{VERSION 3 0 "APPLE_PPC_MAC" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 
"" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text \+
Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 
3 0 3 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 
{CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 
0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 
0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Out
put" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 
-1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 
-1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }
0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT -1 43 "CorrigŽ du TD 3 : ArithmŽ
tique et polyn™mes" }}{PARA 256 "" 0 "" {TEXT -1 25 "Jean SŽbastien RO
Y, 1999." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 47 "Ex 1 : Calcul de la \+
n-i�me dŽcimale de ln(9/10)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Si : r=10^n mod k
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Alors :" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 22 "(10^n-r)/k=10^n/k-r/k;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/*&,&)\"#5%\"nG\"\"\"%\"rG!\"\"\"\"\"%\"kG!\"\",&*&F&F,
F-F.F)*&F*F,F-F.F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "est un enti
er relatif. Et donc: 10^n/k et r/k ont les m�mes parties fractionaires
." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "Ainsi le calcul de r/k donne
 les dŽcimales de 1/k ˆ partir de la n-i�me." }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 9 "Exemple :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "
evalf(1/17,50);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"Sfqk<THN#)eqk<TH
N#)eqk<THN#)e!#^" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "r:=10^1
1 mod 17;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalf(r/17,50);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#$\"S=THN#)eqk<THN#)eqk<THN#)eqk<!#]" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 27 "Mais il vaut mieux Žcrire :" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 19 "r:=10 &^ 11 mod 17;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"rG\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 166 "Ca
r sous la forme &^, Maple ne calcule pas 10^9 puis 1000 mod 17 mais ef
fectue directement le le calcul entier en ne conservant que des nombre
s plus petits que 17^2 :" }}{PARA 0 "" 0 "" {TEXT -1 33 "Comme 11=(2*2
+1)*2+1 on calcule :" }}{PARA 0 "" 0 "" {TEXT -1 30 "(10^2^2*10)^2*10 \+
mod 17 soit :" }}{PARA 0 "" 0 "" {TEXT -1 16 "10^2 mod 17 = 15" }}
{PARA 0 "" 0 "" {TEXT -1 15 "15^2 mod 17 = 4" }}{PARA 0 "" 0 "" {TEXT 
-1 15 "4*10 mod 17 = 6" }}{PARA 0 "" 0 "" {TEXT -1 14 "6^2 mod 17 = 2
" }}{PARA 0 "" 0 "" {TEXT -1 15 "2*10 mod 17 = 3" }}{PARA 0 "" 0 "" 
{TEXT -1 6 "donc :" }}{PARA 0 "" 0 "" {TEXT -1 16 "10^11 mod 17 = 3" }
}{PARA 0 "" 0 "" {TEXT -1 63 "Pour calculer a^b mod c il faut environ \+
ln(b)/ln(2) opŽrations." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 150 "Ainsi
, on a rapidement la 100 001-ieme dŽcimale de 1/17 sans avoir ˆ effect
uer des calculs sur des nombres de plus de 3 chiffres (au lieu de 100 \+
000)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r:=10 &^ 100000 mo
d 17;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalf(r/17,10);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#$\"+THN#)e!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 26 "evalf(frac(10^100000/17));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
$\"+THN#)e!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "Cela marche pare
il en base b (il suffit de remplacer 10 par b)" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 62 "Exemple de calcul : calcul de la n-i�me dŽcimale de \+
ln(9/10) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "sum(1/(k*10^k
),k=1..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%#lnG6##\"\"*
\"#5!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "On cherche la partie
 fractionaire de:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "10^n*S
um(1/(k*10^k),k=1..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)\"
#5%\"nG\"\"\"-%$SumG6$*&\"\"\"F,*&%\"kG\"\"\")F%F.\"\"\"!\"\"/F.;F'%)i
nfinityGF'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Soit la partie frac
tionaire de :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "Sum(10^(n-
k)/k,k=1..n-1)+Sum(10^(n-k)/k,k=n..infinity);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&-%$SumG6$*&)\"#5,&%\"nG\"\"\"%\"kG!\"\"\"\"\"F-!\"\"/
F-;F,,&F+F,F.F,F,-F%6$F'/F-;F+%)infinityGF," }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 125 "Pour la deuxi�me somme, pas de probl�me, il suffit de \+
calculer ses premi�res dŽcimales tel quel ˆ l'aide de quelques termes \+
:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Pour la premi�re somme, on u
tilise la mŽthode dŽcrite plus haut." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 81 "On Žcrit une fonction qui calcule b^n mod j en utilisant la mŽt
hode rapide si n>0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "deci \+
:= proc(b,n,j) if n<=0 then evalf(b^n/j) else evalf((b &^ n mod j)/j) \+
fi:end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%deciGR6%%\"bG%\"nG%\"jG6
\"F*F*@%19%\"\"!-%&evalfG6#*&)9$F-\"\"\"9&!\"\"-F06#*&-%$modG6$-%#&^G6
$F4F-F6F5F6F7F*F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "(Exemple a
vec n=99)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "frac(add(deci(
10,99-j,j),j=1..99+10));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\")sFgw!
\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Attention !  Il faut utili
ser " }{TEXT 256 3 "add" }{TEXT -1 12 " et non pas " }{TEXT 257 3 "sum
" }{TEXT -1 75 " sinon Maple mŽmorise tous les nombres sommŽs et effec
tue la somme ensuite." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "ev
alf(frac(-10^99*ln(9/10)),110);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"
,\"fsFgw!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "M�me exemple, mais
 avec n=9 999 :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "frac(add
(deci(10,9999-j,j),j=1..9999+10));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
$\"'!y#H!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "evalf(frac(
-10^9999*ln(9/10)),10010);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\",b>nx
#H!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "Calculons quelques dŽcim
ales de Pi ˆ l'aide de la formule :" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 75 "16^N * Pi=Sum(16^(N-k)*(4/(8*k+1)-2/(8*k+4)-1/(8*k+5)
-1/(8*k+6)),k=0..inf);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&)\"#;%\"N
G\"\"\"%#PiGF(-%$SumG6$*&)F&,&F'F(%\"kG!\"\"F(,**&\"\"\"F4,&F0\"\")F(F
(!\"\"\"\"%*&F4F4,&F0F6F8F(F7!\"#*&F4F4,&F0F6\"\"&F(F7F1*&F4F4,&F0F6\"
\"'F(F7F1F(/F0;\"\"!%$infG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "VŽr
ifions tout de m�me :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "ev
alf(sum(16^(-k)*(4/(8*k+1)-2/(8*k+4)-1/(8*k+5)-1/(8*k+6)),k=0..infinit
y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+_EfTJ!\"*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "n:=1000;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"nG\"%+5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
100 "add(4*deci(16,n-j,8*j+1)-2*\ndeci(16,n-j,8*j+4)-1*deci(16,n-j,8*j
+5)-1*deci(16,n-j,8*j+6),j=0..n+10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#$!+5b6re!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 324 "Ce qui nous in
tŽresse c'est la partie fractionaire. Comme on n'a pas calculŽ correct
ement la partie enti�re (volontairement), le signe de cette partie ent
i�re n'est pas bon ce qui modifie la valeur de la partie fractionaire \+
(complŽment ˆ 10). On rajoute 1 ˆ la partie fractionaire pour avoir la
 partie fractionaire correcte." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 10 "1+frac(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\")!\\%))G!\")
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 114 "Soit affichŽ en hexadŽcimal \+
(c'est une notation pratique pour la base 16 ou l'on note 0=0, ..., 9=
9, 10=A ... 15=F" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "convert
(trunc(16^8*%),hex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)49F1BD47G" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "VŽrification :" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 32 "t:=frac(evalf(Pi*16^1000,1300)):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "convert(trunc(t*16^8),hex);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)49F1C09BG" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 31 "Ex 2
 : polyn™mes interpolateurs" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "DŽfinissons la fon
ction :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f:=x -> 1/(x^2+1
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&
arrowGF(*&\"\"\"F-,&*$)9$\"\"#F-\"\"\"F3F3!\"\"F(F(F(" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 70 "Essayons d'interpoler cette fonction avec
 le dŽveloppement de Taylor :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "taylor(f(x),x=0,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"xG\"
\"\"\"\"!!\"\"\"\"#F%\"\"%-%\"OG6#F%\"\"'" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 19 "convert(%,polynom);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,(\"\"\"F$*$)%\"xG\"\"#\"\"\"!\"\"*$)F'\"\"%F)F$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "plot([f(x),convert(taylor(f(x),x=0
,3),polynom),\nconvert(taylor(f(x),x=0,5),polynom)],x=-5..5,-1..1,colo
r=[black,red,blue,green],numpoints=200,thickness=3);" }}{PARA 13 "" 1 
"" {GLPLOT2D 398 176 176 {PLOTDATA 2 "6(-%'CURVESG6$7hw7$$!\"&\"\"!$\"
1YQ:YQ:YQ!#<7$$!1V([(\\RUZ\\!#:$\"1'4%zX$3^#RF-7$$!1Qxa4yn,\\F1$\"1%ot
`@td*RF-7$$!1hAX!\\J-&[F1$\"1V()fyU^xSF-7$$!1%ze<:W%)z%F1$\"1zVvA%>B;%
F-7$$!1JiC\\H!pu%F1$\"145BahL\\UF-7$$!1?Rycw6*p%F1$\"1\\uc^_VKVF-7$$!1
d8Fa(Q'\\YF1$\"1ijdoW.@WF-7$$!1jD^-wY)f%F1$\"1)\\\"**Qw]:XF-7$$!1KkGd0
YZXF1$\"1;B85Vn7YF-7$$!1V&3<a$*\\\\%F1$\"1;y?^i(er%F-7$$!1X\"Hec!y[WF1
$\"1gidNMi4[F-7$$!18D]+dv'R%F1$\"1!)3uld[=\\F-7$$!1-/3;s^WVF1$\"1'**=y
h*[J]F-7$$!1>Rycd<%H%F1$\"14)>;OZS9&F-7$$!1CZ%*))3Y[UF1$\"1ck7!o.&\\_F
-7$$!1OsW*[,T>%F1$\"19c0X^4z`F-7$$!1$pQx%>0[TF1$\"1!=K6m$f#\\&F-7$$!1&
3<MQ&[%4%F1$\"1e**>0f5HcF-7$$!1Pu[(*)pq/%F1$\"1%)3F$eXTv&F-7$$!1iBZ%fZ
]*RF1$\"1P*p,_&3'*eF-7$$!1&**)zf+^XRF1$\"1?w6qx2OgF-7$$!1zf>RG#Q*QF1$
\"16^%G13u='F-7$$!1#Ryc$yNYQF1$\"1\\%y1XI8L'F-7$$!1Fa3</;&z$F1$\"1'pYB
_R@\\'F-7$$!1)pRzo!)>u$F1$\"1B$o0_\"flmF-7$$!1NpQxvo&p$F1$\"1U%y%zM;Ao
F-7$$!1V([(\\(*oXOF1$\"13nKRYQ(*pF-7$$!1Qv],r.%f$F1$\"1Cv/=OS&=(F-7$$!
1e:Ji]]VNF1$\"1#=e-NulP(F-7$$!1-/3;Fh%\\$F1$\"1K()G(e%povF-7$$!1Qv],hK
SMF1$\"1g+bUQo!z(F-7$$!1&4>Q;Z:R$F1$\"1&oN(e8M)*zF-7$$!1/4=O_YRLF1$\"1
yxs'3z!H#)F-7$$!1@U%)o7F#H$F1$\"1*pVlfBmW)F-7$$!1D\\)pzv1C$F1$\"1;g``b
:%p)F-7$$!1sW*)y%G@>$F1$\"1Lp.#o-o$*)F-7$$!1!3;Ka#QTJF1$\"180!3J%3,#*F
-7$$!1!*yd:\"p<4$F1$\"1DhM!Gh0Z*F-7$$!1pQxa%G)RIF1$\"1=^W*z$4l(*F-7$$!
1Gc7DM!)*)HF1$\"10oFz]915!#;7$$!1w^.2ckQHF1$\"1N_+)*R\"y.\"Fax7$$!1Pv]
,9\"z)GF1$\"18a?8,mq5Fax7$$!1#Ryc$>HTGF1$\"1[`q#ey@5\"Fax7$$!1rT$owgyy
#F1$\"1#GhB4p*R6Fax7$$!17BY#Hr+u#F1$\"1C.U\\cOv6Fax7$$!1JhAXx6*o#F1$\"
1ny9Ap'[@\"Fax7$$!1v\\**)p[.k#F1$\"1s)G6HyWD\"Fax7$$!1<NqSp>'e#F1$\"1S
_-j#e1I\"Fax7$$!1C\\)p\\0$RDF1$\"13P[n#HEM\"Fax7$$!1CZ%*)G$3'[#F1$\"1'
=@3KRER\"Fax7$$!1.17CqdPCF1$\"1AFT[BbS9Fax7$$!1PtY$z=XQ#F1$\"1%H#Ql#yc
\\\"Fax7$$!1Ryc8&Q(QBF1$\"1L_hSsmX:Fax7$$!1lHf=,g'G#F1$\"1zW)>m7bg\"Fa
x7$$!1v],.qBOAF1$\"1x\"[:rckm\"Fax7$$!16AW)y1f=#F1$\"1Jzy3ikI<Fax7$$!1
T#['H<wN@F1$\"1#Q,y6$3)z\"Fax7$$!1mJjE!)e(3#F1$\"1h&4$o(fj'=Fax7$$!1Z%
*)y(4^N?F1$\"1#QZF:vU%>Fax7$$!1f=Pux(e)>F1$\"1>/c_@xA?Fax7$$!1?T#[;TO$
>F1$\"1'3p2+k,6#Fax7$$!1d8FaWN')=F1$\"1w#4rP%y$>#Fax7$$!1tY$py$4M=F1$
\"19*\\+@G:H#Fax7$$!1f=Pur.%y\"F1$\"1%*))>O&\\2R#Fax7$$!1D]+,C5M<F1$\"
1$\\QlUjb\\#Fax7$$!1<MoO`%>o\"F1$\"1!*R)ez)o6EFax7$$!15>Qwn!Rj\"F1$\"1
@`g<X0DFFax7$$!1!*zf>(3Ze\"F1$\"1Fr_`m%z%GFax7$$!1xa4>#)QI:F1$\"10u;\\
89#*HFax7$$!1#Qw_X07[\"F1$\"1Tfm!=+48$Fax7$$!1qT$o'o!4V\"F1$\"1`oLUTQ
\"G$Fax7$$!1\\**)z\\a(z8F1$\"1Pc=)GbQW$Fax7$$!1Fa3<btK8F1$\"1Gokvn1-OF
ax7$$!1],.1[h#G\"F1$\"1lt)\\Mu0y$Fax7$$!1Fa3<c(GB\"F1$\"13.'3'=GoRFax7
$$!1V'Gd9q'z6F1$\"1W-AlLE\"=%Fax7$$!1`06A'=F8\"F1$\"1@76FF5!Q%Fax7$$!1
kFb5jay5F1$\"1R(4lE[Ei%Fax7$$!1(Rze(*f'H5F1$\"1U:#pY)*Q&[Fax7$$!1_2:I]
*G\")*Fax$\"1.wdNvU%4&Fax7$$!1'Qw_0dFH*Fax$\"13M,BF4m`Fax7$$!1v`2:]^q(
)Fax$\"1zT:Q/@_cFax7$$!1PrU&3_`H)Fax$\"1a`B+\">P#fFax7$$!1;S!3;]2z(Fax
$\"1YJWg%QHA'Fax7$$!1$*******zI)H(Fax$\"1b7c'4MY_'Fax7$$!1gD^-b\\knFax
$\"1k$*[#4o1'oFax7$$!13>Qw#*f-jFax$\"1Y5HG-.drFax7$$!1.<MoY4sdFax$\"1H
>6QX\"4](Fax7$$!1yhBZCRt_Fax$\"1nbjma>CyFax7$$!1R'Gd92&zZFax$\"1913cjU
S\")Fax7$$!1lQxa*G_G%Fax$\"1[fUnFd[%)Fax7$$!1'=Pu['4\"y$Fax$\"1A,-.(f
\"\\()Fax7$$!1Wze<XsYKFax$\"1k9ha\"*RY!*Fax7$$!19Pu[xvcFFax$\"1&*3th]q
$H*Fax7$$!1Le;Lw4tAFax$\"1j%4'R')o3&*Fax7$$!1U#['HH2c<Fax$\"1*H!)=2Y3q
*Fax7$$!1\"f=Put,C\"Fax$\"1RA,;m_[)*Fax7$$!1lpRzeBrxF-$\"1RS;C/(*R**Fa
x7$$!1l#f=Pa'G]F-$\"1'z(**=kxu**Fax7$$!1k:KkG2'G#F-$\"1c\\n+mx%***Fax7
$$\"1gv-/3;#z)!#?$\"0\"zpA********F17$$\"1?'Hf=dOI#F-$\"1esKyfp%***Fax
7$$\"1;**)zffx)\\F-$\"1o%H3*R=v**Fax7$$\"17-05?'=n(F-$\"1\"pEk#p[T**Fa
x7$$\"1W$pQxdL-\"Fax$\"1E,pv#fj*)*Fax7$$\"1oOtY$H&z7Fax$\"1Eo0(p<*Q)*F
ax7$$\"1;Pu[2*pt\"Fax$\"1-iD>G72(*Fax7$$\"1+&)pRRX^AFax$\"1zcUo5b<&*Fa
x7$$\"1rJjEtKpFFax$\"1BSt=%4xG*Fax7$$\"1'ze<NRZG$Fax$\"1kPz%4Dh-*Fax7$
$\"16>QwAfiPFax$\"1Q'ej2e)f()Fax7$$\"1Tv],8QdUFax$\"1Hc([G(el%)Fax7$$
\"1ta4>G4pZFax$\"1y?+)Q@q9)Fax7$$\"1)yc8Fj\"z_Fax$\"1[(*)3Dp/#yFax7$$
\"1\"oNrULQ!eFax$\"1)=W^u*H![(Fax7$$\"1Y'Hf=jfE'Fax$\"1vyf[Xp!=(Fax7$$
\"1%)f>R=@'y'Fax$\"1Qz)G*\\%o%oFax7$$\"1)3<Mo'f3tFax$\"1l&3)oDC=lFax7$
$\"1=>Qw7,7yFax$\"1&\\-7h=,@'Fax7$$\"1tQxa*f\"p#)Fax$\"1QoalE)*QfFax7$
$\"1Y([(\\Rv7))Fax$\"1+iQxAeGcFax7$$\"1mT$oO\\KF*Fax$\"1v;n#)>aw`Fax7$
$\"1c-05]\"*3)*Fax$\"1D.%>;bk4&Fax7$$\"1tY$p)pIG5F1$\"1aQ#*)\\n/'[Fax7
$$\"1\\(\\**GH.3\"F1$\"1Ikn-vV9YFax7$$\"1:JiCo')H6F1$\"1v+v.q^#R%Fax7$
$\"1JhAXSb\"=\"F1$\"1#eQ2%3]tTFax7$$\"1>Pu[!>!H7F1$\"1Rn&oe*G$)RFax7$$
\"1%oOtY;-G\"F1$\"1i**R%*)z$*y$Fax7$$\"17C['>'RL8F1$\"1_h%Hv#y*f$Fax7$
$\"1x^.2$*oz8F1$\"1S'pVloSW$Fax7$$\"1nLnMroH9F1$\"1sOz$RX^G$Fax7$$\"1s
X\"HyR8[\"F1$\"1&[uc8508$Fax7$$\"1a06A=(=`\"F1$\"1![#R/%z!))HFax7$$\"1
4<MoTw!e\"F1$\"1;0(4C5\"eGFax7$$\"1uX\"Hy]]j\"F1$\"1vk=m-GAFFax7$$\"1:
Ig?(HQo\"F1$\"1ZaDU)ptg#Fax7$$\"117C[;\"ft\"F1$\"18FCO'f;\\#Fax7$$\"1!
*yd:c5$y\"F1$\"1&zM(p.l#R#Fax7$$\"1&=Pu3,Z$=F1$\"1wtlH)e.H#Fax7$$\"1Rw
_0%[K)=F1$\"1!Qv,'QV*>#Fax7$$\"1Jg?TV*R$>F1$\"1!z]N%fb4@Fax7$$\"1@U%)o
xg$)>F1$\"1%=l8tlk-#Fax7$$\"1U#['H%[b.#F1$\"1AkG=v@W>Fax7$$\"1$['HfMd&
3#F1$\"1Flv>GHp=Fax7$$\"1MpQx7tO@F1$\"1xAgQ[u'z\"Fax7$$\"1uX\"H[lu=#F1
$\"1S6u/pgG<Fax7$$\"1=Pu[\\3MAF1$\"1y$y[lK\"p;Fax7$$\"1Rze<h^(G#F1$\"1
8+KtLV/;Fax7$$\"1+)f>f0`L#F1$\"1f\\)=@5&\\:Fax7$$\"1!)f>R\"fiQ#F1$\"13
!\\w=BQ\\\"Fax7$$\"1PrU&=G]V#F1$\"1B)R![U8V9Fax7$$\"1$f=P%*z\"*[#F1$\"
1_?!*zwl*Q\"Fax7$$\"1'=PuQrg`#F1$\"10`lOZfX8Fax7$$\"1(Qxaf$H*e#F1$\"1R
VvXE&zH\"Fax7$$\"13:Ig)*zPEF1$\"1Z)RN,*fc7Fax7$$\"1uZ&44e3p#F1$\"1P/)G
g'[87Fax7$$\"1sU&3PQmt#F1$\"1Q1^Y(oz<\"Fax7$$\"1Y\"Heww()y#F1$\"1C%\\P
l0$R6Fax7$$\"1OqS\"))R\"RGF1$\"1,\\^Fcm.6Fax7$$\"1+*zf4q%*)GF1$\"1&f*z
K)G'p5Fax7$$\"1pQxa^hRHF1$\"1tm;=0?P5Fax7$$\"1Y*)yd))y()HF1$\"1?(\\*Hc
O25Fax7$$\"1lE`1f')RIF1$\"1Fmy!ow[w*F-7$$\"1_-05\"*\\*3$F1$\"1c'3`5jJ[
*F-7$$\"1\"*zf>dtTJF1$\"1]%*[[g?*>*F-7$$\"1a2:IC-*=$F1$\"1*QE>VgE&*)F-
7$$\"1Qu[(4$GTKF1$\"1x>')Q5=\"p)F-7$$\"1_-05(R8H$F1$\"1)Hrc\\,5X)F-7$$
\"1'3<M[u7M$F1$\"1.f2-@!4A)F-7$$\"1$pQxaJMR$F1$\"1$)eC%Qq,*zF-7$$\"1,-
/3,ZTMF1$\"1))4)GQ3fy(F-7$$\"1AT#[;o1\\$F1$\"1S9#\\!=^%e(F-7$$\"1LmKl'
))\\a$F1$\"1whzZj&3P(F-7$$\"1Id9H9<%f$F1$\"1d\"zf70\\=(F-7$$\"1Sze<+ZW
OF1$\"1%RVb>T<+(F-7$$\"1h@V'QAcp$F1$\"1R=YZxQAoF-7$$\"1&oOtOTEu$F1$\"1
+$eT?&RjmF-7$$\"1h>Ry?w#z$F1$\"1;,hP)=)*\\'F-7$$\"1&oOtE,D%QF1$\"1D6Ky
#RKM'F-7$$\"1oMpQnq&*QF1$\"1]Q&z4&z\"='F-7$$\"1d:Ji#eE%RF1$\"1qgTi\\GW
gF-7$$\"1[$pQdIo*RF1$\"1e'G!eg8\"*eF-7$$\"19Fa3prXSF1$\"1mR3`KxddF-7$$
\"1OqS\"Q(3%4%F1$\"18kE!zQ,j&F-7$$\"1uW*)y65YTF1$\"1\"RhEFzu\\&F-7$$\"
1tX\"HQD$)>%F1$\"1T<l)pd)o`F-7$$\"1(RzenTeC%F1$\"1)ok<!>kb_F-7$$\"14<M
o=I'H%F1$\"1CG?P*=#R^F-7$$\"16@U%3YbM%F1$\"1:2bfrAH]F-7$$\"1b3<Mt#*)R%
F1$\"1+5l$GpQ\"\\F-7$$\"1?Rycp6XWF1$\"1j1A)psr\"[F-7$$\"1Sze<u;)\\%F1$
\"1tXuFp`4ZF-7$$\"1%\\)pRw.[XF1$\"19%yXzd:h%F-7$$\"1[#\\)phU(f%F1$\"1W
[G'>hu^%F-7$$\"1CZ%*))R&ok%F1$\"1Sz<D.5EWF-7$$\"1#RycBnsp%F1$\"1*f+9I,
dL%F-7$$\"1<LmKWq]ZF1$\"1;+A8n#GC%F-7$$\"1Rxa46q*z%F1$\"1+rB:.BgTF-7$$
\"1Gb5@r1[[F1$\"1jow2s+\"3%F-7$$\"1)Gd9fp(**[F1$\"1>Qfb;w)*RF-7$$\"1^-
05&f8&\\F1$\"1&**H)ob6>RF-7$$\"\"&F*F+-%'COLOURG6&%$RGBGF*F*F*-F$6$7dw
7$F($!#CF*7$F/$!1YZ&QP+xM#!#97$F5$!1r7'[`WEI#F]\\o7$F:$!1wu4^XZ_AF]\\o
7$F?$!1<[vFm]-AF]\\o7$FD$!1di&4w3L:#F]\\o7$FI$!1S)H_nq\"3@F]\\o7$FN$!1
4A_aS\">1#F]\\o7$FS$!1kd8H/f9?F]\\o7$FX$!1$e2?vRz'>F]\\o7$Fgn$!1^,+%p'
\\?>F]\\o7$F\\o$!14**G_[;z=F]\\o7$Fao$!1M,**og9L=F]\\o7$Ffo$!1,>3%)H[(
y\"F]\\o7$F[p$!1u],VX*Ru\"F]\\o7$F`p$!1*H*[#*>%\\q\"F]\\o7$Fep$!1`$y.t
[!f;F]\\o7$Fjp$!1xQ6'\\L1i\"F]\\o7$F_q$!1;;]b5[w:F]\\o7$Fdq$!1(*[^vu(y
`\"F]\\o7$Fiq$!1S*4#G0/'\\\"F]\\o7$F^r$!12v>j\\qc9F]\\o7$Fcr$!1CWIIc=;
9F]\\o7$Fhr$!1c%3+'oWz8F]\\o7$F]s$!1.79fUKS8F]\\o7$Fbs$!1m8*o%>C+8F]\\
o7$Fgs$!16_'pm5eE\"F]\\o7$F\\t$!11B9v`5H7F]\\o7$Fat$!1q7qo-r\">\"F]\\o
7$Fft$!1kFm7Gkb6F]\\o7$F[u$!1&3RN!=B@6F]\\o7$F`u$!109ZoVe$3\"F]\\o7$Fe
u$!1N4W;#f-0\"F]\\o7$Fju$!1ygO1G?:5F]\\o7$F_v$!1Prl2,0R)*F17$Fdv$!1wQ;
@'z>]*F17$Fiv$!1Q\"pdA%o*=*F17$F^w$!1GF#GG%Go))F17$Fcw$!1'GTSEO!f&)F17
$Fhw$!1*)GXMqbS#)F17$F]x$!1OH*3_C*QzF17$Fcx$!1Oru.!Qcj(F17$Fhx$!1Gs&HE
K+M(F17$F]y$!1i5vj)RH2(F17$Fby$!15KDbw;snF17$Fgy$!1$3wxo!*z]'F17$F\\z$
!1o+pZUNJiF17$Faz$!1cWG_7WrfF17$Ffz$!1LU5;YT)o&F17$F[[l$!1ay,2C2[aF17$
F`[l$!19-d>,h!=&F17$Fe[l$!1b1_[<yT\\F17$Fj[l$!1B*)Rw)Hfo%F17$F_\\l$!11
b%[$yppWF17$Fd\\l$!1h$\\B5S&GUF17$Fi\\l$!1YQlLfv+SF17$F^]l$!1Sxv([)=yP
F17$Fc]l$!1Y+$e;y9c$F17$Fh]l$!1b@%*oP-eLF17$F]^l$!1`%36%\\IVJF17$Fb^l$
!1GTuM0rVHF17$Fg^l$!1\"Q-V:o*QFF17$F\\_l$!1*Q\\r7L$eDF17$Fa_l$!1qBF>+!
RO#F17$Ff_l$!1G2aR')y#=#F17$F[`l$!1$Rrr86r+#F17$F``l$!1\"4\"f:,%*G=F17
$Fe`l$!1Bn!RN^'p;F17$Fj`l$!1+*pfs,8^\"F17$F_al$!1Ei9,\")3U8F17$Fdal$!1
90u+'pR>\"F17$Fial$!1#=`:Y%\\Z5F17$F^bl$!1t\\BZZAP!*Fax7$Fcbl$!1-'4]eR
=w(Fax7$Fhbl$!1-wZ1u+^kFax7$F]cl$!1Fx.sG#)*>&Fax7$Fbcl$!1rVBFl@;RFax7$
Fgcl$!1(Hg(oZ^IGFax7$F\\dl$!1'yp+W@Ej\"Fax7$Fadl$!1Agz#fm*>gF-7$Ffdl$
\"1oECF642PF-7$F[el$\"1&4h6jmWO\"Fax7$F`el$\"1RP.Pm!yI#Fax7$Feel$\"1m*
zyP8(=JFax7$Fjel$\"1?K>$>@/$RFax7$F_fl$\"14OrL+ZtYFax7$Fdfl$\"1N(['f+;
CaFax7$Fifl$\"1D]8OUsFgFax7$F^gl$\"1H,(RJ#HomFax7$Fcgl$\"1VKu4K8>sFax7
$Fhgl$\"1))GRW6j:xFax7$F]hl$\"1on^!G\"oj\")Fax7$Fbhl$\"1<!p_$4Lq&)Fax7
$Fghl$\"1L$*o!*z(e%*)Fax7$F\\il$\"1\\TZr'G+C*Fax7$Fail$\"1*e4]r-L[*Fax
7$Ffil$\"1kcd'y?;p*Fax7$F[jl$\"1,\"R&3p>Y)*Fax7$F`jl$\"1tn!H*ygR**Fax7
$Fjjl$\"18!f3(Qx%***Fax7$Fe[m$\"19(pN;$p%***Fax7$F_\\m$\"1[()HLD9T**Fa
x7$Fi\\m$\"1JZ3l/GO)*Fax7$F^]m$\"1uy(QJ'G)p*Fax7$Fc]m$\"15;u:b4$\\*Fax
7$Fh]m$\"1yiz:E3L#*Fax7$F]^m$\"1?25R([5#*)Fax7$Fb^m$\"1>6<O**G%e)Fax7$
Fg^m$\"1&Rd`Wqu=)Fax7$F\\_m$\"1+_Go`dDxFax7$Fa_m$\"1\\dV:N/8sFax7$Ff_m
$\"1^i+b<bJmFax7$F[`m$\"1SuDN0xtgFax7$F``m$\"1FcN()Gt%R&Fax7$Fe`m$\"1v
W\">XT%eYFax7$Fj`m$\"1v\"o<)zC(*QFax7$F_am$\"1<kBk$*4iJFax7$Fdam$\"1)y
=@yONB#Fax7$Fiam$\"1u40=Yo+9Fax7$F^bm$\"1z2hDj=&y$F-7$Fcbm$!1Km'y$f_Td
F-7$Fhbm$!1zKBZP6r;Fax7$F]cm$!1>#RQT!*fw#Fax7$Fbcm$!1IB!zh*pgRFax7$Fgc
m$!1p\"\\<Ay[5&Fax7$F\\dm$!1&>+C.U&*Q'Fax7$Fadm$!1Mw$z;a%zxFax7$Ffdm$!
1i?ZReUN!*Fax7$F[em$!1U00.`+W5F17$F`em$!1$RXCbnV>\"F17$Feem$!13jPz7jY8
F17$Fjem$!1bI\"fN:))\\\"F17$F_fm$!1h&4F1\"Rt;F17$Fdfm$!1Fg)z_#GN=F17$F
ifm$!1,&*\\]#*Q8?F17$F^gm$!11aIOcYz@F17$Fcgm$!1\">V-3GhO#F17$Fhgm$!1&R
ApbCma#F17$F]hm$!1\\p\"=6M.u#F17$Fbhm$!1\\\">1y*pMHF17$Fghm$!1BMW4uXVJ
F17$F\\im$!1)*=7amh\\LF17$Faim$!1)fj<b?cc$F17$Ffim$!1*oU*Q_+&y$F17$F[j
m$!1BK?eb8\"*RF17$F`jm$!1+YA))*HFB%F17$Fejm$!18(Qy?_OX%F17$Fjjm$!1SjRz
EB%p%F17$F_[n$!1uX#QEi$H\\F17$Fd[n$!1)*3@#z;g>&F17$Fi[n$!1uv<#3e;V&F17
$F^\\n$!19-eB8W/dF17$Fc\\n$!1`m+.\"))z&fF17$Fh\\n$!1qnllsrSiF17$F]]n$!
1B>$Gd*=*['F17$Fb]n$!1t%G'\\eFxnF17$Fg]n$!1cf>m_rgqF17$F\\^n$!1!4ibVP!
\\tF17$Fa^n$!1*>w\"esLTwF17$Ff^n$!1txseA)o#zF17$F[_n$!1g'*pHZyS#)F17$F
`_n$!1(H,5v/]a)F17$Fe_n$!1/zzJL]q))F17$Fj_n$!1>Y+gS')p\"*F17$F_`n$!1gx
0=h\"f]*F17$Fd`n$!1yO&p3<H$)*F17$Fi`n$!17MN<:T;5F]\\o7$F^an$!1A)=pwP:0
\"F]\\o7$Fcan$!1CMX];P%3\"F]\\o7$Fhan$!1g;pBkZ=6F]\\o7$F]bn$!1I%HPY%pc
6F]\\o7$Fbbn$!1Y(3i#o!=>\"F]\\o7$Fgbn$!1W(44<;#G7F]\\o7$F\\cn$!1a)4B[i
dE\"F]\\o7$Facn$!1\")*\\/WO2I\"F]\\o7$Ffcn$!16)G$=W]Q8F]\\o7$F[dn$!1.%
[*)f\"[w8F]\\o7$F`dn$!1p,R*4`wT\"F]\\o7$Fedn$!1ftL<aXa9F]\\o7$Fjdn$!1y
;ijaY(\\\"F]\\o7$F_en$!1ToSIDyO:F]\\o7$Fden$!1K'f'[^:w:F]\\o7$Fien$!1:
Ic)\\:!>;F]\\o7$F^fn$!1![#3-Ofi;F]\\o7$Fcfn$!1PMm`rr-<F]\\o7$Fhfn$!1Y;
Ru4#eu\"F]\\o7$F]gn$!1MO=xqP)y\"F]\\o7$Fbgn$!1^:8ph0N=F]\\o7$Fggn$!1%z
[fZ1f(=F]\\o7$F\\hn$!1v\\m65NB>F]\\o7$Fahn$!1D9@PYYo>F]\\o7$Ffhn$!1t9s
QFj8?F]\\o7$F[in$!1\\rX*>D$f?F]\\o7$F`in$!1txL[>V1@F]\\o7$Fein$!1*o_1E
>p:#F]\\o7$Fjin$!1z$*4uIr.AF]\\o7$F_jn$!1WW2\"[v.D#F]\\o7$Fdjn$!1_p$\\
?u2I#F]\\o7$Fijn$!11lx*4'f^BF]\\o7$F^[oFh[o-Fa[o6&Fc[o$\"*++++\"!\")F*
F*-F$6$7dw7$F($\"$,'F*7$F/$\"1)=$y#3nkv&!#87$F5$\"14ET2jVUbF\\bq7$F:$
\"1C:Xe!*))3`F\\bq7$F?$\"1z$z!3hG\"3&F\\bq7$FD$\"1'f1h\\p?'[F\\bq7$FI$
\"1B?Uj1?lYF\\bq7$FN$\"1Q%)ot4onWF\\bq7$FS$\"1(**y+kL+F%F\\bq7$FX$\"1D
CtU3ezSF\\bq7$Fgn$\"1Db1@sN!*QF\\bq7$F\\o$\"1Z2JFq<HPF\\bq7$Fao$\"1&*H
:<\"RPb$F\\bq7$Ffo$\"1F0z;P%QQ$F\\bq7$F[p$\"1nyO?k\"fA$F\\bq7$F`p$\"16
B+(R@t3$F\\bq7$Fep$\"1fy!GcZ$GHF\\bq7$Fjp$\"1vwLyi^)z#F\\bq7$F_q$\"1]c
!RiSHl#F\\bq7$Fdq$\"1jvCx[&)GDF\\bq7$Fiq$\"1rw'[JTxR#F\\bq7$F^r$\"1+S7
Y)fwF#F\\bq7$Fcr$\"1\"=6DI+s:#F\\bq7$Fhr$\"1N!)eD$=30#F\\bq7$F]s$\"1Ol
bX:]S>F\\bq7$Fbs$\"1')\\9:LlI=F\\bq7$Fgs$\"1M%*H6x&)Q<F\\bq7$F\\t$\"1Q
zrg0hV;F\\bq7$Fat$\"1\"=)R\"RW$\\:F\\bq7$Fft$\"1!QD<fu5Y\"F\\bq7$F[u$
\"1<9iPRGz8F\\bq7$F`u$\"1:FW?N^#H\"F\\bq7$Feu$\"1?KOV.2=7F\\bq7$Fju$\"
1p,p=q:U6F\\bq7$F_v$\"1^kGr&fk2\"F\\bq7$Fdv$\"1v<Ujf*y+\"F\\bq7$Fiv$\"
1D>^R!)*RY*F]\\o7$F^w$\"1N$y./v9&))F]\\o7$Fcw$\"16:K.Qh\"G)F]\\o7$Fhw$
\"1)Q_ssLZr(F]\\o7$F]x$\"10G$pqWl>(F]\\o7$Fcx$\"1o9!GdgQp'F]\\o7$Fhx$
\"1C5U)e5;A'F]\\o7$F]y$\"1&**)*z\"=%*4eF]\\o7$Fby$\"1(461CUMO&F]\\o7$F
gy$\"1Hc*zM$>')\\F]\\o7$F\\z$\"17&*y+I61YF]\\o7$Faz$\"1+p<)=bHE%F]\\o7
$Ffz$\"1]73Yvk/RF]\\o7$F[[l$\"1<F\"f`cHh$F]\\o7$F`[l$\"1_j0LJ$>I$F]\\o
7$Fe[l$\"1^K&)f))HOIF]\\o7$Fj[l$\"1&p#HooQkFF]\\o7$F_\\l$\"16o'pl*yWDF
]\\o7$Fd\\l$\"15E&*\\\"44J#F]\\o7$Fi\\l$\"1I?V(R!o+@F]\\o7$F^]l$\"1'Gy
On*G0>F]\\o7$Fc]l$\"1>9:*[gXs\"F]\\o7$Fh]l$\"1jA<SZVj:F]\\o7$F]^l$\"1F
0R*3nBS\"F]\\o7$Fb^l$\"1p2rCU\"4E\"F]\\o7$Fg^l$\"1(\\e/Z\"4C6F]\\o7$F
\\_l$\"1O>m^,M55F]\\o7$Fa_l$\"1#G)Q?L#>&*)F17$Ff_l$\"1*y[W)[NZzF17$F[`
l$\"1O)GTD1c.(F17$F``l$\"1Y%4?1iR<'F17$Fe`l$\"1x#4v*pQdaF17$Fj`l$\"1)
\\*)GjM`z%F17$F_al$\"15XQs&)GVTF17$Fdal$\"1xHB3I`>OF17$Fial$\"1ux`3\"R
Z9$F17$F^bl$\"1gQ/'yO/s#F17$Fcbl$\"1\"=Nf\\X'yBF17$Fhbl$\"1\\?B1dDh?F1
7$F]cl$\"1S%4i'QO!z\"F17$Fbcl$\"1t_gr\"*)\\a\"F17$Fgcl$\"1JxV:'pJO\"F1
7$F\\dl$\"1MFnrm\"**=\"F17$Fadl$\"1)z0dmBQ1\"F17$Ffdl$\"1:9!>TLIk*Fax7
$F[el$\"1<Tf(G5<#))Fax7$F`el$\"1e*f.^!zC#)Fax7$Feel$\"1\"yca$R#R&yFax7
$Fjel$\"1BqR#))*R9wFax7$F_fl$\"1*H))==i1^(Fax7$Fdfl$\"1@,iv6*z^(Fax7$F
ifl$\"1JRb5<i0wFax7$F^gl$\"1\"=&[C*>$yxFax7$Fcgl$\"1M&e-AbC*zFax7$Fhgl
$\"1j'R7DluB)Fax7$F]hl$\"1@#pW#z)3])Fax7$Fbhl$\"1%*Qt)HEZx)Fax7$Fghl$
\"1\\1u6`*p0*Fax7$F\\il$\"1$G#\\8Vy(H*Fax7$Fail$\"1O7WB.+5&*Fax7$Ffil$
\"1&)G]g08,(*Fax7$F[jl$\"1%RLwWi&[)*Fax7$F`jl$\"1*omNhs*R**Fax7$Fjjl$
\"1$f,@gwZ***Fax7$Fe[m$\"1/5#)zfp%***Fax7$F_\\m$\"1(RPM&*)[T**Fax7$Fi
\\m$\"1>gpt3'*Q)*Fax7$F^]m$\"1:srG%*Q2(*Fax7$Fc]m$\"1OxNJ2z=&*Fax7$Fh]
m$\"1mc@V))*=H*Fax7$F]^m$\"1N.W@BYP!*Fax7$Fb^m$\"1cPlMMr%y)Fax7$Fg^m$
\"1(o-Sy'*f^)Fax7$F\\_m$\"1,.#)3h(GC)Fax7$Fa_m$\"1@77ghv*)zFax7$Ff_m$
\"1)REH6'>mxFax7$F[`m$\"11(QiJ)H:wFax7$F``m$\"16gB09e:vFax7$Fe`m$\"1Hq
<Cim6vFax7$Fj`m$\"1O9P,ig@wFax7$F_am$\"1>SpuyyPyFax7$Fdam$\"1o*)et=Ll#
)Fax7$Fiam$\"1([t=72bz)Fax7$F^bm$\"18&eH+4ej*Fax7$Fcbm$\"1'=)Qr<rg5F17
$Fhbm$\"1[_G'eP]>\"F17$F]cm$\"1E%y521JN\"F17$Fbcm$\"1]FUw8%Hb\"F17$Fgc
m$\"11QwQc3r<F17$F\\dm$\"13\"yqn;s/#F17$Fadm$\"1'=/$)[WJQ#F17$Ffdm$\"1
,K&\\yJ*>FF17$F[em$\"1)>[eP_R8$F17$F`em$\"1!zzFS\")3i$F17$Feem$\"1y4(>
3Z+;%F17$Fjem$\"1IQ.FGEXZF17$F_fm$\"1$zl9rGOZ&F17$Fdfm$\"13o^&[WN?'F17
$Fifm$\"1Xk_Cb7nqF17$F^gm$\"1M:9'4O&HzF17$Fcgm$\"1;&eB<!pk*)F17$Fhgm$
\"1eU3>@>.5F]\\o7$F]hm$\"1a/i:l(\\7\"F]\\o7$Fbhm$\"1C&)Heira7F]\\o7$Fg
hm$\"1=GW*=yCS\"F]\\o7$F\\im$\"1n#p$Q[&pb\"F]\\o7$Faim$\"1bA4Zq#zs\"F]
\\o7$Ffim$\"1Hmx*)p76>F]\\o7$F[jm$\"1Qd@g)H?4#F]\\o7$F`jm$\"1US99L([J#
F]\\o7$Fejm$\"1NDi>q')GDF]\\o7$Fjjm$\"1()3x7`+tFF]\\o7$F_[n$\"1IU=fuzA
IF]\\o7$Fd[n$\"1`[rH2Y>LF]\\o7$Fi[n$\"1`iQgnX$f$F]\\o7$F^\\n$\"1!)\\x8
#4X#RF]\\o7$Fc\\n$\"1Zv&Q.hbC%F]\\o7$Fh\\n$\"1GBbDps=YF]\\o7$F]]n$\"1[
#)\\)3x)f\\F]\\o7$Fb]n$\"1\"ee\"zV(3P&F]\\o7$Fg]n$\"1f)[O`T9z&F]\\o7$F
\\^n$\"18b[m)QdB'F]\\o7$Fa^n$\"1&zO^BPJq'F]\\o7$Ff^n$\"1!4Y-YMi<(F]\\o
7$F[_n$\"1w]4p<8:xF]\\o7$F`_n$\"1-Oc%46iD)F]\\o7$Fe_n$\"1iN7pKjb))F]\\
o7$Fj_n$\"1,p*Q4FcU*F]\\o7$F_`n$\"1\"3;Od$o35F\\bq7$Fd`n$\"1$fe_v\">v5
F\\bq7$Fi`n$\"11SMCNtW6F\\bq7$F^an$\"11&[>X&)3A\"F\\bq7$Fcan$\"1CCNT!*
H%H\"F\\bq7$Fhan$\"1_Ks_r$GP\"F\\bq7$F]bn$\"1d_zG:hj9F\\bq7$Fbbn$\"1Q'
=O>%e\\:F\\bq7$Fgbn$\"1o^dzlLT;F\\bq7$F\\cn$\"1*=a)44tQ<F\\bq7$Facn$\"
1%[f:$*))>$=F\\bq7$Ffcn$\"1H'=(>XWN>F\\bq7$F[dn$\"1#RQ@v\\B/#F\\bq7$F`
dn$\"1r&\\,i0:;#F\\bq7$Fedn$\"1Edv-h)3F#F\\bq7$Fjdn$\"1b=5h$\\@S#F\\bq
7$F_en$\"1QV!))zy`_#F\\bq7$Fden$\"1IA^n0)=l#F\\bq7$Fien$\"1\\NWMF6$z#F
\\bq7$F^fn$\"1WQ*e%oZSHF\\bq7$Fcfn$\"1ggu?u^zIF\\bq7$Fhfn$\"1i\\1sHZKK
F\\bq7$F]gn$\"1TU\"zFIrQ$F\\bq7$Fbgn$\"1<4ygn$4c$F\\bq7$Fggn$\"1-:5adh
;PF\\bq7$F\\hn$\"1#=R_@9;!RF\\bq7$Fahn$\"1\\In\"\\*p\"3%F\\bq7$Ffhn$\"
1'3B.3!3mUF\\bq7$F[in$\"1T\\1(z_nX%F\\bq7$F`in$\"1U=\"yu)pdYF\\bq7$Fei
n$\"18)RIi#*z([F\\bq7$Fjin$\"1vkO?Es'3&F\\bq7$F_jn$\"1z%GRNF#*H&F\\bq7
$Fdjn$\"1cpfi$RO`&F\\bq7$Fijn$\"1E<YEQ;vdF\\bq7$F^[oFgaq-Fa[o6&Fc[oF*F
*F`aq-%*THICKNESSG6#\"\"$-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F(F^[o;$
!\"\"F*$\"\"\"F*" 1 2 0 1 3 2 9 1 4 2 1.000000 45.000000 45.000000 0 }
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Ca diverge tr�s rapidement." }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "Essayons avec les polyn™mes inter
polateurs de Lagrange. Premi�re dŽfinition des xi :" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 23 "x1:=(i,n) -> -5+10*i/n;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%#x1GR6$%\"iG%\"nG6\"6$%)operatorG%&arrowGF),&!\"&
\"\"\"*&9$\"\"\"9%!\"\"\"#5F)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
122 "La fonction suivante renvoie le i-i�me polynome interpolateur de \+
Lagrange de degrŽ n, pour les points dŽfinis par x(i,n) :" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 79 "Cette fonction ne marche que si x est dŽf
inie et si i, n ont chacun une valeur." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 106 "La:=(i,n,x) -> product((X-x(j,n))/(x(i,n)-x(j,n)),j=
0..i-1)*\nproduct((X-x(j,n))/(x(i,n)-x(j,n)),j=i+1..n);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%#LaGR6%%\"iG%\"nG%\"xG6\"6$%)operatorG%&arrowG
F**&-%(productG6$*&,&%\"XG\"\"\"-9&6$%\"jG9%!\"\"\"\"\",&-F76$9$F:F5F6
F;!\"\"/F9;\"\"!,&F@F5F;F5F5-F06$F2/F9;,&F@F5F5F5F:F5F*F*F*" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 99 "A partir des poyn™mes La, on const
ruit le polyn™me interpolateur en les x(i,n) pour la fonction f :" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 114 "Les '' autour de La(i,n,x) indiqu
ent ˆ Maple de ne pas calculer La(i,n,x) avant de donner une valeur ˆ \+
i, n et x. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "fLa:=(f,n,x)
 -> sum(f(x(i,n))*'La(i,n,x)',i=0..n);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$fLaGR6%%\"fG%\"nG%\"xG6\"6$%)operatorG%&arrowGF*-%$sumG6$*&-9
$6#-9&6$%\"iG9%\"\"\".-%#LaG6%F8F9F6F:/F8;\"\"!F9F*F*F*" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 9 "Exemple :" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "fLa(f,2,x1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&%
\"XG\"\"\",&F%#!\"\"\"#5#F&\"\"#F&F&#F)\"$I\"*&,&F%#F&\"\"&F&F&F&,&F%#
F)F2F&F&F&F&*&,&F%#F&F*F+F&F&F%\"\"\"#F&F." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 120 "plot([f(X),fLa(f,5,x1),fLa(f,15,x1),fLa(f,20,x1)],
X=-5..5,-1..1,color=[black,red,blue,green],numpoints=200,thickness=3);
" }}{PARA 13 "" 1 "" {GLPLOT2D 398 200 200 {PLOTDATA 2 "6)-%'CURVESG6$
7hw7$$!\"&\"\"!$\"1YQ:YQ:YQ!#<7$$!1V([(\\RUZ\\!#:$\"1'4%zX$3^#RF-7$$!1
Qxa4yn,\\F1$\"1%ot`@td*RF-7$$!1hAX!\\J-&[F1$\"1V()fyU^xSF-7$$!1%ze<:W%
)z%F1$\"1zVvA%>B;%F-7$$!1JiC\\H!pu%F1$\"145BahL\\UF-7$$!1?Rycw6*p%F1$
\"1\\uc^_VKVF-7$$!1d8Fa(Q'\\YF1$\"1ijdoW.@WF-7$$!1jD^-wY)f%F1$\"1)\\\"
**Qw]:XF-7$$!1KkGd0YZXF1$\"1;B85Vn7YF-7$$!1V&3<a$*\\\\%F1$\"1;y?^i(er%
F-7$$!1X\"Hec!y[WF1$\"1gidNMi4[F-7$$!18D]+dv'R%F1$\"1!)3uld[=\\F-7$$!1
-/3;s^WVF1$\"1'**=yh*[J]F-7$$!1>Rycd<%H%F1$\"14)>;OZS9&F-7$$!1CZ%*))3Y
[UF1$\"1ck7!o.&\\_F-7$$!1OsW*[,T>%F1$\"19c0X^4z`F-7$$!1$pQx%>0[TF1$\"1
!=K6m$f#\\&F-7$$!1&3<MQ&[%4%F1$\"1e**>0f5HcF-7$$!1Pu[(*)pq/%F1$\"1%)3F
$eXTv&F-7$$!1iBZ%fZ]*RF1$\"1P*p,_&3'*eF-7$$!1&**)zf+^XRF1$\"1?w6qx2OgF
-7$$!1zf>RG#Q*QF1$\"16^%G13u='F-7$$!1#Ryc$yNYQF1$\"1\\%y1XI8L'F-7$$!1F
a3</;&z$F1$\"1'pYB_R@\\'F-7$$!1)pRzo!)>u$F1$\"1B$o0_\"flmF-7$$!1NpQxvo
&p$F1$\"1U%y%zM;AoF-7$$!1V([(\\(*oXOF1$\"13nKRYQ(*pF-7$$!1Qv],r.%f$F1$
\"1Cv/=OS&=(F-7$$!1e:Ji]]VNF1$\"1#=e-NulP(F-7$$!1-/3;Fh%\\$F1$\"1K()G(
e%povF-7$$!1Qv],hKSMF1$\"1g+bUQo!z(F-7$$!1&4>Q;Z:R$F1$\"1&oN(e8M)*zF-7
$$!1/4=O_YRLF1$\"1yxs'3z!H#)F-7$$!1@U%)o7F#H$F1$\"1*pVlfBmW)F-7$$!1D\\
)pzv1C$F1$\"1;g``b:%p)F-7$$!1sW*)y%G@>$F1$\"1Lp.#o-o$*)F-7$$!1!3;Ka#QT
JF1$\"180!3J%3,#*F-7$$!1!*yd:\"p<4$F1$\"1DhM!Gh0Z*F-7$$!1pQxa%G)RIF1$
\"1=^W*z$4l(*F-7$$!1Gc7DM!)*)HF1$\"10oFz]915!#;7$$!1w^.2ckQHF1$\"1N_+)
*R\"y.\"Fax7$$!1Pv],9\"z)GF1$\"18a?8,mq5Fax7$$!1#Ryc$>HTGF1$\"1[`q#ey@
5\"Fax7$$!1rT$owgyy#F1$\"1#GhB4p*R6Fax7$$!17BY#Hr+u#F1$\"1C.U\\cOv6Fax
7$$!1JhAXx6*o#F1$\"1ny9Ap'[@\"Fax7$$!1v\\**)p[.k#F1$\"1s)G6HyWD\"Fax7$
$!1<NqSp>'e#F1$\"1S_-j#e1I\"Fax7$$!1C\\)p\\0$RDF1$\"13P[n#HEM\"Fax7$$!
1CZ%*)G$3'[#F1$\"1'=@3KRER\"Fax7$$!1.17CqdPCF1$\"1AFT[BbS9Fax7$$!1PtY$
z=XQ#F1$\"1%H#Ql#yc\\\"Fax7$$!1Ryc8&Q(QBF1$\"1L_hSsmX:Fax7$$!1lHf=,g'G
#F1$\"1zW)>m7bg\"Fax7$$!1v],.qBOAF1$\"1x\"[:rckm\"Fax7$$!16AW)y1f=#F1$
\"1Jzy3ikI<Fax7$$!1T#['H<wN@F1$\"1#Q,y6$3)z\"Fax7$$!1mJjE!)e(3#F1$\"1h
&4$o(fj'=Fax7$$!1Z%*)y(4^N?F1$\"1#QZF:vU%>Fax7$$!1f=Pux(e)>F1$\"1>/c_@
xA?Fax7$$!1?T#[;TO$>F1$\"1'3p2+k,6#Fax7$$!1d8FaWN')=F1$\"1w#4rP%y$>#Fa
x7$$!1tY$py$4M=F1$\"19*\\+@G:H#Fax7$$!1f=Pur.%y\"F1$\"1%*))>O&\\2R#Fax
7$$!1D]+,C5M<F1$\"1$\\QlUjb\\#Fax7$$!1<MoO`%>o\"F1$\"1!*R)ez)o6EFax7$$
!15>Qwn!Rj\"F1$\"1@`g<X0DFFax7$$!1!*zf>(3Ze\"F1$\"1Fr_`m%z%GFax7$$!1xa
4>#)QI:F1$\"10u;\\89#*HFax7$$!1#Qw_X07[\"F1$\"1Tfm!=+48$Fax7$$!1qT$o'o
!4V\"F1$\"1`oLUTQ\"G$Fax7$$!1\\**)z\\a(z8F1$\"1Pc=)GbQW$Fax7$$!1Fa3<bt
K8F1$\"1Gokvn1-OFax7$$!1],.1[h#G\"F1$\"1lt)\\Mu0y$Fax7$$!1Fa3<c(GB\"F1
$\"13.'3'=GoRFax7$$!1V'Gd9q'z6F1$\"1W-AlLE\"=%Fax7$$!1`06A'=F8\"F1$\"1
@76FF5!Q%Fax7$$!1kFb5jay5F1$\"1R(4lE[Ei%Fax7$$!1(Rze(*f'H5F1$\"1U:#pY)
*Q&[Fax7$$!1_2:I]*G\")*Fax$\"1.wdNvU%4&Fax7$$!1'Qw_0dFH*Fax$\"13M,BF4m
`Fax7$$!1v`2:]^q()Fax$\"1zT:Q/@_cFax7$$!1PrU&3_`H)Fax$\"1a`B+\">P#fFax
7$$!1;S!3;]2z(Fax$\"1YJWg%QHA'Fax7$$!1$*******zI)H(Fax$\"1b7c'4MY_'Fax
7$$!1gD^-b\\knFax$\"1k$*[#4o1'oFax7$$!13>Qw#*f-jFax$\"1Y5HG-.drFax7$$!
1.<MoY4sdFax$\"1H>6QX\"4](Fax7$$!1yhBZCRt_Fax$\"1nbjma>CyFax7$$!1R'Gd9
2&zZFax$\"1913cjUS\")Fax7$$!1lQxa*G_G%Fax$\"1[fUnFd[%)Fax7$$!1'=Pu['4
\"y$Fax$\"1A,-.(f\"\\()Fax7$$!1Wze<XsYKFax$\"1k9ha\"*RY!*Fax7$$!19Pu[x
vcFFax$\"1&*3th]q$H*Fax7$$!1Le;Lw4tAFax$\"1j%4'R')o3&*Fax7$$!1U#['HH2c
<Fax$\"1*H!)=2Y3q*Fax7$$!1\"f=Put,C\"Fax$\"1RA,;m_[)*Fax7$$!1lpRzeBrxF
-$\"1RS;C/(*R**Fax7$$!1l#f=Pa'G]F-$\"1'z(**=kxu**Fax7$$!1k:KkG2'G#F-$
\"1c\\n+mx%***Fax7$$\"1gv-/3;#z)!#?$\"0\"zpA********F17$$\"1?'Hf=dOI#F
-$\"1esKyfp%***Fax7$$\"1;**)zffx)\\F-$\"1o%H3*R=v**Fax7$$\"17-05?'=n(F
-$\"1\"pEk#p[T**Fax7$$\"1W$pQxdL-\"Fax$\"1E,pv#fj*)*Fax7$$\"1oOtY$H&z7
Fax$\"1Eo0(p<*Q)*Fax7$$\"1;Pu[2*pt\"Fax$\"1-iD>G72(*Fax7$$\"1+&)pRRX^A
Fax$\"1zcUo5b<&*Fax7$$\"1rJjEtKpFFax$\"1BSt=%4xG*Fax7$$\"1'ze<NRZG$Fax
$\"1kPz%4Dh-*Fax7$$\"16>QwAfiPFax$\"1Q'ej2e)f()Fax7$$\"1Tv],8QdUFax$\"
1Hc([G(el%)Fax7$$\"1ta4>G4pZFax$\"1y?+)Q@q9)Fax7$$\"1)yc8Fj\"z_Fax$\"1
[(*)3Dp/#yFax7$$\"1\"oNrULQ!eFax$\"1)=W^u*H![(Fax7$$\"1Y'Hf=jfE'Fax$\"
1vyf[Xp!=(Fax7$$\"1%)f>R=@'y'Fax$\"1Qz)G*\\%o%oFax7$$\"1)3<Mo'f3tFax$
\"1l&3)oDC=lFax7$$\"1=>Qw7,7yFax$\"1&\\-7h=,@'Fax7$$\"1tQxa*f\"p#)Fax$
\"1QoalE)*QfFax7$$\"1Y([(\\Rv7))Fax$\"1+iQxAeGcFax7$$\"1mT$oO\\KF*Fax$
\"1v;n#)>aw`Fax7$$\"1c-05]\"*3)*Fax$\"1D.%>;bk4&Fax7$$\"1tY$p)pIG5F1$
\"1aQ#*)\\n/'[Fax7$$\"1\\(\\**GH.3\"F1$\"1Ikn-vV9YFax7$$\"1:JiCo')H6F1
$\"1v+v.q^#R%Fax7$$\"1JhAXSb\"=\"F1$\"1#eQ2%3]tTFax7$$\"1>Pu[!>!H7F1$
\"1Rn&oe*G$)RFax7$$\"1%oOtY;-G\"F1$\"1i**R%*)z$*y$Fax7$$\"17C['>'RL8F1
$\"1_h%Hv#y*f$Fax7$$\"1x^.2$*oz8F1$\"1S'pVloSW$Fax7$$\"1nLnMroH9F1$\"1
sOz$RX^G$Fax7$$\"1sX\"HyR8[\"F1$\"1&[uc8508$Fax7$$\"1a06A=(=`\"F1$\"1!
[#R/%z!))HFax7$$\"14<MoTw!e\"F1$\"1;0(4C5\"eGFax7$$\"1uX\"Hy]]j\"F1$\"
1vk=m-GAFFax7$$\"1:Ig?(HQo\"F1$\"1ZaDU)ptg#Fax7$$\"117C[;\"ft\"F1$\"18
FCO'f;\\#Fax7$$\"1!*yd:c5$y\"F1$\"1&zM(p.l#R#Fax7$$\"1&=Pu3,Z$=F1$\"1w
tlH)e.H#Fax7$$\"1Rw_0%[K)=F1$\"1!Qv,'QV*>#Fax7$$\"1Jg?TV*R$>F1$\"1!z]N
%fb4@Fax7$$\"1@U%)oxg$)>F1$\"1%=l8tlk-#Fax7$$\"1U#['H%[b.#F1$\"1AkG=v@
W>Fax7$$\"1$['HfMd&3#F1$\"1Flv>GHp=Fax7$$\"1MpQx7tO@F1$\"1xAgQ[u'z\"Fa
x7$$\"1uX\"H[lu=#F1$\"1S6u/pgG<Fax7$$\"1=Pu[\\3MAF1$\"1y$y[lK\"p;Fax7$
$\"1Rze<h^(G#F1$\"18+KtLV/;Fax7$$\"1+)f>f0`L#F1$\"1f\\)=@5&\\:Fax7$$\"
1!)f>R\"fiQ#F1$\"13!\\w=BQ\\\"Fax7$$\"1PrU&=G]V#F1$\"1B)R![U8V9Fax7$$
\"1$f=P%*z\"*[#F1$\"1_?!*zwl*Q\"Fax7$$\"1'=PuQrg`#F1$\"10`lOZfX8Fax7$$
\"1(Qxaf$H*e#F1$\"1RVvXE&zH\"Fax7$$\"13:Ig)*zPEF1$\"1Z)RN,*fc7Fax7$$\"
1uZ&44e3p#F1$\"1P/)Gg'[87Fax7$$\"1sU&3PQmt#F1$\"1Q1^Y(oz<\"Fax7$$\"1Y
\"Heww()y#F1$\"1C%\\Pl0$R6Fax7$$\"1OqS\"))R\"RGF1$\"1,\\^Fcm.6Fax7$$\"
1+*zf4q%*)GF1$\"1&f*zK)G'p5Fax7$$\"1pQxa^hRHF1$\"1tm;=0?P5Fax7$$\"1Y*)
yd))y()HF1$\"1?(\\*HcO25Fax7$$\"1lE`1f')RIF1$\"1Fmy!ow[w*F-7$$\"1_-05
\"*\\*3$F1$\"1c'3`5jJ[*F-7$$\"1\"*zf>dtTJF1$\"1]%*[[g?*>*F-7$$\"1a2:IC
-*=$F1$\"1*QE>VgE&*)F-7$$\"1Qu[(4$GTKF1$\"1x>')Q5=\"p)F-7$$\"1_-05(R8H
$F1$\"1)Hrc\\,5X)F-7$$\"1'3<M[u7M$F1$\"1.f2-@!4A)F-7$$\"1$pQxaJMR$F1$
\"1$)eC%Qq,*zF-7$$\"1,-/3,ZTMF1$\"1))4)GQ3fy(F-7$$\"1AT#[;o1\\$F1$\"1S
9#\\!=^%e(F-7$$\"1LmKl'))\\a$F1$\"1whzZj&3P(F-7$$\"1Id9H9<%f$F1$\"1d\"
zf70\\=(F-7$$\"1Sze<+ZWOF1$\"1%RVb>T<+(F-7$$\"1h@V'QAcp$F1$\"1R=YZxQAo
F-7$$\"1&oOtOTEu$F1$\"1+$eT?&RjmF-7$$\"1h>Ry?w#z$F1$\"1;,hP)=)*\\'F-7$
$\"1&oOtE,D%QF1$\"1D6Ky#RKM'F-7$$\"1oMpQnq&*QF1$\"1]Q&z4&z\"='F-7$$\"1
d:Ji#eE%RF1$\"1qgTi\\GWgF-7$$\"1[$pQdIo*RF1$\"1e'G!eg8\"*eF-7$$\"19Fa3
prXSF1$\"1mR3`KxddF-7$$\"1OqS\"Q(3%4%F1$\"18kE!zQ,j&F-7$$\"1uW*)y65YTF
1$\"1\"RhEFzu\\&F-7$$\"1tX\"HQD$)>%F1$\"1T<l)pd)o`F-7$$\"1(RzenTeC%F1$
\"1)ok<!>kb_F-7$$\"14<Mo=I'H%F1$\"1CG?P*=#R^F-7$$\"16@U%3YbM%F1$\"1:2b
frAH]F-7$$\"1b3<Mt#*)R%F1$\"1+5l$GpQ\"\\F-7$$\"1?Rycp6XWF1$\"1j1A)psr
\"[F-7$$\"1Sze<u;)\\%F1$\"1tXuFp`4ZF-7$$\"1%\\)pRw.[XF1$\"19%yXzd:h%F-
7$$\"1[#\\)phU(f%F1$\"1W[G'>hu^%F-7$$\"1CZ%*))R&ok%F1$\"1Sz<D.5EWF-7$$
\"1#RycBnsp%F1$\"1*f+9I,dL%F-7$$\"1<LmKWq]ZF1$\"1;+A8n#GC%F-7$$\"1Rxa4
6q*z%F1$\"1+rB:.BgTF-7$$\"1Gb5@r1[[F1$\"1jow2s+\"3%F-7$$\"1)Gd9fp(**[F
1$\"1>Qfb;w)*RF-7$$\"1^-05&f8&\\F1$\"1&**H)ob6>RF-7$$\"\"&F*F+-%'COLOU
RG6&%$RGBGF*F*F*-F$6$7dw7$F($\"1,R:YQ:YQF-7$F/$\"1od9nzo!\\#F-7$F5$\"1
]#\\`1;tS\"F-7$F:$\"1$zINY'[GH!#=7$F?$!1v#Q*)eb!4sFc\\o7$FD$!127iaZ@D;
F-7$FI$!1>sFfM,tBF-7$FN$!1HTHPE/eIF-7$FS$!1D(=E))3Pn$F-7$FX$!1eglbKJ'>
%F-7$Fgn$!1vBW1j%>k%F-7$F\\o$!1ZzwKXhf\\F-7$Fao$!1'[C1R-gB&F-7$Ffo$!1^
3afZuHaF-7$F[p$!1)=<?a,(RbF-7$F`p$!1SPF)R`kd&F-7$Fep$!1^zB_HnWbF-7$Fjp
$!1\"=<]l(ybaF-7$F_q$!1KRl$e?NG&F-7$Fdq$!1p=ueqYr]F-7$Fiq$!1[%)fVL$px%
F-7$F^r$!1(p$H^igQWF-7$Fcr$!1Z]FXJ(y-%F-7$Fhr$!1%4`pay3g$F-7$F]s$!1s1d
/J5*3$F-7$Fbs$!1a18M6s.DF-7$Fgs$!1QR087`^>F-7$F\\t$!1J[p(peEJ\"F-7$Fat
$!1y40!G8\\3'Fc\\o7$Fft$\"1z1-yvH;7Fc\\o7$F[u$\"1`'))ex\"e[')Fc\\o7$F`
u$\"1aoZ%Ge,t\"F-7$Feu$\"1r(HU!yfTDF-7$Fju$\"1+EjQAHTMF-7$F_v$\"1w%RZ=
iWG%F-7$Fdv$\"1*=aL#\\nM_F-7$Fiv$\"1i1B5Z/ahF-7$F^w$\"1ow\\7ZQRrF-7$Fc
w$\"1#4[wwu\\7)F-7$Fhw$\"1Z,Ou4Vy\"*F-7$F]x$\"1kg)oC87-\"Fax7$Fcx$\"1(
yioPy'G6Fax7$Fhx$\"1')*GYZEoB\"Fax7$F]y$\"1+*GO8LuL\"Fax7$Fby$\"1ey#Hm
5SX\"Fax7$Fgy$\"1U1Q>UFf:Fax7$F\\z$\"1w>#)[%zBn\"Fax7$Faz$\"1/k*4+H8y
\"Fax7$Ffz$\"1wxj#QAH!>Fax7$F[[l$\"1PF=_nf3?Fax7$F`[l$\"1<,!GD2)G@Fax7
$Fe[l$\"13@&Qgt%QAFax7$Fj[l$\"1ua4F3ReBFax7$F_\\l$\"10wM\"R,<Y#Fax7$Fd
\\l$\"1jELv?/zDFax7$Fi\\l$\"1<*pktH>p#Fax7$F^]l$\"1Xt%*3'fT!GFax7$Fc]l
$\"1M/A8nE:HFax7$Fh]l$\"1xmq^9A@IFax7$F]^l$\"17WW\">pZ8$Fax7$Fb^l$\"1,
mO1\"4>C$Fax7$Fg^l$\"1SBp4WS`LFax7$F\\_l$\"1pONC/6`MFax7$Fa_l$\"1K=)30
N=c$Fax7$Ff_l$\"1cxJ<$=Wm$Fax7$F[`l$\"1$>gD;H^w$Fax7$F``l$\"1b#H\\)=[o
QFax7$Fe`l$\"1yD#[=:>'RFax7$Fj`l$\"1!)>#*))[wbSFax7$F_al$\"1)eVvK>r:%F
ax7$Fdal$\"1/*f'\\AuYUFax7$Fial$\"1iTtL1?OVFax7$F^bl$\"1#=1-e5[U%Fax7$
Fcbl$\"1vQ&G!43/XFax7$Fhbl$\"1Z:*>M1ie%Fax7$F]cl$\"1(z$>F7@lYFax7$Fbcl
$\"1?q'R1*)ou%Fax7$Fgcl$\"18!QRhok\"[Fax7$F\\dl$\"1bG9iUw$*[Fax7$Fadl$
\"1+OFs$32'\\Fax7$Ffdl$\"1@qo+^EC]Fax7$F[el$\"1z'>%eJd*3&Fax7$F`el$\"1
jziu#>>:&Fax7$Feel$\"1P$z5L'y0_Fax7$Fjel$\"1Jsx())f*f_Fax7$F_fl$\"1jm#
\\Ht(4`Fax7$Fdfl$\"1s%HCg9.O&Fax7$Fifl$\"1XycMw5,aFax7$F^gl$\"1qFg0\\b
WaFax7$Fcgl$\"1w;xLD/#[&Fax7$Fhgl$\"1$)\\7P=$f^&Fax7$F]hl$\"1K&*))RcfY
bFax7$Fbhl$\"1Eo)>!H\\ubFax7$Fghl$\"1I^mKHJ+cFax7$F\\il$\"1#4_>fu0i&Fa
x7$Fail$\"1kA89pNPcFax7$Ffil$\"1hN%4)eu^cFax7$F[jl$\"1e'eecLCm&Fax7$F`
jl$\"1wKVKm*)ocFax7$Fjjl$\"1$y)Q>^rscFax7$Fe[m$\"1SX7K&4Fn&Fax7$F_\\m$
\"1&zu:%G+pcFax7$Fi\\m$\"1!eo$[wuhcFax7$F^]m$\"18$*[el?_cFax7$Fc]m$\"1
t8e\\H.QcFax7$Fh]m$\"1.<w]d4?cFax7$F]^m$\"1*3'fpTg)f&Fax7$Fb^m$\"1$3bh
l^ad&Fax7$Fg^m$\"1%)f<*)eA[bFax7$F\\_m$\"16BQl:h;bFax7$Fa_m$\"1;2+gui
\"[&Fax7$Ff_m$\"1)eU$o'e?W&Fax7$F[`m$\"1r\"eN^DUS&Fax7$F``m$\"1ou>$HH$
e`Fax7$Fe`m$\"1hwh'oj(3`Fax7$Fj`m$\"1(\\vP$4ud_Fax7$F_am$\"1-M\"3^v'3_
Fax7$Fdam$\"1ncC1$)*p9&Fax7$Fiam$\"1dR$o^g>4&Fax7$F^bm$\"1Y6N[oxC]Fax7
$Fcbm$\"1,\\%zkAD'\\Fax7$Fhbm$\"1YK!H\">F\"*[Fax7$F]cm$\"1xhmp!=1#[Fax
7$Fbcm$\"1lJ!o$z/WZFax7$Fgcm$\"1'\\et*4BrYFax7$F\\dm$\"1Uw9`M2!f%Fax7$
Fadm$\"1\\+,D=)H]%Fax7$Ffdm$\"1Vp(*[>#\\U%Fax7$F[em$\"1Rhjo;MQVFax7$F`
em$\"18_@G.]YUFax7$Feem$\"1/+:)p$QaTFax7$Fjem$\"1lo6di?jSFax7$F_fm$\"1
q8y8/rfRFax7$Fdfm$\"1W$pi%=ykQFax7$Fifm$\"1AR<\\'4:w$Fax7$F^gm$\"1a[5&
G7jm$Fax7$Fcgm$\"13K%3\"4egNFax7$Fhgm$\"1Jh7rlhfMFax7$F]hm$\"1kS?;_l_L
Fax7$Fbhm$\"10*4/7#yYKFax7$Fghm$\"198#R$zoMJFax7$F\\im$\"1N(><&RjDIFax
7$Faim$\"1/2$Q)f78HFax7$Ffim$\"1UD#=(Rp+GFax7$F[jm$\"1!yFVUTnp#Fax7$F`
jm$\"1(H2\"*H%)pd#Fax7$Fejm$\"1Y!fpGR%pCFax7$Fjjm$\"1V*p^zfWN#Fax7$F_[
n$\"1l>>\\kBWAFax7$Fd[n$\"1o$\\'o!3=7#Fax7$Fi[n$\"10'3')*[*e,#Fax7$F^
\\n$\"1_B;FZ&f*=Fax7$Fc\\n$\"1/7kv*Qqy\"Fax7$Fh\\n$\"19.EsJ]o;Fax7$F]]
n$\"1hN%o*z'oc\"Fax7$Fb]n$\"1b#)e7<+_9Fax7$Fg]n$\"1Ln9\"[.@M\"Fax7$F\\
^n$\"1\">6tF#[L7Fax7$Fa^n$\"1lQv8jiE6Fax7$Ff^n$\"1b0)*)z7a-\"Fax7$F[_n
$\"1\"G\"GvQmx\"*F-7$F`_n$\"1;G)3Gm0<)F-7$Fe_n$\"1/[n*RXC8(F-7$Fj_n$\"
1W$y?RfO@'F-7$F_`n$\"1CV2@cKB_F-7$Fd`n$\"1%=BV0h8I%F-7$Fi`n$\"1^*eq([[
4MF-7$F^an$\"1iuiD#y'4DF-7$Fcan$\"14Jk\"40:r\"F-7$Fhan$\"1<5$*Q!)Rj#*F
c\\o7$F]bn$\"1.6ct-Gj**!#>7$Fbbn$!1wgX)4)y.hFc\\o7$Fgbn$!1:ES>)QlH\"F-
7$F\\cn$!1U)GW]E2&>F-7$Facn$!1\"*RPB%>8^#F-7$Ffcn$!15S+;V'Q1$F-7$F[dn$
!1j\\j\\3:kNF-7$F`dn$!1I/+L0&Q/%F-7$Fedn$!1Q0D1)euT%F-7$Fjdn$!1#)='zLs
!)y%F-7$F_en$!1BZo#\\;Y1&F-7$Fden$!1%='3Y-(>G&F-7$Fien$!1<aOz#)z]aF-7$
F^fn$!1\"Q3Ak9+b&F-7$Fcfn$!1qZh(4\"ywbF-7$Fhfn$!1]h\\!*oaObF-7$F]gn$!1
%z$R/5sEaF-7$Fbgn$!1Efg*f]hA&F-7$Fggn$!1G\"4poj=)\\F-7$F\\hn$!1p!*Q%=$
e<YF-7$Fahn$!1`\\f=))*3>%F-7$Ffhn$!1\"f$>Y*y_o$F-7$F[in$!1f`!*>+&R4$F-
7$F`in$!1bp]s8D+CF-7$Fein$!1X2yx^,i:F-7$Fjin$!1A,E]OgvpFc\\o7$F_jn$\"1
@3Pb>I$[#Fc\\o7$Fdjn$\"19OsS;.k8F-7$Fijn$\"1Tw`3%G!)e#F-7$F^[oFh[o-Fa[
o6&Fc[o$\"*++++\"!\")F*F*-F$6$7ez7$F($\"1\\:=YQ:YQF-7$$!1#f=P*zU$*\\F1
$\"1t;A6\"G!3AFax7$$!1'=Pu)f&o)\\F1$\"1dPm;`EARFax7$$!1zd:\")RG!)\\F1$
\"1X9(>*RVJbFax7$$!1rV([(>rt\\F1$\"1Y?4a]_RqFax7$$!1kHfo*Rr'\\F1$\"1)3
dK&fT]%)Fax7$$!1e:Jizcg\\F1$\"1bn(GBtyw*Fax7$$!1],.cf*R&\\F1$\"1i)\\U]
b&*4\"F17$F/$\"1<PYg8q87F17$$!1\"\\)p9u)f$\\F1$\"1_Fcg()z#R\"F17$$!1S#
['z3bC\\F1$\"1?T51(p&[:F17$$!1*)zfWV68\\F1$\"1'QUH8qEo\"F17$F5$\"1%[K$
)\\qmz\"F17$$!1+++]Y&f([F1$\"1PQ?h2@()>F17$F:$\"1#3,i\\!)*)4#F17$$!1&*
)ydl%GP[F1$\"17'fl4B)H@F17$$!1Fb5@yLC[F1$\"1)yMXJ'yX@F17$$!1g@V')4R6[F
1$\"1YIe#\\]$[@F17$F?$\"1z#e'Q%**)Q@F17$$!17D]]NnsZF1$\"1`m%e2c$*3#F17
$FD$\"1SFa<$Gk+#F17$$!1w],..,BZF1$\"1H1`a(om!>F17$FI$\"1#Q]HLR0z\"F17$
$!1Qw_0#yVn%F1$\"1r1f***)3e;F17$FN$\"1wZj$*zm<:F17$$!1g>RyJ0CYF1$\"11L
KsF6o8F17$FS$\"1`8!z&ej<7F17$$!1(\\**)zS'Hd%F1$\"1,r0p\"4'p5F17$FX$\"1
)z_7hm(e#*Fax7$$!1)[(\\\\qA@XF1$\"1z9oG$=X%yFax7$Fgn$\"1LpI&3u1^'Fax7$
$!1W)oP0()=Z%F1$\"1%oUGr[:T&Fax7$F\\o$\"1=F[p(\\\"*Q%Fax7$Fao$\"1s#\\#
=gG%Q#Fax7$Ffo$\"1*pl%R_fDzF-7$F[p$!1%R@%)y%4gNF-7$F`p$!1!GhTBpv4\"Fax
7$Fep$!1w'Gezf.l\"Fax7$$!1lHf=n2rTF1$!1$Qn(479!z\"Fax7$Fjp$!1=]OIva!)=
Fax7$$!1*)ydl'o77%F1$!1)Gx9h3)H>Fax7$F_q$!1PzSe`*e#>Fax7$$!1iAXSwxqSF1
$!1Qg?JWx$)=Fax7$Fdq$!1%og\\0B.\"=Fax7$Fiq$!1,we[BQh:Fax7$F^r$!1Zqj%fk
ZC\"Fax7$Fcr$!1DXY\"*4z!o)F-7$Fhr$!1&G;+F!3r]F-7$F]s$!1&G#HB;c[7F-7$Fb
s$\"19%*=!y:oW#F-7$Fgs$\"1\"3SsP='=`F-7$F\\t$\"1NCGdgP\")zF-7$Fat$\"1_
KlEn(4-\"Fax7$Fft$\"1qruocc'=\"Fax7$F[u$\"1)GgGt/\"*H\"Fax7$F`u$\"1]2%
)z)=NP\"Fax7$Feu$\"1HvF%\\r/S\"Fax7$Fju$\"14M_+4Y%R\"Fax7$F_v$\"1UJ)>D
xVO\"Fax7$Fdv$\"1>(\\L6@>J\"Fax7$Fiv$\"1a&38!oZ]7Fax7$F^w$\"1d&=i5n-=
\"Fax7$Fcw$\"1n:.b*o96\"Fax7$Fhw$\"1J]'pY\"oW5Fax7$F]x$\"1+b*p,pr*)*F-
7$Fcx$\"1oEgz-Jk%*F-7$Fhx$\"1Y;m$fj#)=*F-7$F]y$\"1FJ8N:*>3*F-7$Fby$\"1
)z@PUP-9*F-7$Fgy$\"1NMZ9*fRN*F-7$F\\z$\"1!oUjJ`?u*F-7$Faz$\"1cJT/zeD5F
ax7$Ffz$\"1*4Fw2()p4\"Fax7$F[[l$\"19-kR))4p6Fax7$F`[l$\"1V\"H4U0,E\"Fa
x7$Fe[l$\"15AtW*=$\\8Fax7$Fj[l$\"1tAe8SG^9Fax7$F_\\l$\"1+V.tX3T:Fax7$F
d\\l$\"1+picd[V;Fax7$Fi\\l$\"1hz)QH.4u\"Fax7$F^]l$\"1kSBJ,[N=Fax7$Fc]l
$\"1T$=W$G/E>Fax7$Fh]l$\"1jH]iQ74?Fax7$F]^l$\"1MqTxA]%4#Fax7$Fb^l$\"1
\"HSZ#R(=<#Fax7$Fg^l$\"1uN,T9\")\\AFax7$F\\_l$\"1G9&G4?#=BFax7$Fa_l$\"
14>(R%=%GR#Fax7$Ff_l$\"1(fB![3'\\Y#Fax7$F[`l$\"1XY4%eP$RDFax7$F``l$\"1
;t)fq-<i#Fax7$Fe`l$\"1!)Rvn.t.FFax7$Fj`l$\"1`%4p$3!ez#Fax7$F_al$\"1PA2
(H*=4HFax7$Fdal$\"1v\"pS,=W-$Fax7$Fial$\"1Z#QE8jj:$Fax7$F^bl$\"1],HOjr
1LFax7$Fcbl$\"1c#*R0.TgMFax7$Fhbl$\"1g-&)o7XTOFax7$F]cl$\"1dTBTW@RQFax
7$Fbcl$\"1c$Qc]F42%Fax7$Fgcl$\"1$Rfv%e_#H%Fax7$F\\dl$\"1dz..UXnXFax7$F
adl$\"1$)z([8CA$[Fax7$Ffdl$\"1**)yy,9%3^Fax7$F[el$\"1=I7eFI>aFax7$F`el
$\"1&oWnDMNu&Fax7$Feel$\"1DsGP^mYgFax7$Fjel$\"14GP[hHujFax7$F_fl$\"1$=
q$Q0z'p'Fax7$Fdfl$\"1(p.$4n%e/(Fax7$Fifl$\"1(4YcUbVM(Fax7$F^gl$\"1IA`M
gYzwFax7$Fcgl$\"1.u!R'QQ$)zFax7$Fhgl$\"1\")=j?lJq#)Fax7$F]hl$\"1q(QOF9
-a)Fax7$Fbhl$\"1;KKO.Z%z)Fax7$Fghl$\"15_6?!ot.*Fax7$F\\il$\"1AD]J>=L#*
Fax7$Fail$\"13l+z!)*))R*Fax7$Ffil$\"1Td3\"fiNa*Fax7$F[jl$\"1J'G)[`d_'*
Fax7$F`jl$\"1\"\\DVf[\">(*Fax7$Fjjl$\"1)3S608(e(*Fax7$Fe[m$\"1L))oL]le
(*Fax7$F_\\m$\"1#zT`sY-s*Fax7$Fi\\m$\"1dIp&))Qbk*Fax7$F^]m$\"1q\")G!*Q
B[&*Fax7$Fc]m$\"1lg&eATcS*Fax7$Fh]m$\"1JfF&z+&G#*Fax7$F]^m$\"1*z-\">[1
@!*Fax7$Fb^m$\"1o<TS%eL!))Fax7$Fg^m$\"1xK?-?%[b)Fax7$F\\_m$\"1;QfCD>w#
)Fax7$Fa_m$\"1'znV0U*zzFax7$Ff_m$\"1YvcO1sfwFax7$F[`m$\"16BRdc!yO(Fax7
$F``m$\"1WnfVrqJqFax7$Fe`m$\"1]J![]X+p'Fax7$Fj`m$\"1ha$pz6/O'Fax7$F_am
$\"1g;)R$3bjgFax7$Fdam$\"11doZc#pr&Fax7$Fiam$\"1p\"*fEG@JaFax7$F^bm$\"
13hvx3u5^Fax7$Fcbm$\"1=\"3UEk(R[Fax7$Fhbm$\"1x'pfn)3eXFax7$F]cm$\"1IF`
hE\\1VFax7$Fbcm$\"10s:9%oB1%Fax7$Fgcm$\"1HtD\\%4`&QFax7$F\\dm$\"19/b0.
d]OFax7$Fadm$\"1TR4$)R9eMFax7$Ffdm$\"1$Gmg$*=pI$Fax7$F[em$\"1?`r**GvfJ
Fax7$F`em$\"1X\\+Wa3CIFax7$Feem$\"1DA&=\\3f!HFax7$Fjem$\"1\\f.tFf.GFax
7$F_fm$\"10<`)y$p,FFax7$Fdfm$\"1w`j*Q='=EFax7$Fifm$\"15e&fmyl`#Fax7$F^
gm$\"1R`&*R.KmCFax7$Fcgm$\"1(o'*zKu>R#Fax7$Fhgm$\"1,gZ/!pEK#Fax7$F]hm$
\"1r(p3@%H\\AFax7$Fbhm$\"1bz#>dG`<#Fax7$Fghm$\"1Ckf#[UW4#Fax7$F\\im$\"
1z\"=Kr6D,#Fax7$Faim$\"1b@\"yKIV#>Fax7$Ffim$\"1b\\zxFgK=Fax7$F[jm$\"1$
R^5$>,X<Fax7$F`jm$\"1K\\)yo&pT;Fax7$Fejm$\"1f/sR=%ya\"Fax7$Fjjm$\"1@[P
PA*yW\"Fax7$F_[n$\"1a4qp:8a8Fax7$Fd[n$\"1[/KF*)ea7Fax7$Fi[n$\"1z%eXRvV
<\"Fax7$F^\\n$\"18!Q:\\QD4\"Fax7$Fc\\n$\"1s$GG3F'G5Fax7$Fh\\n$\"1Sj=&>
-is*F-7$F]]n$\"1'>n^%=.v$*F-7$Fb]n$\"1jC6*y;w8*F-7$Fg]n$\"1p**[\"[013*
F-7$F\\^n$\"1?%pHw/V>*F-7$Fa^n$\"1y4$4xL6Z*F-7$Ff^n$\"1b&3e#=Yx)*F-7$F
[_n$\"1#3w\"QlsW5Fax7$F`_n$\"1')\\1^@S36Fax7$Fe_n$\"1pLwwFw!=\"Fax7$Fj
_n$\"1c]w)G#HY7Fax7$F_`n$\"1l'\\L;HEJ\"Fax7$Fd`n$\"1jVbX+fj8Fax7$Fi`n$
\"1#o3m!**=&R\"Fax7$F^an$\"1SXqT#e+S\"Fax7$Fcan$\"1NJDouXs8Fax7$Fhan$
\"1nwtCwB18Fax7$F]bn$\"134'yuJC=\"Fax7$Fbbn$\"10h1#pn/-\"Fax7$Fgbn$\"1
6MGf[AS!)F-7$F\\cn$\"1>*=&p#*RA`F-7$Facn$\"16^>.XG.CF-7$Ffcn$!1w]*>InX
2\"F-7$F[dn$!1Ig$[t`!yZF-7$F`dn$!14Z8)pwE#))F-7$Fedn$!1=#p0x5\\A\"Fax7
$Fjdn$!1k9'=$obr:Fax7$F_en$!1O,HX;G0=Fax7$$\"1v[(\\9-*pSF1$!1+D@=/f\")
=Fax7$Fden$!1udkNDZD>Fax7$$\"1b2:!G%4?TF1$!1*))*yo!*pI>Fax7$Fien$!1tAc
6$)3')=Fax7$$\"1CX!4G8A<%F1$!1F_d#HQWy\"Fax7$F^fn$!1)HM-B')*=;Fax7$Fcf
n$!1%*e`aO,K6Fax7$Fhfn$!1NyPj`xZJF-7$F]gn$\"1uqpg<$*)>)F-7$Fbgn$\"11t$
**H\"efCFax7$$\"1)Qxa9A?U%F1$\"1m_=xas0LFax7$Fggn$\"1UoPRaNMUFax7$$\"1
If=(=U;Z%F1$\"1E&)*Q&QI+aFax7$F\\hn$\"1]u$4-htm'Fax7$$\"1<KkGD5BXF1$\"
1T\"f(*>:J%zFax7$Fahn$\"10.v*3s1H*Fax7$$\"1rQx/>tsXF1$\"1\"*>Kl\"y#o5F
17$Ffhn$\"16lQZ^`67F17$$\"1')pRz+9AYF1$\"1q(=(4O&oN\"F17$F[in$\"1)z#ou
q`,:F17$$\"1e:J711sYF1$\"18W\"G$)3_k\"F17$F`in$\"1RnqeR+\"y\"F17$$\"1b
3<Me)Rs%F1$\"11e>;r46>F17$Fein$\"1dQC0'Q/-#F17$$\"1Gb5rF?vZF1$\"1ogo$y
Me4#F17$Fjin$\"1h3lMqIS@F17$$\"1'=PCh#z6[F1$\"1BsPS%e%[@F17$$\"1LmK:T)
Q#[F1$\"1m%f&yV4Y@F17$$\"1!3;#=c(f$[F1$\"1Guv+y3K@F17$F_jn$\"1ngF[$Q_5
#F17$$\"139Gc$=R([F1$\"1h$z19R()*>F17$Fdjn$\"1KjeP4%Q\"=F17$$\"1Gb5rqm
7\\F1$\"1**R*eK'\\(o\"F17$$\"1pPv]XcD\\F1$\"1I$y$[>mN:F17$$\"15?SI?YQ
\\F1$\"1=r***>#3c8F17$Fijn$\"11\")>,FOY6F17$$\"1pRHr&Ru&\\F1$\"1NQa:ZK
O5F17$$\"1)oPDj>N'\\F1$\"1,*R%>&)[(=*Fax7$$\"119y$p*fp\\F1$\"1ja&p#y\\
LzFax7$$\"1D^-b(zc(\\F1$\"1+'HpRV$)f'Fax7$$\"1X)oi\")f<)\\F1$\"1uctfM,
z^Fax7$$\"1jD^x)Ry)\\F1$\"17(QMW9Cn$Fax7$$\"1#Gc(Q*>R*\\F1$\"1iA]I#p`2
#Fax7$F^[oFhaq-Fa[o6&Fc[oF*F*Faaq-F$6$7jz7$F($\"1R!QU%Q:YQF-7$$!1'Hfo*
Rr'*\\F1$!1-ZP%ol-(QF17$F[bq$!1;T(=ng,g(F17$$!1*)yd!*>9!*\\F1$!1@A<<wl
:6!#97$F`bq$!10%o!HRZa9Fggt7$$!1#['H%)*pN)\\F1$!1ol'\\Rvpx\"Fggt7$Febq
$!1<owH.m$3#Fggt7$$!1v],yz*p(\\F1$!1YQd3_,vBFggt7$Fjbq$!1ph/+\\^^EFggt
7$F_cq$!1AIKO:zhJFggt7$Fdcq$!1qo2#ol!=OFggt7$Ficq$!1#)Q9l8uBSFggt7$F/$
!1A\"3!)*z0#Q%Fggt7$Fadq$!13Idxyv,\\Fggt7$Ffdq$!1G6-7\\X-`Fggt7$F[eq$!
1IiF%*H,)f&Fggt7$F5$!13HFD<4,eFggt7$$!1qQxHi\")))[F1$!1GSa(*>JLfFggt7$
Fceq$!1b\\Q`-*z(fFggt7$$!1IhAqI4j[F1$!1!p\")e2`%[fFggt7$F:$!1l9PRniceF
ggt7$F`fq$!1l&)Q\"f*zCbFggt7$F?$!1ibaZtYb]Fggt7$F]gq$!1')4c-+G3XFggt7$
FD$!1Oq0u$pU#RFggt7$Fegq$!1^cDj$e\"yLFggt7$FI$!1S/qeR3ZGFggt7$F]hq$!1;
_,D?ZFBFggt7$FN$!1-(>K_H([=Fggt7$Fehq$!1Pd.!GDKS\"Fggt7$FS$!1,gr=(H:,
\"Fggt7$F]iq$!1\"3!*)R!GMv'F17$FX$!1Q15yE7?RF17$Fgn$\"14kJ`GRXPFax7$F
\\o$\"1f&)='[jMo#F17$$!1He;L\"oFU%F1$\"1TMs:u.'[$F17$Fao$\"1r/<'yBS*RF
17$$!1d9HekjqVF1$\"1H5he6OcUF17$Ffo$\"1_C?:/A;VF17$$!1h@V'[Y$>VF1$\"1-
nol]l@UF17$F[p$\"1y4jY&R?,%F17$$!1@V'GK=8F%F1$\"19lE$*4QZPF17$F`p$\"1#
p)H5`aKMF17$Fep$\"1y\"*ohlYyDF17$Fjp$\"1/9pEh`R=F17$F_q$\"1-U_lB>h5F17
$Fdq$\"16YgxF_E\\Fax7$Fiq$\"1gK!=?)G'3#F-7$F^r$!1\"\\j(**=J;GFax7$Fcr$
!1<Vc\\,.2YFax7$Fhr$!1jQW$z(GP_Fax7$F]s$!1!GUtEFE4&Fax7$Fbs$!1x85:l$fK
%Fax7$Fgs$!1nJ5\\:1iLFax7$F\\t$!1Dt!=m2o>#Fax7$Fat$!1_6%H`+<,\"Fax7$Ff
t$\"15Q@?NNg>Fc\\o7$F[u$\"1XUy%exhM)F-7$F`u$\"1DPz\"z$*o\\\"Fax7$Feu$
\"1)\\QU!>3u=Fax7$Fju$\"14Rx<0/r?Fax7$F_v$\"1N$oF]$f'4#Fax7$Fdv$\"1%3o
vRm()*>Fax7$Fiv$\"1Qn(zh$*f#=Fax7$F^w$\"1.lRz'e4g\"Fax7$Fcw$\"1<L;0EDq
8Fax7$Fhw$\"1DU77'eh9\"Fax7$F]x$\"1n6KH5Ur'*F-7$Fcx$\"1,>KgaDS$)F-7$Fh
x$\"1\"G#y+d]svF-7$F]y$\"1!H\">eueZtF-7$Fby$\"1F!)ReD-.wF-7$Fgy$\"1f\"
)*f]A,A)F-7$F\\z$\"1#)RTeDH$=*F-7$Faz$\"1'*[@UZ:I5Fax7$Ffz$\"1hP2<.[l6
Fax7$F[[l$\"1`#*o6w$QG\"Fax7$F`[l$\"13zU-+t69Fax7$Fe[l$\"1#**e*HHM<:Fa
x7$Fj[l$\"1XCYvXb<;Fax7$F_\\l$\"1L6z))fB!p\"Fax7$Fd\\l$\"1#3([kf<e<Fax
7$Fi\\l$\"1%Rzz-x4\"=Fax7$F^]l$\"1HZj2^Ua=Fax7$Fc]l$\"1X8suuK#*=Fax7$F
h]l$\"1Kg.)>8v#>Fax7$F]^l$\"1h0D^LQo>Fax7$Fb^l$\"1/KFjis8?Fax7$Fg^l$\"
1qJX![u92#Fax7$F\\_l$\"1'H[$f\"RZ8#Fax7$Fa_l$\"1(R/#*\\N$=AFax7$Ff_l$
\"1K*)3O2`7BFax7$F[`l$\"1QG0_X=?CFax7$F``l$\"1b*f?4qka#Fax7$Fe`l$\"1m?
e:z=uEFax7$Fj`l$\"1I;=23(\\\"GFax7$F_al$\"10&ei'HV!)HFax7$Fdal$\"1Wq\\
pm%y8$Fax7$Fial$\"13CBHi40LFax7$F^bl$\"1g+$)*eR3[$Fax7$Fcbl$\"1hs8)Rqq
k$Fax7$Fhbl$\"1HqJ,pIHQFax7$F]cl$\"1(GW^oVe,%Fax7$Fbcl$\"1&4EjLXFA%Fax
7$Fgcl$\"1'*equ&zGT%Fax7$F\\dl$\"1CMOL^wUYFax7$Fadl$\"1qG+n!y9'[Fax7$F
fdl$\"1dOq_Z!)*3&Fax7$F[el$\"1(Q/6:E)\\`Fax7$F`el$\"1\\jje=*oi&Fax7$Fe
el$\"1,H(*)3DJ*eFax7$Fjel$\"1_KF\"yd,>'Fax7$F_fl$\"18Gk+k1$\\'Fax7$Fdf
l$\"1$)*zgr$pLoFax7$Fifl$\"1;P!=zLh8(Fax7$F^gl$\"1\\NCpPT)[(Fax7$Fcgl$
\"1Q`\"Gd>*>yFax7$Fhgl$\"1qn;tEiV\")Fax7$F]hl$\"16xvz[wd%)Fax7$Fbhl$\"
1*H$R4KOi()Fax7$Fghl$\"1!f-A>p71*Fax7$F\\il$\"1&>Ul'))*yI*Fax7$Fail$\"
1_Q$Qg'e?&*Fax7$Ffil$\"1`uM?mB4(*Fax7$F[jl$\"1H%=zBMK&)*Fax7$F`jl$\"1/
O`y3&>%**Fax7$Fjjl$\"1JiLz\\&\\***Fax7$Fe[m$\"1(zf65x[***Fax7$F_\\m$\"
1'>k!=#>M%**Fax7$Fi\\m$\"1#[P0$=*Q%)*Fax7$F^]m$\"1ltr:YP:(*Fax7$Fc]m$
\"11FIA#=$H&*Fax7$Fh]m$\"1ZEf]P%>I*Fax7$F]^m$\"19\"\\\\aj4/*Fax7$Fb^m$
\"1U`a)4kJx)Fax7$Fg^m$\"1=()>`-1v%)Fax7$F\\_m$\"1jsg#yh.:)Fax7$Fa_m$\"
1N6`1.5;yFax7$Ff_m$\"1JM.A[FnuFax7$F[`m$\"1_-BU8MgrFax7$F``m$\"1Tc_poi
>oFax7$Fe`m$\"1_G%=y<m['Fax7$Fj`m$\"1XCL<%et<'Fax7$F_am$\"1gT;Lu=3fFax
7$Fdam$\"1\")RFhk(Qg&Fax7$Fiam$\"1tnSDP))f`Fax7$F^bm$\"1U'H%pft\"4&Fax
7$Fcbm$\"1-CU*e(pn[Fax7$Fhbm$\"1iUh3++NYFax7$F]cm$\"1>0i#H&oCWFax7$Fbc
m$\"1DGoZJF:UFax7$Fgcm$\"1^n['**o0.%Fax7$F\\dm$\"1r;(>:l\"QQFax7$Fadm$
\"1]'Gvh.Zk$Fax7$Ffdm$\"1qO(\\)p1\"[$Fax7$F[em$\"1CVJyHA4LFax7$F`em$\"
1&G,a/3u8$Fax7$Feem$\"1gw.\"z*yvHFax7$Fjem$\"1p7\\&)HlEGFax7$F_fm$\"1u
lrb!H5n#Fax7$Fdfm$\"1)y6Vtu;a#Fax7$Fifm$\"1gh?9<0;CFax7$F^gm$\"1ggKX_T
9BFax7$Fcgm$\"1Ros7\"ys@#Fax7$Fhgm$\"1l>h:cHR@Fax7$F]hm$\"1$\\m/UV52#F
ax7$Fbhm$\"1A9nv7+;?Fax7$Fghm$\"1U9&[#>No>Fax7$F\\im$\"1PfK_M,H>Fax7$F
aim$\"1'Gcy\")>;*=Fax7$Ffim$\"1#4_N$>=`=Fax7$F[jm$\"1XFU)Q**H\"=Fax7$F
`jm$\"1!=**yj2rv\"Fax7$Fejm$\"1@8&>wy^p\"Fax7$Fjjm$\"1:6!>)*QXh\"Fax7$
F_[n$\"1*R-g#*RD_\"Fax7$Fd[n$\"1[0A=%*e/9Fax7$Fi[n$\"1QEvi0(=H\"Fax7$F
^\\n$\"1\"e%f7zhd6Fax7$Fc\\n$\"1DqG=iMO5Fax7$Fh\\n$\"1JTGKBMY\"*F-7$F]
]n$\"1ukx9!fiF)F-7$Fb]n$\"1y*G4c&\\%f(F-7$Fg]n$\"1Aztu;wZtF-7$F\\^n$\"
17#QVVJye(F-7$Fa^n$\"1-*QY$HNg$)F-7$Ff^n$\"1#p<Efy)3'*F-7$F[_n$\"1Vke$
=3j9\"Fax7$F`_n$\"1y9Mpf!*f8Fax7$Fe_n$\"1o[&[C*f-;Fax7$Fj_n$\"1,&4Sr_J
\"=Fax7$F_`n$\"1\"f3SH90+#Fax7$Fd`n$\"1*Qp^'o'e4#Fax7$Fi`n$\"1]ET1(*Qn
?Fax7$F^an$\"1szW1-:j=Fax7$Fcan$\"1^[[4\">c[\"Fax7$Fhan$\"1SGjij7:*)F-
7$F]bn$!183s^&fk:)Fi[q7$Fbbn$!1)*48)f\\Y,\"Fax7$Fgbn$!1TN%ojq!o@Fax7$F
\\cn$!1kd\\2;fgLFax7$Facn$!1'zbU[g\"QVFax7$Ffcn$!1Rqy]gTp]Fax7$F[dn$!1
')4%Q#3)GD&Fax7$F`dn$!1Ybk2IajXFax7$Fedn$!1;L#*z?\\\\HFax7$Fjdn$\"1c$
\\-44jV$F-7$F_en$\"1fAB)o=Ly%Fax7$Fden$\"1)pP_(Q!f0\"F17$Fien$\"1A![@>
=#4=F17$F^fn$\"12e*Hs^rk#F17$Fcfn$\"1'[TX-mSR$F17$$\"1`06s<2rUF1$\"1;o
b\\%>Uu$F17$Fhfn$\"1@DnEXULSF17$$\"15>QwR#4K%F1$\"1p)o^$[HJUF17$F]gn$
\"1z.4l.;<VF17$$\"1(HfoR\"*)eVF1$\"1\">dB&Rs0VF17$$\"1$['H4nBsVF1$\"1
\\CQx(flC%F17$$\"1pOt@?e&Q%F1$\"10Iz\\?*Q8%F17$Fbgn$\"1AZ;?mohRF17$Fc]
t$\"1a1Q9>Z/NF17$Fggn$\"1%)ys!G%>;GF17$F\\hn$\"1mexVg?)o\"Fax7$Fahn$!1
wO*pyn&yRF17$F[_t$!1)pjh(HGDnF17$Ffhn$!1a*e'G)Qu'**F17$Fc_t$!1TsC?G0s8
Fggt7$F[in$!1Gk\\$f3xz\"Fggt7$F[`t$!1od-s_w!G#Fggt7$F`in$!1Bf2,Y+2GFgg
t7$Fc`t$!1&*e7[2F+MFggt7$Fein$!1L)Q*zcP6SFggt7$F[at$!1\\-Wr\">Uc%Fggt7
$Fjin$!1e\\S9R^!3&Fggt7$Fhat$!1_$G$H=d<bFggt7$F_jn$!1nH3%3De$eFggt7$$
\"1oMpQF*4'[F1$!1F7AagTPfFggt7$Febt$!1QV=7f$z(fFggt7$$\"1[$pQ(R%o)[F1$
!1(\\`tW'\\XfFggt7$Fdjn$!1N)oa`+o#eFggt7$F]ct$!1$flcL9wg&Fggt7$Fbct$!1
(y#eE.Qr_Fggt7$Fgct$!1%=s8y&*)*z%Fggt7$Fijn$!1xC#Q(p*H<%Fggt7$F_dt$!1/
l?(=#G<QFggt7$Fddt$!1/?ql\"*f>MFggt7$Fidt$!1x<`#>?t(HFggt7$F^et$!1f`2
\\Zp([#Fggt7$Fcet$!1ByzS[%y%>Fggt7$Fhet$!18!zG<gZN\"Fggt7$$\"1AW83*z3*
\\F1$!1Vn0*ows.\"Fggt7$F]ft$!1[v[9<$H0(F17$$\"1T\"y$p*fp*\\F1$!1QFE1)Q
Re$F17$F^[oFhft-Fa[o6&Fc[oF*FaaqF*-%*THICKNESSG6#\"\"$-%+AXESLABELSG6$
Q\"X6\"%!G-%%VIEWG6$;F(F^[o;$!\"\"F*$\"\"\"F*" 1 2 0 1 3 2 9 1 4 2 
1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 
"On voit apparaitre un phŽnom�ne (appelŽ phŽnom�ne de Runge), au bord \+
de l'intervalle :" }}{PARA 0 "" 0 "" {TEXT -1 98 "Le polyn™me interpol
ateur oscille fortement au bord de l'intervalle, d'autant plus que n a
ugmente." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "On reprend la m�me dŽ
marche avec une autre dŽfinition pour les xi :" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 37 "x2:=(i,n) -> 5*cos(Pi/(n+1)*(i+1/2));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x2GR6$%\"iG%\"nG6\"6$%)operatorG%&a
rrowGF),$-%$cosG6#*&*&%#PiG\"\"\",&9$F4#F4\"\"#F4F4\"\"\",&9%F4F4F4!\"
\"\"\"&F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "plot([f(X
),fLa(f,5,x2),fLa(f,15,x2),fLa(f,20,x2)],X=-5..5,0..1,color=[black,red
,blue,green],numpoints=200,thickness=3);" }}{PARA 13 "" 1 "" 
{GLPLOT2D 396 164 164 {PLOTDATA 2 "6)-%'CURVESG6$7hw7$$!\"&\"\"!$\"1YQ
:YQ:YQ!#<7$$!1V([(\\RUZ\\!#:$\"1'4%zX$3^#RF-7$$!1Qxa4yn,\\F1$\"1%ot`@t
d*RF-7$$!1hAX!\\J-&[F1$\"1V()fyU^xSF-7$$!1%ze<:W%)z%F1$\"1zVvA%>B;%F-7
$$!1JiC\\H!pu%F1$\"145BahL\\UF-7$$!1?Rycw6*p%F1$\"1\\uc^_VKVF-7$$!1d8F
a(Q'\\YF1$\"1ijdoW.@WF-7$$!1jD^-wY)f%F1$\"1)\\\"**Qw]:XF-7$$!1KkGd0YZX
F1$\"1;B85Vn7YF-7$$!1V&3<a$*\\\\%F1$\"1;y?^i(er%F-7$$!1X\"Hec!y[WF1$\"
1gidNMi4[F-7$$!18D]+dv'R%F1$\"1!)3uld[=\\F-7$$!1-/3;s^WVF1$\"1'**=yh*[
J]F-7$$!1>Rycd<%H%F1$\"14)>;OZS9&F-7$$!1CZ%*))3Y[UF1$\"1ck7!o.&\\_F-7$
$!1OsW*[,T>%F1$\"19c0X^4z`F-7$$!1$pQx%>0[TF1$\"1!=K6m$f#\\&F-7$$!1&3<M
Q&[%4%F1$\"1e**>0f5HcF-7$$!1Pu[(*)pq/%F1$\"1%)3F$eXTv&F-7$$!1iBZ%fZ]*R
F1$\"1P*p,_&3'*eF-7$$!1&**)zf+^XRF1$\"1?w6qx2OgF-7$$!1zf>RG#Q*QF1$\"16
^%G13u='F-7$$!1#Ryc$yNYQF1$\"1\\%y1XI8L'F-7$$!1Fa3</;&z$F1$\"1'pYB_R@
\\'F-7$$!1)pRzo!)>u$F1$\"1B$o0_\"flmF-7$$!1NpQxvo&p$F1$\"1U%y%zM;AoF-7
$$!1V([(\\(*oXOF1$\"13nKRYQ(*pF-7$$!1Qv],r.%f$F1$\"1Cv/=OS&=(F-7$$!1e:
Ji]]VNF1$\"1#=e-NulP(F-7$$!1-/3;Fh%\\$F1$\"1K()G(e%povF-7$$!1Qv],hKSMF
1$\"1g+bUQo!z(F-7$$!1&4>Q;Z:R$F1$\"1&oN(e8M)*zF-7$$!1/4=O_YRLF1$\"1yxs
'3z!H#)F-7$$!1@U%)o7F#H$F1$\"1*pVlfBmW)F-7$$!1D\\)pzv1C$F1$\"1;g``b:%p
)F-7$$!1sW*)y%G@>$F1$\"1Lp.#o-o$*)F-7$$!1!3;Ka#QTJF1$\"180!3J%3,#*F-7$
$!1!*yd:\"p<4$F1$\"1DhM!Gh0Z*F-7$$!1pQxa%G)RIF1$\"1=^W*z$4l(*F-7$$!1Gc
7DM!)*)HF1$\"10oFz]915!#;7$$!1w^.2ckQHF1$\"1N_+)*R\"y.\"Fax7$$!1Pv],9
\"z)GF1$\"18a?8,mq5Fax7$$!1#Ryc$>HTGF1$\"1[`q#ey@5\"Fax7$$!1rT$owgyy#F
1$\"1#GhB4p*R6Fax7$$!17BY#Hr+u#F1$\"1C.U\\cOv6Fax7$$!1JhAXx6*o#F1$\"1n
y9Ap'[@\"Fax7$$!1v\\**)p[.k#F1$\"1s)G6HyWD\"Fax7$$!1<NqSp>'e#F1$\"1S_-
j#e1I\"Fax7$$!1C\\)p\\0$RDF1$\"13P[n#HEM\"Fax7$$!1CZ%*)G$3'[#F1$\"1'=@
3KRER\"Fax7$$!1.17CqdPCF1$\"1AFT[BbS9Fax7$$!1PtY$z=XQ#F1$\"1%H#Ql#yc\\
\"Fax7$$!1Ryc8&Q(QBF1$\"1L_hSsmX:Fax7$$!1lHf=,g'G#F1$\"1zW)>m7bg\"Fax7
$$!1v],.qBOAF1$\"1x\"[:rckm\"Fax7$$!16AW)y1f=#F1$\"1Jzy3ikI<Fax7$$!1T#
['H<wN@F1$\"1#Q,y6$3)z\"Fax7$$!1mJjE!)e(3#F1$\"1h&4$o(fj'=Fax7$$!1Z%*)
y(4^N?F1$\"1#QZF:vU%>Fax7$$!1f=Pux(e)>F1$\"1>/c_@xA?Fax7$$!1?T#[;TO$>F
1$\"1'3p2+k,6#Fax7$$!1d8FaWN')=F1$\"1w#4rP%y$>#Fax7$$!1tY$py$4M=F1$\"1
9*\\+@G:H#Fax7$$!1f=Pur.%y\"F1$\"1%*))>O&\\2R#Fax7$$!1D]+,C5M<F1$\"1$
\\QlUjb\\#Fax7$$!1<MoO`%>o\"F1$\"1!*R)ez)o6EFax7$$!15>Qwn!Rj\"F1$\"1@`
g<X0DFFax7$$!1!*zf>(3Ze\"F1$\"1Fr_`m%z%GFax7$$!1xa4>#)QI:F1$\"10u;\\89
#*HFax7$$!1#Qw_X07[\"F1$\"1Tfm!=+48$Fax7$$!1qT$o'o!4V\"F1$\"1`oLUTQ\"G
$Fax7$$!1\\**)z\\a(z8F1$\"1Pc=)GbQW$Fax7$$!1Fa3<btK8F1$\"1Gokvn1-OFax7
$$!1],.1[h#G\"F1$\"1lt)\\Mu0y$Fax7$$!1Fa3<c(GB\"F1$\"13.'3'=GoRFax7$$!
1V'Gd9q'z6F1$\"1W-AlLE\"=%Fax7$$!1`06A'=F8\"F1$\"1@76FF5!Q%Fax7$$!1kFb
5jay5F1$\"1R(4lE[Ei%Fax7$$!1(Rze(*f'H5F1$\"1U:#pY)*Q&[Fax7$$!1_2:I]*G
\")*Fax$\"1.wdNvU%4&Fax7$$!1'Qw_0dFH*Fax$\"13M,BF4m`Fax7$$!1v`2:]^q()F
ax$\"1zT:Q/@_cFax7$$!1PrU&3_`H)Fax$\"1a`B+\">P#fFax7$$!1;S!3;]2z(Fax$
\"1YJWg%QHA'Fax7$$!1$*******zI)H(Fax$\"1b7c'4MY_'Fax7$$!1gD^-b\\knFax$
\"1k$*[#4o1'oFax7$$!13>Qw#*f-jFax$\"1Y5HG-.drFax7$$!1.<MoY4sdFax$\"1H>
6QX\"4](Fax7$$!1yhBZCRt_Fax$\"1nbjma>CyFax7$$!1R'Gd92&zZFax$\"1913cjUS
\")Fax7$$!1lQxa*G_G%Fax$\"1[fUnFd[%)Fax7$$!1'=Pu['4\"y$Fax$\"1A,-.(f\"
\\()Fax7$$!1Wze<XsYKFax$\"1k9ha\"*RY!*Fax7$$!19Pu[xvcFFax$\"1&*3th]q$H
*Fax7$$!1Le;Lw4tAFax$\"1j%4'R')o3&*Fax7$$!1U#['HH2c<Fax$\"1*H!)=2Y3q*F
ax7$$!1\"f=Put,C\"Fax$\"1RA,;m_[)*Fax7$$!1lpRzeBrxF-$\"1RS;C/(*R**Fax7
$$!1l#f=Pa'G]F-$\"1'z(**=kxu**Fax7$$!1k:KkG2'G#F-$\"1c\\n+mx%***Fax7$$
\"1gv-/3;#z)!#?$\"0\"zpA********F17$$\"1?'Hf=dOI#F-$\"1esKyfp%***Fax7$
$\"1;**)zffx)\\F-$\"1o%H3*R=v**Fax7$$\"17-05?'=n(F-$\"1\"pEk#p[T**Fax7
$$\"1W$pQxdL-\"Fax$\"1E,pv#fj*)*Fax7$$\"1oOtY$H&z7Fax$\"1Eo0(p<*Q)*Fax
7$$\"1;Pu[2*pt\"Fax$\"1-iD>G72(*Fax7$$\"1+&)pRRX^AFax$\"1zcUo5b<&*Fax7
$$\"1rJjEtKpFFax$\"1BSt=%4xG*Fax7$$\"1'ze<NRZG$Fax$\"1kPz%4Dh-*Fax7$$
\"16>QwAfiPFax$\"1Q'ej2e)f()Fax7$$\"1Tv],8QdUFax$\"1Hc([G(el%)Fax7$$\"
1ta4>G4pZFax$\"1y?+)Q@q9)Fax7$$\"1)yc8Fj\"z_Fax$\"1[(*)3Dp/#yFax7$$\"1
\"oNrULQ!eFax$\"1)=W^u*H![(Fax7$$\"1Y'Hf=jfE'Fax$\"1vyf[Xp!=(Fax7$$\"1
%)f>R=@'y'Fax$\"1Qz)G*\\%o%oFax7$$\"1)3<Mo'f3tFax$\"1l&3)oDC=lFax7$$\"
1=>Qw7,7yFax$\"1&\\-7h=,@'Fax7$$\"1tQxa*f\"p#)Fax$\"1QoalE)*QfFax7$$\"
1Y([(\\Rv7))Fax$\"1+iQxAeGcFax7$$\"1mT$oO\\KF*Fax$\"1v;n#)>aw`Fax7$$\"
1c-05]\"*3)*Fax$\"1D.%>;bk4&Fax7$$\"1tY$p)pIG5F1$\"1aQ#*)\\n/'[Fax7$$
\"1\\(\\**GH.3\"F1$\"1Ikn-vV9YFax7$$\"1:JiCo')H6F1$\"1v+v.q^#R%Fax7$$
\"1JhAXSb\"=\"F1$\"1#eQ2%3]tTFax7$$\"1>Pu[!>!H7F1$\"1Rn&oe*G$)RFax7$$
\"1%oOtY;-G\"F1$\"1i**R%*)z$*y$Fax7$$\"17C['>'RL8F1$\"1_h%Hv#y*f$Fax7$
$\"1x^.2$*oz8F1$\"1S'pVloSW$Fax7$$\"1nLnMroH9F1$\"1sOz$RX^G$Fax7$$\"1s
X\"HyR8[\"F1$\"1&[uc8508$Fax7$$\"1a06A=(=`\"F1$\"1![#R/%z!))HFax7$$\"1
4<MoTw!e\"F1$\"1;0(4C5\"eGFax7$$\"1uX\"Hy]]j\"F1$\"1vk=m-GAFFax7$$\"1:
Ig?(HQo\"F1$\"1ZaDU)ptg#Fax7$$\"117C[;\"ft\"F1$\"18FCO'f;\\#Fax7$$\"1!
*yd:c5$y\"F1$\"1&zM(p.l#R#Fax7$$\"1&=Pu3,Z$=F1$\"1wtlH)e.H#Fax7$$\"1Rw
_0%[K)=F1$\"1!Qv,'QV*>#Fax7$$\"1Jg?TV*R$>F1$\"1!z]N%fb4@Fax7$$\"1@U%)o
xg$)>F1$\"1%=l8tlk-#Fax7$$\"1U#['H%[b.#F1$\"1AkG=v@W>Fax7$$\"1$['HfMd&
3#F1$\"1Flv>GHp=Fax7$$\"1MpQx7tO@F1$\"1xAgQ[u'z\"Fax7$$\"1uX\"H[lu=#F1
$\"1S6u/pgG<Fax7$$\"1=Pu[\\3MAF1$\"1y$y[lK\"p;Fax7$$\"1Rze<h^(G#F1$\"1
8+KtLV/;Fax7$$\"1+)f>f0`L#F1$\"1f\\)=@5&\\:Fax7$$\"1!)f>R\"fiQ#F1$\"13
!\\w=BQ\\\"Fax7$$\"1PrU&=G]V#F1$\"1B)R![U8V9Fax7$$\"1$f=P%*z\"*[#F1$\"
1_?!*zwl*Q\"Fax7$$\"1'=PuQrg`#F1$\"10`lOZfX8Fax7$$\"1(Qxaf$H*e#F1$\"1R
VvXE&zH\"Fax7$$\"13:Ig)*zPEF1$\"1Z)RN,*fc7Fax7$$\"1uZ&44e3p#F1$\"1P/)G
g'[87Fax7$$\"1sU&3PQmt#F1$\"1Q1^Y(oz<\"Fax7$$\"1Y\"Heww()y#F1$\"1C%\\P
l0$R6Fax7$$\"1OqS\"))R\"RGF1$\"1,\\^Fcm.6Fax7$$\"1+*zf4q%*)GF1$\"1&f*z
K)G'p5Fax7$$\"1pQxa^hRHF1$\"1tm;=0?P5Fax7$$\"1Y*)yd))y()HF1$\"1?(\\*Hc
O25Fax7$$\"1lE`1f')RIF1$\"1Fmy!ow[w*F-7$$\"1_-05\"*\\*3$F1$\"1c'3`5jJ[
*F-7$$\"1\"*zf>dtTJF1$\"1]%*[[g?*>*F-7$$\"1a2:IC-*=$F1$\"1*QE>VgE&*)F-
7$$\"1Qu[(4$GTKF1$\"1x>')Q5=\"p)F-7$$\"1_-05(R8H$F1$\"1)Hrc\\,5X)F-7$$
\"1'3<M[u7M$F1$\"1.f2-@!4A)F-7$$\"1$pQxaJMR$F1$\"1$)eC%Qq,*zF-7$$\"1,-
/3,ZTMF1$\"1))4)GQ3fy(F-7$$\"1AT#[;o1\\$F1$\"1S9#\\!=^%e(F-7$$\"1LmKl'
))\\a$F1$\"1whzZj&3P(F-7$$\"1Id9H9<%f$F1$\"1d\"zf70\\=(F-7$$\"1Sze<+ZW
OF1$\"1%RVb>T<+(F-7$$\"1h@V'QAcp$F1$\"1R=YZxQAoF-7$$\"1&oOtOTEu$F1$\"1
+$eT?&RjmF-7$$\"1h>Ry?w#z$F1$\"1;,hP)=)*\\'F-7$$\"1&oOtE,D%QF1$\"1D6Ky
#RKM'F-7$$\"1oMpQnq&*QF1$\"1]Q&z4&z\"='F-7$$\"1d:Ji#eE%RF1$\"1qgTi\\GW
gF-7$$\"1[$pQdIo*RF1$\"1e'G!eg8\"*eF-7$$\"19Fa3prXSF1$\"1mR3`KxddF-7$$
\"1OqS\"Q(3%4%F1$\"18kE!zQ,j&F-7$$\"1uW*)y65YTF1$\"1\"RhEFzu\\&F-7$$\"
1tX\"HQD$)>%F1$\"1T<l)pd)o`F-7$$\"1(RzenTeC%F1$\"1)ok<!>kb_F-7$$\"14<M
o=I'H%F1$\"1CG?P*=#R^F-7$$\"16@U%3YbM%F1$\"1:2bfrAH]F-7$$\"1b3<Mt#*)R%
F1$\"1+5l$GpQ\"\\F-7$$\"1?Rycp6XWF1$\"1j1A)psr\"[F-7$$\"1Sze<u;)\\%F1$
\"1tXuFp`4ZF-7$$\"1%\\)pRw.[XF1$\"19%yXzd:h%F-7$$\"1[#\\)phU(f%F1$\"1W
[G'>hu^%F-7$$\"1CZ%*))R&ok%F1$\"1Sz<D.5EWF-7$$\"1#RycBnsp%F1$\"1*f+9I,
dL%F-7$$\"1<LmKWq]ZF1$\"1;+A8n#GC%F-7$$\"1Rxa46q*z%F1$\"1+rB:.BgTF-7$$
\"1Gb5@r1[[F1$\"1jow2s+\"3%F-7$$\"1)Gd9fp(**[F1$\"1>Qfb;w)*RF-7$$\"1^-
05&f8&\\F1$\"1&**H)ob6>RF-7$$\"\"&F*F+-%'COLOURG6&%$RGBGF*F*F*-F$6$7dw
7$F($\"1xw/!QuU)fF-7$F/$\"1i6^%fl1L&F-7$F5$\"1n8^[]_<[F-7$F:$\"1IzBZ9`
+VF-7$F?$\"1*\\q8I(eUQF-7$FD$\"1?erp`CZMF-7$FI$\"11#yX31I8$F-7$FN$\"1R
4Os96fGF-7$FS$\"1!*HQ9$=$HEF-7$FX$\"1?;-nXq_CF-7$Fgn$\"17\\pl\\\"RK#F-
7$F\\o$\"1!3p&z$*[`AF-7$Fao$\"1i>y<I%3A#F-7$Ffo$\"1dW3-B6OAF-7$F[p$\"1
Pj6%*\\z%H#F-7$F`p$\"1(eej)4>%Q#F-7$Fep$\"1dWB'=IO`#F-7$Fjp$\"15\"))RL
#f&p#F-7$F_q$\"1w(*y`![K#HF-7$Fdq$\"1=F/\\ZmeJF-7$Fiq$\"1!f*elY6_MF-7$
F^r$\"1Cs,%orVw$F-7$Fcr$\"1a/\"32kG7%F-7$Fhr$\"1([#f`JA![%F-7$F]s$\"1X
g#3\\fX*[F-7$Fbs$\"1O6`/U?b`F-7$Fgs$\"1AU&)3T6!y&F-7$F\\t$\"1(Q!)\\d9G
E'F-7$Fat$\"1NMu9X8'y'F-7$Fft$\"1J%=R\"3/@tF-7$F[u$\"1G85sA**eyF-7$F`u
$\"1V)GuuC%y%)F-7$Feu$\"1,>hI\"oO0*F-7$Fju$\"1Nl3/\")3'o*F-7$F_v$\"1%=
XWiMu-\"Fax7$Fdv$\"1'[Y\"fLG$4\"Fax7$Fiv$\"1z86a4gc6Fax7$F^w$\"1%>W%zK
3C7Fax7$Fcw$\"18))RKXB\"H\"Fax7$Fhw$\"1=4ukjmi8Fax7$F]x$\"1rTlp\"\\CV
\"Fax7$Fcx$\"1Nh&fP.Z]\"Fax7$Fhx$\"1d$*z*HVrd\"Fax7$F]y$\"1fyJ]pIW;Fax
7$Fby$\"1$z#yXV)=s\"Fax7$Fgy$\"1])Qt+A<z\"Fax7$F\\z$\"1)Qj?vcl'=Fax7$F
az$\"1je7X_XQ>Fax7$Ffz$\"12L/cq\\=?Fax7$F[[l$\"1`2!z_**y3#Fax7$F`[l$\"
1#z,#Q'zm;#Fax7$Fe[l$\"1:OUoBSQAFax7$Fj[l$\"1$4k$)QymJ#Fax7$F_\\l$\"1/
U!G>&*RQ#Fax7$Fd\\l$\"1L212wKgCFax7$Fi\\l$\"1*z`13VO`#Fax7$F^]l$\"1hw>
Y1U1EFax7$Fc]l$\"1T&Guzm$yEFax7$Fh]l$\"1If'*G`)ou#Fax7$F]^l$\"1DW85(>-
#GFax7$Fb^l$\"1\">$=G+L*)GFax7$Fg^l$\"1-w&GOl6'HFax7$F\\_l$\"1FY2/]LDI
Fax7$Fa_l$\"1#\\$4/mB&4$Fax7$Ff_l$\"1-hx.K7hJFax7$F[`l$\"1'>/QiYdA$Fax
7$F``l$\"1**=%*o]+#H$Fax7$Fe`l$\"1%*p5XN&=N$Fax7$Fj`l$\"1Vc.7=#>T$Fax7
$F_al$\"1xG@vAuwMFax7$Fdal$\"1ErW$)p,MNFax7$Fial$\"1Yx)o]Z6f$Fax7$F^bl
$\"1ryb'z)pZOFax7$Fcbl$\"1b&zJwe#)p$Fax7$Fhbl$\"18#Rq\"*41v$Fax7$F]cl$
\"1yE2dQ%4!QFax7$Fbcl$\"1n%>z__H&QFax7$Fgcl$\"1hm]TaB(*QFax7$F\\dl$\"1
)=&R#z0k%RFax7$Fadl$\"1TaN+<(*))RFax7$Ffdl$\"135PYtOHSFax7$F[el$\"1w(*
3R(f32%Fax7$F`el$\"1a;k\"4b/6%Fax7$Feel$\"1rYh-PlWTFax7$Fjel$\"1:#e*[g
.zTFax7$F_fl$\"1tlHj;k5UFax7$Fdfl$\"1L&z/'**pUUFax7$Fifl$\"1up\"=Ho&oU
Fax7$F^gl$\"1pxZ<L6'H%Fax7$Fcgl$\"1:].3Z()>VFax7$Fhgl$\"1(=$zJ6NTVFax7
$F]hl$\"1esf)3!ygVFax7$Fbhl$\"1(=s>N`%yVFax7$Fghl$\"1)3$f>$3[R%Fax7$F
\\il$\"1fK)e#4k2WFax7$Fail$\"1]]&\\()o#=WFax7$Ffil$\"15Ez2/QFWFax7$F[j
l$\"1>^ZJx9MWFax7$F`jl$\"19_C!*)R#QWFax7$Fjjl$\"1?WpSvlSWFax7$Fe[m$\"1
n\"*=.SlSWFax7$F_\\m$\"1.2`OrIQWFax7$Fi\\m$\"19dZFMrLWFax7$F^]m$\"1Ad^
6@nFWFax7$Fc]m$\"1wajwpp=WFax7$Fh]m$\"1*>+/nPtS%Fax7$F]^m$\"1!y=8-EPR%
Fax7$Fb^m$\"1]p%yog!zVFax7$Fg^m$\"1/i^WH\"=O%Fax7$F\\_m$\"1nGp]=yTVFax
7$Fa_m$\"1][yT;h>VFax7$Ff_m$\"1)H`L\"4`%H%Fax7$F[`m$\"1_n'*3_aqUFax7$F
``m$\"1:n^`3WTUFax7$Fe`m$\"1$yri<,+@%Fax7$Fj`m$\"1pXhczixTFax7$F_am$\"
1A\"4Dl([YTFax7$Fdam$\"1U+ur.L2TFax7$Fiam$\"1`r,(>wB2%Fax7$F^bm$\"1gK!
4a#pHSFax7$Fcbm$\"1f`^X]7!*RFax7$Fhbm$\"1,#GTq?[%RFax7$F]cm$\"1yXipc()
**QFax7$Fbcm$\"1Oth.R9^QFax7$Fgcm$\"1%3V#Rzx/QFax7$F\\dm$\"1\"Q2RGuIv$
Fax7$Fadm$\"1`ZlZzb(p$Fax7$Ffdm$\"1R&R'\\)pxk$Fax7$F[em$\"1.UDgV^#f$Fa
x7$F`em$\"1#GTNViQ`$Fax7$Feem$\"13U#yS$*\\Z$Fax7$Fjem$\"1Tj*4n#o;MFax7
$F_fm$\"10/8F=W]LFax7$Fdfm$\"1nvwPSj*G$Fax7$Fifm$\"1#y$f&4DMA$Fax7$F^g
m$\"1%=B%e!RB;$Fax7$Fcgm$\"1#owtqIW4$Fax7$Fhgm$\"1IK(=0?&HIFax7$F]hm$
\"1r</WHogHFax7$Fbhm$\"1%*eEO9Z#*GFax7$Fghm$\"1'yHTEn,#GFax7$F\\im$\"1
#*R\"3#pt\\FFax7$Faim$\"1Q=MK:)pn#Fax7$Ffim$\"1O*e_)[</EFax7$F[jm$\"1h
#[O`ln`#Fax7$F`jm$\"1\"p3-5!**eCFax7$Fejm$\"1O'Q)3H.*Q#Fax7$Fjjm$\"1;I
&e![69BFax7$F_[n$\"1LJ%*)fn@C#Fax7$Fd[n$\"1%QMHW(4i@Fax7$Fi[n$\"1K^F'R
(o#4#Fax7$F^\\n$\"12lkye\"R,#Fax7$Fc\\n$\"1YS!ef=A%>Fax7$Fh\\n$\"1,pY4
a*R'=Fax7$F]]n$\"1INeIGv'z\"Fax7$Fb]n$\"1x:\\2'\\0s\"Fax7$Fg]n$\"1v>i
\\)>uk\"Fax7$F\\^n$\"1/ZwXr!\\d\"Fax7$Fa^n$\"1\"ed2HEL]\"Fax7$Ff^n$\"1
&GHt:y_V\"Fax7$F[_n$\"1qD()pWhi8Fax7$F`_n$\"1,FeIIL%H\"Fax7$Fe_n$\"1N9
*eH4OA\"Fax7$Fj_n$\"1()Q1<Wpg6Fax7$F_`n$\"17\")y5%*\\#4\"Fax7$Fd`n$\"1
o=0R'4'G5Fax7$Fi`n$\"1qvh!4<Qm*F-7$F^an$\"1[;F+>8J!*F-7$Fcan$\"1pj$z!3
9l%)F-7$Fhan$\"1iT%RPLK!zF-7$F]bn$\"1%H\"RC[-0tF-7$Fbbn$\"1J`3`Au%y'F-
7$Fgbn$\"1>-)4$)))[F'F-7$F\\cn$\"1#e!\\hws!y&F-7$Facn$\"1T&H(z$)H\\`F-
7$Ffcn$\"1WX%Q>\"o9\\F-7$F[dn$\"1\"=0&HnS5XF-7$F`dn$\"1m&HpFG#4TF-7$Fe
dn$\"1O82rUH$y$F-7$Fjdn$\"1.mlvVYTMF-7$F_en$\"1i$H\"\\p$e;$F-7$Fden$\"
1Z^R2N4DHF-7$Fien$\"1J&GBT^Jq#F-7$F^fn$\"1[/5L\"y._#F-7$Fcfn$\"1rw#RYH
.R#F-7$Fhfn$\"10g\"=6k9H#F-7$F]gn$\"1z)e)3wNNAF-7$Fbgn$\"1Dg![&)Q7A#F-
7$Fggn$\"1G#4qc\"f\\AF-7$F\\hn$\"1&*=4bV@IBF-7$Fahn$\"1'3$>xgTaCF-7$Ff
hn$\"1wcU3W>DEF-7$F[in$\"1X74M?AXGF-7$F`in$\"1![hN[H=7$F-7$Fein$\"1\")
y^^XQuMF-7$Fjin$\"1#HDPLuH&QF-7$F_jn$\"1zZ2(**\\,G%F-7$Fdjn$\"1=gZ:JA(
z%F-7$Fijn$\"1j7BN^?x`F-7$F^[oFh[o-Fa[o6&Fc[o$\"*++++\"!\")F*F*-F$6$7_
x7$F($\"1YSna8^ENF-7$$!1rV([(>rt\\F1$\"1Y\\(oI>\"3RF-7$F/$\"1z+.D#Hy9%
F-7$$!1S#['z3bC\\F1$\"1O:HVCSoUF-7$F5$\"18kvloiFVF-7$$!1+++]Y&f([F1$\"
1&Qp5Dr7M%F-7$F:$\"1,!>^(*otJ%F-7$F?$\"1Ng[l&e`@%F-7$FD$\"1t>eu4u6TF-7
$FI$\"1!*oG.(R!eSF-7$FN$\"1b3uNswlSF-7$FS$\"1)3`&RR#e9%F-7$FX$\"16YwFU
I\"H%F-7$Fgn$\"1\"RF\"4QH%\\%F-7$F\\o$\"1[5r$eEHq%F-7$Fao$\"1%4!*yO>R&
\\F-7$Ffo$\"1\"f9gB*>1_F-7$F[p$\"1QM7KKtNaF-7$F`p$\"1_V_%pUSi&F-7$Fep$
\"1;J*)*z`f\"eF-7$Fjp$\"1F52kfT[fF-7$F_q$\"1Z3POEcngF-7$Fdq$\"1>'GH'=/
WhF-7$Fiq$\"1oX([d*e,iF-7$F^r$\"1\\CcFP7PiF-7$Fcr$\"1rR9,a=iiF-7$Fhr$
\"1*\\.&)4i>G'F-7$F]s$\"1!36FUj\"3jF-7$Fbs$\"1!p;aK['\\jF-7$Fgs$\"1(Q8
)[jL/kF-7$F\\t$\"15Izcr*))['F-7$Fat$\"1e%y)GWS4mF-7$Fft$\"1.6#ewGRw'F-
7$F[u$\"1A!=!4fJ]pF-7$F`u$\"1t#fKa\"*3?(F-7$Feu$\"1w3!3![ykuF-7$Fju$\"
1K*3>ec^y(F-7$F_v$\"12Kr;vA2\")F-7$Fdv$\"1r_jv(G**[)F-7$Fiv$\"1/Ufa=vu
))F-7$F^w$\"1P]:3,L(H*F-7$Fcw$\"1f\\zNZ.D(*F-7$Fhw$\"1nB2x*3#=5Fax7$F]
x$\"1#3EIGYD1\"Fax7$Fcx$\"1*R\"\\qwk26Fax7$Fhx$\"18-BvQj^6Fax7$F]y$\"1
1$*4MD.\">\"Fax7$Fby$\"19)ec:QYB\"Fax7$Fgy$\"1w69kA-s7Fax7$F\\z$\"16a`
f1358Fax7$Faz$\"1O_**z%oZM\"Fax7$Ffz$\"1*3cxkN9Q\"Fax7$F[[l$\"1'>&fa<&
=T\"Fax7$F`[l$\"1v%Hg%[GX9Fax7$Fe[l$\"1@fArABv9Fax7$Fj[l$\"1&zdIG(43:F
ax7$F_\\l$\"1?jp9)yr`\"Fax7$Fd\\l$\"1x%*Q+W%>d\"Fax7$Fi\\l$\"1t5(*p=43
;Fax7$F^]l$\"1(4[Wi6xk\"Fax7$Fc]l$\"1**z\"4Jn;p\"Fax7$Fh]l$\"1!y*4>l1R
<Fax7$F]^l$\"13AN+c3(z\"Fax7$Fb^l$\"1q(R84n*f=Fax7$Fg^l$\"1Qk>l`AN>Fax
7$F\\_l$\"1QN!p)QE7?Fax7$Fa_l$\"1S9>[&z\"3@Fax7$Ff_l$\"15e\\VTY6AFax7$
F[`l$\"17\"='zOKEBFax7$F``l$\"1&Q3O'H_fCFax7$Fe`l$\"1D\"**)4]e%f#Fax7$
Fj`l$\"1vlNIa\\XFFax7$F_al$\"1(G7Lpwq#HFax7$Fdal$\"1yP)3)[+0JFax7$Fial
$\"1o5cop1+LFax7$F^bl$\"11M00^k6NFax7$Fcbl$\"1_U2IfQ<PFax7$Fhbl$\"1_..
C+!z%RFax7$F]cl$\"1h,xFQC(=%Fax7$Fbcl$\"1;J(R]!z`WFax7$Fgcl$\"1#\\0$)G
Jpp%Fax7$F\\dl$\"1HG(f/,_)\\Fax7$Fadl$\"1=3dUY)4D&Fax7$Ffdl$\"1EN=^Nt<
bFax7$F[el$\"1\">?(R0,2eFax7$F`el$\"1t(*)Q%*Q!)4'Fax7$Feel$\"1)>9O!pdh
jFax7$Fjel$\"1Rx8%[m#QmFax7$F_fl$\"1B6]T()G.pFax7$Fdfl$\"1%Q&=Vd%G=(Fa
x7$Fifl$\"1^YWP^];uFax7$F^gl$\"1<B_`#HMn(Fax7$Fcgl$\"1+\\[;.$>!zFax7$F
hgl$\"1nK.@#QS6)Fax7$F]hl$\"1gJW^uc5$)Fax7$Fbhl$\"1C`PbmA$\\)Fax7$Fghl
$\"1UL4'f2cm)Fax7$F\\il$\"1E3RKD9.))Fax7$Fail$\"1D%[zv\"e=*)Fax7$Ffil$
\"1xoCE[m=!*Fax7$F[jl$\"1AF'>=pO4*Fax7$$!1W\"Hem['35Fax$\"1Pe\">%e2>\"
*Fax7$F`jl$\"1VdxoDIR\"*Fax7$Fejl$\"18![lD7l:*Fax7$Fjjl$\"123AZ=Om\"*F
ax7$F_[m$\"1eu;%[H*o\"*Fax7$Fe[m$\"1PkE+AKm\"*Fax7$Fj[m$\"1h[+iKrc\"*F
ax7$F_\\m$\"1d>a>U0S\"*Fax7$Fd\\m$\"1cDT*Q:w6*Fax7$Fi\\m$\"1]BSC%Q))3*
Fax7$F^]m$\"1[.R`g)=-*Fax7$Fc]m$\"1lJ#>,hK#*)Fax7$Fh]m$\"1%RL71p)*z)Fa
x7$F]^m$\"1Fc-b**4a')Fax7$Fb^m$\"1Qq&\\<q&*\\)Fax7$Fg^m$\"1%o\\n))R6K)
Fax7$F\\_m$\"1!GO\\)pM=\")Fax7$Fa_m$\"1')==U_O**yFax7$Ff_m$\"1*)3b'fR%
ewFax7$F[`m$\"1UFCLOmMuFax7$F``m$\"1Res;%e;<(Fax7$Fe`m$\"1tj'3m9y*oFax
7$Fj`m$\"1>jmK%*pEmFax7$F_am$\"1V\"R#\\`.wjFax7$Fdam$\"1%f&\\n\"GX2'Fa
x7$Fiam$\"1*osU\"Q)y\"eFax7$F^bm$\"1%=:*y(R*>bFax7$Fcbm$\"1(e!*\\'>Se_
Fax7$Fhbm$\"1DpMt*)fv\\Fax7$F]cm$\"1%H'*zg8>r%Fax7$Fbcm$\"1UQ?w<=WWFax
7$Fgcm$\"1HfxTP@1UFax7$F\\dm$\"1\\2igj?fRFax7$Fadm$\"1$=z$4HU9PFax7$Ff
dm$\"1%4')Q-B>^$Fax7$F[em$\"1uZun*e\\I$Fax7$F`em$\"1Zw,d:]/JFax7$Feem$
\"13uS\"e3>#HFax7$Fjem$\"19f')><:eFFax7$F_fm$\"1rHTJ#G7f#Fax7$Fdfm$\"1
L:ul#pWX#Fax7$Fifm$\"1)enr%*[>K#Fax7$F^gm$\"1')=^@o\\8AFax7$Fcgm$\"1F'
))ph'*p5#Fax7$Fhgm$\"1'[VBwRw,#Fax7$F]hm$\"1!f)3,HoM>Fax7$Fbhm$\"1D(pn
SOI'=Fax7$Fghm$\"1k<Jx5/(z\"Fax7$F\\im$\"1c;dSI<T<Fax7$Faim$\"1YY^\"fo
2p\"Fax7$Ffim$\"1G_;,BUY;Fax7$F[jm$\"1M7qntq4;Fax7$F`jm$\"1zK0UKJr:Fax
7$Fejm$\"1?KZ$o/%R:Fax7$Fjjm$\"1HYE*H4q]\"Fax7$F_[n$\"1$Q3xl-oZ\"Fax7$
Fd[n$\"1*fU_&>OV9Fax7$Fi[n$\"1_l$pm6RT\"Fax7$F^\\n$\"1GKK%o'Qz8Fax7$Fc
\\n$\"1t@9%GOlM\"Fax7$Fh\\n$\"1AvdG<\")38Fax7$F]]n$\"1\"H;&3aku7Fax7$F
b]n$\"1)y\"3Wh!RB\"Fax7$Fg]n$\"10r*>#G#G>\"Fax7$F\\^n$\"1f#e:!zH]6Fax7
$Fa^n$\"1$f4OQ)z16Fax7$Ff^n$\"1FfiP/Lk5Fax7$F[_n$\"1,#z&Ge<=5Fax7$F`_n
$\"1mdG)*e&[u*F-7$Fe_n$\"1^!=UHIVH*F-7$Fj_n$\"1u,N)ov+!*)F-7$F_`n$\"1l
b.%ec_[)F-7$Fd`n$\"1p()*R(p'Q6)F-7$Fi`n$\"1SyL&R!RtxF-7$F^an$\"1BA9zf#
RX(F-7$Fcan$\"1mxQv\"Q^>(F-7$Fhan$\"1p(e$))G(p'pF-7$F]bn$\"1SKw!R[)enF
-7$Fbbn$\"1u9:;M/4mF-7$Fgbn$\"1u`H;aL\"\\'F-7$F\\cn$\"1&\\(*>?GWS'F-7$
Facn$\"1TEZOy+\\jF-7$Ffcn$\"1#)HaIXl4jF-7$F[dn$\"1yJ)RtdOG'F-7$F`dn$\"
1UB3MvQhiF-7$Fedn$\"1v2&=C\\(QiF-7$Fjdn$\"1>$)fDL++iF-7$F_en$\"1**o!Gr
ie9'F-7$Fden$\"1_5o!)GJogF-7$Fien$\"1&y9:*fS`fF-7$F^fn$\"1wN9rnR-eF-7$
Fcfn$\"1BmH%**GTj&F-7$Fhfn$\"19?Pf`XEaF-7$F]gn$\"1l7dRwK,_F-7$Fbgn$\"1
^v^xOKV\\F-7$Fggn$\"12ld4mB?ZF-7$F\\hn$\"1K&ftq93[%F-7$Fahn$\"1-qq'GS$
*G%F-7$Ffhn$\"1\\A_@$y\"[TF-7$F[in$\"1EOY>6EoSF-7$F`in$\"1&4?/'G5dSF-7
$Fein$\"1hD6%3l\"=TF-7$Fjin$\"1@v4#4M\"=UF-7$F_jn$\"1.T<ZY;9VF-7$$\"13
9Gc$=R([F1$\"1)z'y+3_SVF-7$Fdjn$\"1F#o:'3LIVF-7$$\"1pPv]XcD\\F1$\"1/]E
^+\\kUF-7$Fijn$\"1W+(R9F&>TF-7$$\"1D^-b(zc(\\F1$\"1xn4iN%\\)QF-7$F^[o$
\"1^Sna8^ENF--Fa[o6&Fc[oF*F*F_aq-F$6$7ix7$F($\"12.FUI8RWF-7$$!1'=Pu)f&
o)\\F1$\"1<'=A;`S*QF-7$Fiaq$\"1)z&Q6y+dNF-7$$!1e:Jizcg\\F1$\"1sB/n?l\"
Q$F-7$F/$\"1**yGfl$*GLF-7$Fabq$\"10^z'zKdV$F-7$F5$\"1-9Xr[z%o$F-7$F:$
\"1kA4n#GvL%F-7$$!1Fb5@yLC[F1$\"1QwQBmB)e%F-7$F?$\"1\"ze.<H1v%F-7$$!17
D]]NnsZF1$\"1DM/URsA[F-7$FD$\"1wd@MrV:[F-7$$!1w],..,BZF1$\"1$fAyM5Av%F
-7$FI$\"1\\)=zTv1l%F-7$FN$\"161\"Qs(p'Q%F-7$FS$\"1,0M<8xVTF-7$$!1(\\**
)zS'Hd%F1$\"1>SBaPOkSF-7$FX$\"1U#H6=ZC-%F-7$$!1)[(\\\\qA@XF1$\"1@>HOw%
>-%F-7$Fgn$\"1$H\\6d%=lSF-7$F\\o$\"1g+5Wt+SUF-7$Fao$\"1TVMRhzcXF-7$Ffo
$\"1*3opq/)\\\\F-7$F[p$\"1=,P)=ZUM&F-7$F`p$\"1Uu'H%4KvcF-7$Fep$\"1e!e_
2!4(*fF-7$Fjp$\"1o!Q(*yJ&*='F-7$F_q$\"1*Q#=Za$QJ'F-7$Fdq$\"1CP2cN+TjF-
7$Fiq$\"1'G****R(e*H'F-7$F^r$\"1$Q/]'>T:iF-7$Fcr$\"1/A.h&Q56'F-7$Fhr$
\"1bcgNShEgF-7$F]s$\"1<'=z'RftfF-7$Fbs$\"1O<5)G%H$)fF-7$Fgs$\"1)fv6^^&
egF-7$F\\t$\"16Q@IyZ;iF-7$Fat$\"17ua)>_KY'F-7$Fft$\"1_vBt\")G!y'F-7$F[
u$\"1\"pqE1xn9(F-7$F`u$\"1FZ+>'*[/wF-7$Feu$\"1A)3g[;H/)F-7$Fju$\"1%f(Q
yf#*=&)F-7$F_v$\"188<mtgS*)F-7$Fdv$\"1*Gg.LzZP*F-7$Fiv$\"1z?AFE_X(*F-7
$F^w$\"1'[-m\"[\\35Fax7$Fcw$\"10s(o))*[O5Fax7$Fhw$\"1*z)zAoJg5Fax7$F]x
$\"1]()[*oP%y5Fax7$Fcx$\"1L*)RE!yH4\"Fax7$Fhx$\"1$H$Q7Em/6Fax7$F]y$\"1
EL:1:H96Fax7$Fby$\"1u\"f%**ptD6Fax7$Fgy$\"1FQmD<#z8\"Fax7$F\\z$\"1!>x2
@\"fa6Fax7$Faz$\"1$o2GBJb<\"Fax7$Ffz$\"10PCnB(f?\"Fax7$F[[l$\"1Q3jKmTR
7Fax7$F`[l$\"1$*R\"HuChG\"Fax7$Fe[l$\"1`dA.3;P8Fax7$Fj[l$\"1-P@ZOE-9Fa
x7$F_\\l$\"1u**GNt&fY\"Fax7$Fd\\l$\"1w#)=\")\\OY:Fax7$Fi\\l$\"1F/yvl6J
;Fax7$F^]l$\"1WAAZ7o@<Fax7$Fc]l$\"1Flr`Jb;=Fax7$Fh]l$\"10b!f'H!4\">Fax
7$F]^l$\"1-x%Hgr^,#Fax7$Fb^l$\"1O$\\nVJc6#Fax7$Fg^l$\"1x&3aI'[@AFax7$F
\\_l$\"12iFc.x;BFax7$Fa_l$\"1]SxZ:0@CFax7$Ff_l$\"1+XIO_%)>DFax7$F[`l$
\"1.R*)e2h<EFax7$F``l$\"13K$3iu&>FFax7$Fe`l$\"1BDiP!*H9GFax7$Fj`l$\"1:
Q&eikL\"HFax7$F_al$\"136?@o(p-$Fax7$Fdal$\"1=SxY+dNJFax7$Fial$\"1$)ekf
@IaKFax7$F^bl$\"1c%>$G&z^Q$Fax7$Fcbl$\"1J<-@eR;NFax7$Fhbl$\"12I]8hqpOF
ax7$F]cl$\"1$o>qARt$QFax7$Fbcl$\"1)>%e3Q\\NSFax7$Fgcl$\"1%\\i!\\@pFUFa
x7$F\\dl$\"1ezU-EcqWFax7$Fadl$\"1^%4*\\w[4ZFax7$Ffdl$\"1(ef>*z:k\\Fax7
$F[el$\"1A^&zs)\\d_Fax7$F`el$\"1i^6f>'3d&Fax7$Feel$\"1Hkz/_`qeFax7$Fje
l$\"1h\"o$\\$*\\,iFax7$F_fl$\"1\\$*p\"G<U`'Fax7$Fdfl$\"13y-`.$=!pFax7$
Fifl$\"1hw!z:v@A(Fax7$F^gl$\"1)))H$ez7)e(Fax7$Fcgl$\"1/It=\">c#zFax7$F
hgl$\"1,1Kcl)*[#)Fax7$F]hl$\"1f'z&zqBd&)Fax7$Fbhl$\"1>`$3*z9^))Fax7$Fg
hl$\"1H4\\Qh/N\"*Fax7$F\\il$\"15(4UG$3m$*Fax7$Fail$\"1^#Hsx%4j&*Fax7$F
fil$\"1`Q\\!=wht*Fax7$F[jl$\"1+)*4$4qs')*Fax7$F[er$\"10,pFX%>\"**Fax7$
F`jl$\"1Z44]wgZ**Fax7$Fejl$\"1&RUH')=!y**Fax7$Fjjl$\"1>b5H?X&***Fax7$F
_[m$\"004F$********F17$Fe[m$\"1\"RUc\"=Q&***Fax7$Fj[m$\"1;\"omUu$y**Fa
x7$F_\\m$\"1I\"3DfM*[**Fax7$Fd\\m$\"18mYIGP4**Fax7$Fi\\m$\"1LHUf6ze)*F
ax7$F^]m$\"1NI7l>yT(*Fax7$Fc]m$\"1A(G?*)R6d*Fax7$Fh]m$\"1j3N#zP0O*Fax7
$F]^m$\"1z$4F1(*e6*Fax7$Fb^m$\"1yN+OJ[h))Fax7$Fg^m$\"1$R-zMaSd)Fax7$F
\\_m$\"1]E7Celb#)Fax7$Fa_m$\"1xTo8zw@zFax7$Ff_m$\"1'ew%[OQmvFax7$F[`m$
\"1*\\?JHovC(Fax7$F``m$\"1ib?#G\"z')oFax7$Fe`m$\"1WHI*[*=FlFax7$Fj`m$
\"1)H(y#zFt='Fax7$F_am$\"1Va$p2:u)eFax7$Fdam$\"1q()RhM'[a&Fax7$Fiam$\"
1&))G?Aw)o_Fax7$F^bm$\"1*Hz5IFj'\\Fax7$Fcbm$\"1m>/VhO;ZFax7$Fhbm$\"17j
QeK?iWFax7$F]cm$\"1m)>J'y!*RUFax7$Fbcm$\"1]29&oF\"GSFax7$Fgcm$\"1*\\P-
_G5&QFax7$F\\dm$\"1=umX8UxOFax7$Fadm$\"1r-XK:Z9NFax7$Ffdm$\"1wt@*y``Q$
Fax7$F[em$\"1J'p0F&HdKFax7$F`em$\"1\\96iUENJFax7$Feem$\"1s))4gezBIFax7
$Fjem$\"1%QWD&3W@HFax7$F_fm$\"1Z'=?XD?\"GFax7$Fdfm$\"1!H1#o?)er#Fax7$F
ifm$\"1]'H_2wSh#Fax7$F^gm$\"1N+?!*[n@DFax7$Fcgm$\"1S+j/m%)>CFax7$Fhgm$
\"1M))Q.3+BBFax7$F]hm$\"1s*QH1s2A#Fax7$Fbhm$\"1f\">$e_B?@Fax7$Fghm$\"1
mu<lg4:?Fax7$F\\im$\"1\"HCf\\+\\\">Fax7$Faim$\"1;(>sn#o9=Fax7$Ffim$\"1
O['G6+)=<Fax7$F[jm$\"1>:f^r([j\"Fax7$F`jm$\"1HY#[([)[a\"Fax7$Fejm$\"1n
!\\$H?+r9Fax7$Fjjm$\"1VDb\"=x**R\"Fax7$F_[n$\"1'zMw!z1S8Fax7$Fd[n$\"1J
r!>(H9$G\"Fax7$Fi[n$\"1]\\U5O)>C\"Fax7$F^\\n$\"1:gixW+/7Fax7$Fc\\n$\"1
Q;NhQyw6Fax7$Fh\\n$\"1'H_M?UR:\"Fax7$F]]n$\"1Dj#*\\!3*Q6Fax7$Fb]n$\"16
x]#eEb7\"Fax7$Fg]n$\"1%z^SCKZ6\"Fax7$F\\^n$\"1#*H72*HV5\"Fax7$Fa^n$\"1
4_F$oKF4\"Fax7$Ff^n$\"1Y8yG%z!z5Fax7$F[_n$\"1kE1p:Ig5Fax7$F`_n$\"1`ptc
kkP5Fax7$Fe_n$\"1fv*>)oF35Fax7$Fj_n$\"1f\"zwJyxw*F-7$F_`n$\"1XJ)3Q())p
$*F-7$Fd`n$\"1RQ+K)Q([*)F-7$Fi`n$\"1,-W\"4vC])F-7$F^an$\"1%f$G-wsD!)F-
7$Fcan$\"1-y))G'RWf(F-7$Fhan$\"18&=o2w%yrF-7$F]bn$\"1!)od$[<+x'F-7$Fbb
n$\"159BdZ]ikF-7$Fgbn$\"1l#eT>R8A'F-7$F\\cn$\"1#)\\3&*[qegF-7$Facn$\"1
v4pcKp#)fF-7$Ffcn$\"1:aqa&eC(fF-7$F[dn$\"1ls_NT&4-'F-7$F`dn$\"1F+-fQy9
hF-7$Fedn$\"1R(Q(=R\")4iF-7$Fjdn$\"1#G2Imo>I'F-7$F_en$\"1/\\R*\\t2M'F-
7$Fden$\"11GJU,P9jF-7$Fien$\"1nU([9Kf>'F-7$F^fn$\"1c6TP*fb(fF-7$Fcfn$
\"1<u*f5kGp&F-7$Fhfn$\"1CUf'4[zK&F-7$F]gn$\"1D5\"4$4sT\\F-7$Fbgn$\"1e0
s<JnTXF-7$Fggn$\"1J\")=LtmeUF-7$F\\hn$\"1K-kmkndSF-7$Fahn$\"1rl\\'=^H-
%F-7$Ffhn$\"1*4^qZm)RTF-7$F[in$\"1;A(\\+j;P%F-7$F`in$\"1')Q:s+oTYF-7$$
\"1b3<Me)Rs%F1$\"1'*HO,<lbZF-7$Fein$\"1n4(Q\"f!4#[F-7$$\"1Gb5rF?vZF1$
\"1?M*e\"yQ>[F-7$Fjin$\"1)[Xwpp[u%F-7$$\"1LmK:T)Q#[F1$\"1>&=%H,(=f%F-7
$F_jn$\"1%3e*[&>:O%F-7$Fdjn$\"1Q#>js`)3PF-7$F]is$\"1K]N]t;FMF-7$Fijn$
\"1-%)yjH\"RL$F-7$$\"1)oPDj>N'\\F1$\"1F=U*)>24MF-7$Feis$\"1oII)oJhf$F-
7$$\"1jD^x)Ry)\\F1$\"15l4sf-FRF-7$F^[o$\"1+.FUI8RWF--Fa[o6&Fc[oF*F_aqF
*-%*THICKNESSG6#\"\"$-%+AXESLABELSG6$Q\"X6\"%!G-%%VIEWG6$;F(F^[o;F*$\"
\"\"F*" 1 2 0 1 3 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 23 "Le phŽnom�ne a disparu." }}{PARA 0 "" 0 "
" {TEXT -1 86 "Reste ˆ determiner le lien entre ces xi particuliers et
 les polyn™mes de Tchebycheff :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 16 "with(orthopoly):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "T(n,x
) est le n-i�me polynome de Tchebycheff en x." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 7 "T(2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%
\"xG\"\"#\"\"\"F'!\"\"\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 15 "T(8,x2(3,7)/5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)-%$cosG6
#,$%#PiG#\"\"(\"#;\"\")\"\"\"\"$G\"*$)F&\"\"'F/!$c#*$)F&\"\"%F/\"$g\"*
$)F&\"\"#F/!#K\"\"\"F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "ev
alf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 31 "x2(i,n)/5 est racine de T(n+1)." }}}}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 48 "Ex 3 : Racines rationnelles de polyn™mes \+
de Z[X]" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "si p/q irrŽductible est
 racine de an*x^n+...+a0 alors :" }}{PARA 0 "" 0 "" {TEXT -1 54 "an*p^
n=-q*(a(n-1)*p^(n-1)+...+a0*q^n-1) c'est ˆ dire :" }}{PARA 0 "" 0 "" 
{TEXT -1 78 "q divise an*p^n. Or q est premier avec p et donc avec p^n
 et donc q divise an." }}{PARA 0 "" 0 "" {TEXT -1 20 "De m�me p divise
 a0." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 128 "Application : Faisons un
e fonction qui renvoie tous les nombres rŽpondant ˆ la condition nŽces
saire que l'on vient de dŽmontrer." }}{PARA 0 "" 0 "" {TEXT -1 12 "Un \+
exemple :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "poly:=27*(x-4/
3)*(x-7/9);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%polyG,$*&,&%\"xG\"\"
\"#!\"%\"\"$F)F),&F(F)#!\"(\"\"*F)F)\"#F" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "expand(poly);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$
)%\"xG\"\"#\"\"\"\"#FF&!#d\"#G\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "lcoeff(poly,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
#F" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "tcoeff(poly,x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#G" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "divisors(28);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<(\"
\"\"\"\"#\"\"%\"\"(\"#9\"#G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "D'
ou la fonction :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "possib
les:= (p,x) -> \{seq(seq(seq(s*i/j,j=divisors(lcoeff(p,x))),i=divisors
(tcoeff(p,x))),s=\{-1,1\})\}:" }}{PARA 7 "" 1 "" {TEXT -1 42 "Warning,
 `s` in call to `seq` is not local" }}{PARA 7 "" 1 "" {TEXT -1 42 "War
ning, `i` in call to `seq` is not local" }}{PARA 7 "" 1 "" {TEXT -1 
42 "Warning, `j` in call to `seq` is not local" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 18 "possibles(poly,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<R#!\"(\"\"*#!\"#\"\"$#F%F)#F%\"#F#!#9F)#F.F&#F.F,#!#GF
)#F2F&#F2F,#!\"%F,#\"\"\"F&#F8F,#\"\"#F)#F;F&#F;F,#\"\"%F)#F?F&#F?F,#F
8F)!\"\"F8F(F;F6F?F%\"\"(F.\"#9F2\"#G#FEF)#FEF&#FEF,#FFF)#FFF&#FDF)#FD
F&#FDF,#F6F)#FCF&#FCF,#F6F&#FFF,#F(F&#F(F,#FCF)" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 49 "Reste ˆ ne selectionner que les 'vraies' racines." }
}{PARA 0 "" 0 "" {TEXT -1 103 "On crŽe une fonction qui renvoie true (
vrai) si 'v' est une racine du polyn™me 'p' d'indŽterminŽe 'x' :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "estnul:=(v,p,x) -> subs(x=v,
p)=0:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Et on utilise " }{TEXT 
258 6 "select" }{TEXT -1 67 " pour ne prendre dans les possibles (poss
) que les vraies racines :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
47 "vraies:= (p,x,poss) -> select(estnul,poss,p,x):" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 20 "On combine le tout :" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 53 "toutesracines := (p,x) -> vraies(p,x,possibles(p,x
)):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "RŽsultat :" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "toutesracines(poly,x);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#<$#\"\"%\"\"$#\"\"(\"\"*" }}}}}{MARK "2 25 0 0
" 0 }{VIEWOPTS 1 1 0 1 1 1803 }