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-1 -1 "" 0 1 0 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 
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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 23 "TD MAPLE N\260 7 9/11/2
001" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "?Gcd" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 204 "scinde := proc(g, x, a, p)\n  loca
l T, Q0, Q1, Q2;\n  Q0 := Gcd(f, x-a ) mod p;\n  T := Powmod(x-a, (p-1
)/2, g, x) mod p;\n  Q1 := Gcd(g, T - 1) mod p;\n  Q2 := Gcd(g, T + 1)
 mod p;\n  return [Q0, Q1, Q2];\nend;" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#>%'scindeGR6&%\"gG%\"xG%\"aG%\"pG6&%\"TG%#Q0G%#Q1G%#Q2G6\"F0C'>8
%-%$modG6$-%$GcdG6$%\"fG,&9%\"\"\"9&!\"\"9'>8$-F56$-%'PowmodG6&F;,&F@#
F=\"\"##F=FJF?9$F<F@>8&-F56$-F86$FL,&FBF=F=F?F@>8'-F56$-F86$FL,&FBF=F=
F=F@O7%F3FNFUF0F0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 624 "rac
ines1 := proc(f, x, p, debut)\n  local A, D, L, L2, N;\n  D := degree(
f, x);\n  L := [];\n  N := 0;\n  A := debut;\n  if D = 0 then return [
]; end if;\n  if D = 1 then return [f]; end if;\n  L2 := scinde(f, x, \+
A, p);\n  print(L2);\n  while (N < p) and (L2[1] = 1) and ((L2[2] = 1)
 or (L2[3] = 1)) do\n    A := (A + 1) mod p;\n    N := N + 1;\n    L2 \+
:= scinde(f, x, A, p);\n  od;\n  if N = p then return [f]; end if;\n  \+
if L2[1] <> 1 then L := [op(L), L2[1]] end if;\n  if L2[2] <> 1 then L
 := [op(L), op(racines1(L2[2], x, p, A + 1))]; end if;\n  if L2[3] <> \+
1 then L := [op(L), op(racines1(L2[3], x, p, A + 1))]; end if;\n  retu
rn L;\nend;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "hensel := proc(f, g
1, h1, x, p, r)\n  local N, g, h;\n  for N from 1 to r do\n    A := (f
 - \n\n  end do;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)racines1GR6&%\"fG%\"xG%\"pG%&debutG
6'%\"AG%\"DG%\"LG%#L2G%\"NG6\"F1C0>8%-%'degreeG6$9$9%>8&7\">8(\"\"!>8$
9'@$/F4F?OF<@$/F4\"\"\"O7#F8>8'-%'scindeG6&F8F9FA9&-%&printG6#FL?(F1FH
FHF1332F>FP/&FL6#FHFH5/&FL6#\"\"#FH/&FL6#\"\"$FHC%>FA-%$modG6$,&FAFHFH
FHFP>F>,&F>FHFHFH>FLFM@$/F>FPOFJ@$0FYFH>F;7$-%#opG6#F;FY@$0FgnFH>F;7$F
^p-F_p6#-F$6&FgnF9FPFco@$0F[oFH>F;7$F^p-F_p6#-F$6&F[oF9FPFcoOF;F1F1F1
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "scinde(X^31+X^15+1,X, 0
, nextprime(10^38));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"\"F$,(*$
)%\"XG\"\"#F$F$*&\"Gs%\\(*zK%GHfZuLO5W')yUGF$F(F$F$\"GG7/`h9Q%)fW'=N?]
&z3,IF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "ops(3,[1, X+5, X
+3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$opsG6$\"\"$7%\"\"\",&%\"XG
F(\"\"&F(,&F*F(F&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "nops
([1, X+5, X+3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "racines1(X^31+X^15+1, X, nextprime(
10^38), 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"\"F$,(*$)%\"XG\"
\"#F$F$*&\"Gs%\\(*zK%GHfZuLO5W')yUGF$F(F$F$\"GG7/`h9Q%)fW'=N?]&z3,IF$
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$,&%\"XG\"\"\"\"G_zuxsbmqn?]#=4$e
96m\")F&,&F%F&\"G`;+Ab(='e\"pU7X%z&=xmn%F&" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 24 "Factor(X^2+4*X+1) mod 7;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*$)%\"XG\"\"#\"\"\"F(*&\"\"%F(F&F(F(F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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