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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 10 "TP MAPLE 6" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "Racine carr
\351e" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "cherche_b:=proc(p)
\nlocal i;\nfor i from 1 to p-1 do\n     if (i&^((p-1)/2) mod p <> 1) \+
then RETURN(i) fi;\nod;\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*ch
erche_bGR6#%\"pG6#%\"iG6\"F*?(8$\"\"\"F-,&9$F-F-!\"\"%%trueG@$0-%$modG
6$-%#&^G6$F,,&F/#F-\"\"##F-F<F0F/F--%'RETURNG6#F,F*F*F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 386 "sqroot := proc(a,p)\n     local b,
i,e1,e2,racine,x;\n     if a&^((p-1)/2) mod p <> 1 then RETURN(0) fi;
\n\n     b:=cherche_b(p);\n     e1:=(p-1)/2;\n     e2:=0;\n\n     whil
e (e1 mod 2 = 0) do\n        e1:=e1/2;\n        e2:=e2/2;\n        x:=
a&^(e1)*b&^(e2) mod p;\n        if x=-1 then e2:= e2 + (p-1)/2 fi;\n  \+
   od;\n     racine:=a&^((e1+1)/2)*b&^(e2/2) mod p;\n     RETURN([raci
ne,-racine]);\nend;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'sqrootGR6$%
\"aG%\"pG6(%\"bG%\"iG%#e1G%#e2G%'racineG%\"xG6\"F0C)@$0-%$modG6$-%#&^G
6$9$,&9%#\"\"\"\"\"##F>F?!\"\"F<F>-%'RETURNG6#\"\"!>8$-%*cherche_bG6#F
<>8&F;>8'FE?(F0F>F>F0/-F56$FLF?FEC&>FL,$FLF=>FN,$FNF=>8)-F56$*&-F86$F:
FLF>-F86$FGFNF>F<@$/FYFA>FN,(FNF>*&F=F>F<F>F>#F>F?FA>8(-F56$*&-F86$F:,
&FLF=F=F>F>-F86$FGFWF>F<-FC6#7$Fbo,$FboFAF0F0F0" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 12 "sqroot(2,7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#7$\"\"%!\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "CA MARCHE .....
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" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "cbroot1 :=proc(x,p)\nl
ocal inv_de_3_mod_p;\ninv_de_3_mod_p:=msolve(X^3-1,p);\nRETURN(x&^inv_
de_3_mod_p mod p);\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(cbroot1
GR6$%\"xG%\"pG6#%/inv_de_3_mod_pG6\"F+C$>8$-%'msolveG6$,&*$)%\"XG\"\"$
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "cherche_un_autre_b := proc(p)\nloc
al i;\nfor i from 1 to p-1 do\n     if (i&^((p-1)/3) mod p <> 1) then \+
RETURN(i) fi;\nod;\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%3cherche
_un_autre_bGR6#%\"pG6#%\"iG6\"F*?(8$\"\"\"F-,&9$F-F-!\"\"%%trueG@$0-%$
modG6$-%#&^G6$F,,&F/#F-\"\"$#F-F<F0F/F--%'RETURNG6#F,F*F*F*" }}}
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" {MPLTEXT 1 0 567 "cbroot2 :=proc(a,p)\nlocal b,i,racine,j,j2,x,e1,e2
,L;\n\nif (a&^((p-1)/3) mod p <>1 ) then RETURN('toto') fi;\n\nb:=cher
che_un_autre_b(p);\nprint(b);\nj:=b&^((p-1)/3) mod p;\nj2:= b&^(2*(p-1
)/3) mod p;\ne1:=(p-1)/3;\ne2:=0;\n\nL:=[];\n\nwhile (e1 mod 3 = 0) do
\ne1:=e1/3;\ne2:=e2/3;\nx:=a&^e1*b&^e2 mod p;\n\nif (x=j) then e2:=e2 \+
+ 2*(p-1)/3\nelif (x=j2) then e2:=e2 + (p-1)/3 fi;\nod;\n\nif (e1 mod \+
3 = 2) then\n    x:=a&^((e1+1)/3)*b&^(e2/3) mod p; \nelse #=1\n    x:=
a&^((e1+2)/6)*b&^(e2/6) mod p ; if (x^3 mod p) = (p - a) then x:=-x fi
; \nfi;\n\nL:=[x,j*x mod p,j2*x mod p];\nRETURN(L);\n\nend;" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(cbroot2GR6$%\"aG%\"pG6+%\"bG%\"iG%'
racineG%\"jG%#j2G%\"xG%#e1G%#e2G%\"LG6\"F3C.@$0-%$modG6$-%#&^G6$9$,&9%
#\"\"\"\"\"$#FAFB!\"\"F?FA-%'RETURNG6#.%%totoG>8$-%3cherche_un_autre_b
G6#F?-%&printG6#FK>8'-F86$-F;6$FKF>F?>8(-F86$-F;6$FK,&F?#\"\"#FB#FjnFB
FDF?>8*F>>8+\"\"!>8,7\"?(F3FAFAF3/-F86$F]oFBF`oC&>F]o,$F]oF@>F_o,$F_oF
@>8)-F86$*&-F;6$F=F]oFA-F;6$FKF_oFAF?@&/F^pFS>F_o,(F_oFA*&FinFAF?FAFA#
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6$FK,$F_oFdrFAF?@$/-F86$*$)F^pFBFAF?,&F?FAF=FD>F^p,$F^pFD>Fbo7%F^p-F86
$*&FSFAF^pFAF?-F86$*&FYFAF^pFAF?-FF6#FboF3F3F3" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 13 "cbroot2(6,7);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"'\"\"$\"\"&" }}}
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\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "\{9,%\};" }}{PARA 
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