat_list(sum2sqr(i))[1]^2+flat_list(sum2sqr(i)
)[2]^2,i=1..N)\n#ne marche pas car la liste vide n'a ni premier ni der
nier \351l\351ment\n\n#solution du m\352me esprit\nsumlist:=L->sum(L[k
],k=1..2): #fonction sommant les 2 premiers termes d'une liste\n#on pr
end les carr\351s de la liste et on fait la somme ac sumliste\nbon:=\{
seq(sumlist(map(x->x^2,flat_list(sum2sqr(i)))),i=1..10)\};\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$bonG<*\"\"!\"\"\"\"\"#\"\"%\"\"&\"\")\"\"
*\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "#Q9\nmauvais:=\{se
q(i,i=1..10)\} minus bon;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(mauvai
sG<%\"\"$\"\"'\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 142 "#Q1
1 si tous les membres satisfont f alors l'ensemble map(f,e) sera \351g
al \340 \{true\}\nfor_all:=(f,e)->evalb(map(f,e)=\{true\}):\nfor_all(i
sprime,E1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "#Q12 si il existe un \351l\351ment
 de e satisfaisant f alors true fait partie de map(f,e)\nexiste:=(f,e)
->evalb(member(true,map(f,e))):\nexiste(isprime,E1);\n" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 81 "#Q13\nest_carre_parfait:=x->evalb(sqrt(x)-floor(sqrt(x))=0):\nes
t_carre_parfait(9);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 267 "#Q14\nest_bon:=x->existe(es
t_carre_parfait,\{seq(i,i=1..floor(sqrt(x)))\});\nEt:=\{seq(i,i=10^6..
10^6+99)\}:\nselect(est_bon,Et); # select est une fonction pr\351d\351
finie qui s\351lectionne les \351l\351ments d'une liste ou d'un ensemb
le e qui v\351rifient un crit\350re f syntaxe: select(f,e)" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%(est_bonGf*6#%\"xG6\"6$%)operatorG%&arrowG
F(-%'existeG6$%2est_carre_parfaitG<#-%$seqG6$%\"iG/F4;\"\"\"-%&floorG6
#-%%sqrtG6#9$F(F(F(" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<`q\"(+++\"\"(,
++\"\"(-++\"\"(.++\"\"(/++\"\"(0++\"\"(1++\"\"(2++\"\"(3++\"\"(4++\"\"
(5++\"\"(6++\"\"(7++\"\"(8++\"\"(9++\"\"(:++\"\"(;++\"\"(<++\"\"(=++\"
\"(>++\"\"(?++\"\"(@++\"\"(A++\"\"(B++\"\"(C++\"\"(D++\"\"(E++\"\"(F++
\"\"(G++\"\"(H++\"\"(I++\"\"(J++\"\"(K++\"\"(L++\"\"(M++\"\"(N++\"\"(O
++\"\"(P++\"\"(Q++\"\"(R++\"\"(S++\"\"(T++\"\"(U++\"\"(V++\"\"(W++\"\"
(X++\"\"(Y++\"\"(Z++\"\"([++\"\"(\\++\"\"(]++\"\"(^++\"\"(_++\"\"(`++
\"\"(a++\"\"(b++\"\"(c++\"\"(d++\"\"(e++\"\"(f++\"\"(g++\"\"(h++\"\"(i
++\"\"(j++\"\"(k++\"\"(l++\"\"(m++\"\"(n++\"\"(o++\"\"(p++\"\"(q++\"\"
(r++\"\"(s++\"\"(t++\"\"(u++\"\"(v++\"\"(w++\"\"(x++\"\"(y++\"\"(z++\"
\"(!3+5\"(\"3+5\"(#3+5\"($3+5\"(%3+5\"(&3+5\"('3+5\"((3+5\"()3+5\"(*3+
5\"(!4+5\"(\"4+5\"(#4+5\"($4+5\"(%4+5\"(&4+5\"('4+5\"((4+5\"()4+5\"(*4
+5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 386 "#Q15\nC:=\{seq(a^2,a
=0..10)\}: liste des carr\351s parfaits entre 0 et 10\najoute:=(x,E)->
map(a->a+x,E):# fonction ajoutant x \340 tous les \351l\351ments d'un \+
ensemble\nB:=flatset(\{seq(ajoute(i,C),i in C)\}):# ensembles des bons
 (somme(i^2+j^2))\nR:=flatset(\{seq(ajoute(i,B),i in C)\}):#ensemble d
es remarquables\n(somme(i^2+j^2+k^2)\nNR:=\{seq(i,i=1..300)\} minus R:
# ensemble des non remarquables\nNR[1..10];" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<,\"\"(\"#:\"#B\"#
G\"#J\"#R\"#Z\"#b\"#g\"#j" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
77 "#Q16\nEX:=flatset(\{seq(ajoute(i,R),i in C)\}):\nNEX:=\{seq(i,i=1.
.100)\} minus EX;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$NEXG<\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "17 0 0" 0 }
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