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{SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "Exercice 33" }}{PARA 0 "
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rt:assume(n,integer);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "P:
=(n,X)->product((1+X^(2^k)),k=0..n);Q:=(n,X)->sum(X^j,j=0..2^(n+1)-1);
 " }{TEXT -1 29 "les deux polyn\364mes \340 comparer" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"PGf*6$%\"nG%\"XG6\"6$%)operatorG%&arrowGF)-%(pro
ductG6$,&\"\"\"F1)9%)\"\"#%\"kGF1/F6;\"\"!9$F)F)F)" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"QGf*6$%\"nG%\"XG6\"6$%)operatorG%&arrowGF)-%$sumG
6$)9%%\"jG/F2;\"\"!,&)\"\"#,&9$\"\"\"F;F;F;F;!\"\"F)F)F)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "m:=1:expand(P(m,X));expand(Q(m,X));
 " }{TEXT -1 25 "ils sont bien \351gaux pour " }{XPPEDIT 18 0 "n = 1;
" "6#/%\"nG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*\"\"\"F$*$)%\"X
G\"\"#F$F$F'F$*$)F'\"\"$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*\"\"
\"F$*$)%\"XG\"\"#F$F$F'F$*$)F'\"\"$F$F$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 48 "m:=2:sort(expand(P(m,X)));sort(expand(Q(m,X))); " }
{TEXT -1 26 "ils sont aussi \351gaux pour " }{XPPEDIT 18 0 "n = 2;" "6
#/%\"nG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,2*$)%\"XG\"\"(\"\"\"F
(*$)F&\"\"'F(F(*$)F&\"\"&F(F(*$)F&\"\"%F(F(*$)F&\"\"$F(F(*$)F&\"\"#F(F
(F&F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,2*$)%\"XG\"\"(\"\"\"F(*$
)F&\"\"'F(F(*$)F&\"\"&F(F(*$)F&\"\"%F(F(*$)F&\"\"$F(F(*$)F&\"\"#F(F(F&
F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "for m from 0 to 1
5 do normal(P(m,X)-Q(m,X),expanded);od; " }{TEXT -1 58 "les deux polyn
\364mes sont \351gaux lorsque n est inf\351rieur \340 15" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
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{XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "for m from 0 to 5 do seq(coe
ff(expand(P(m,X)),X^j),j=1..2^(m+1)-1);od; " }{TEXT -1 84 "une m\351th
ode un peu plus longue (d\351conseill\351e) : montrer pour des valeurs
 donn\351es de " }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 25 " que les \+
coefficients de " }{XPPEDIT 18 0 "P;" "6#%\"PG" }{TEXT -1 28 " sont le
s m\352mes que ceux de " }{XPPEDIT 18 0 "Q;" "6#%\"QG" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"F#
F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6)\"\"\"F#F#F#F#F#F#" }}{PARA 11 "
" 1 "" {XPPMATH 20 "61\"\"\"F#F#F#F#F#F#F#F#F#F#F#F#F#F#" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6A\"\"\"F#F#F#F#F#F#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 12 "" 1 "" {XPPMATH 20 "6[o\"\"\"F#F#F#F#F
#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F
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0 "" {MPLTEXT 1 0 32 "normal(P(n,X)-Q(n,X),expanded); " }{TEXT -1 75 "
Maple ne parvient pas \340 identifier les deux polyn\364mes lorsque la
 valeur de " }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 17 " est ind\351t
ermin\351e" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,**&-%(productG6$,&\"
\"\"F*)%\"XG)\"\"#%\"kGF*/F/;\"\"!%#n|irGF*F,F*F*F&!\"\"*$))F,)F.F3F.F
*F4F*F*F*,&F,F*F*F4F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "ev
alb(simplify(P(n,X)-Q(n,X))=0); " }{TEXT -1 26 "de cette fa\347on l
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