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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra
ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "p := x -> x^4 + x + 1:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "Primitive(p(x)) mod 2;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "fs := 2^(d
egree(p(x)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#fsG\"#;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "field := vector(fs);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&fieldG-%&arrayG6$;\"\"\"\"#;7\"" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "for i from 1 to fs-1 do" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "    field[i] := Powmod(a, i, p(a), \+
a) mod 2:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 15 "field[fs] := 0:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "evalm(field);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%
'vectorG6#72%\"aG*$)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'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 18 "ftable := table():" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 23 "for i from 1 to fs-1 do" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "    ftable[ field[i] ] := a^i:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "ftab
le[ field[fs] ] := 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "pr
int(ftable);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%&TABLEG6#72/\"\"!F(/
\"\"\"*$)%\"aG\"#:F*/,(*$)F-\"\"$F*F**$)F-\"\"#F*F*F-F**$)F-\"#6F*/F1F
1/,&F-F*F*F**$)F-\"\"%F*/,(F1F*F4F*F*F**$)F-\"#8F*/,&F1F*F*F**$)F-\"#9
F*/,*F1F*F4F*F-F*F*F**$)F-\"#7F*/F-F-/,&F1F*F4F**$)F-\"\"'F*/,(F4F*F-F
*F*F**$)F-\"#5F*/F4F4/,&F4F*F-F**$)F-\"\"&F*/,(F1F*F-F*F*F**$)F-\"\"(F
*/,&F1F*F-F**$)F-\"\"*F*/,&F4F*F*F**$)F-\"\")F*" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 18 "ftable[a^3 + a^2];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*$)%\"aG\"\"'\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "f := s -> x^(fs-1) - 1;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"fGf*6#%\"sG6\"6$%)operatorG%&arrowGF(,&)%\"xG,&%#fsG\"\"\"F1
!\"\"F1F1F2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "factf \+
:= Factor(f(x)) mod 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&factfG*,,
(*$)%\"xG\"\"#\"\"\"F+F)F+F+F+F+,(*$)F)\"\"%F+F+*$)F)\"\"$F+F+F+F+F+,,
F-F+F0F+F'F+F)F+F+F+F+,(F-F+F)F+F+F+F+,&F)F+F+F+F+" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 19 "f3 := op(3, factf);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#f3G,,*$)%\"xG\"\"%\"\"\"F**$)F(\"\"$F*F**$)F(\"\"#F*
F*F(F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f3 := unapply
(f3, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f3Gf*6#%\"xG6\"6$%)oper
atorG%&arrowGF(,,*$)9$\"\"%\"\"\"F1*$)F/\"\"$F1F1*$)F/\"\"#F1F1F/F1F1F
1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "f3(a^6);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"aG\"#C\"\"\"F(*$)F&\"#=F(F(*$)
F&\"#7F(F(*$)F&\"\"'F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 28 "Rem(f3(a^6), p(a), a) mod 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "nops(factf);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "t := 3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "
for i from 1 to 2*t do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "    for j
 from 1 to nops(factf) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "      \+
  fj := op(j, factf):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "        fj
 := unapply(fj, x):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "        if R
em(fj(a^i), p(a), a) mod 2 = 0 then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
53 "           print(a^i, `    is a root of    `, fj(x)):" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 17 "           break:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "        fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "    \+
od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%%\"aG%5~~~~is~a~root~of~~~~G,(*$)%\"xG\"\"%\"\"\"F*F(F*
F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%*$)%\"aG\"\"#\"\"\"%5~~~~is~a~
root~of~~~~G,(*$)%\"xG\"\"%F'F'F,F'F'F'" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6%*$)%\"aG\"\"$\"\"\"%5~~~~is~a~root~of~~~~G,,*$)%\"xG\"\"%F'F'*$)
F,F&F'F'*$)F,\"\"#F'F'F,F'F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%*$)%
\"aG\"\"%\"\"\"%5~~~~is~a~root~of~~~~G,(*$)%\"xGF&F'F'F,F'F'F'" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%*$)%\"aG\"\"&\"\"\"%5~~~~is~a~root~of~
~~~G,(*$)%\"xG\"\"#F'F'F,F'F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%*$)
%\"aG\"\"'\"\"\"%5~~~~is~a~root~of~~~~G,,*$)%\"xG\"\"%F'F'*$)F,\"\"$F'
F'*$)F,\"\"#F'F'F,F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 
"m1 := x -> x^4 + x + 1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 
"m3 := x -> x^4 + x^3 + x^2 + x + 1:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "m5 := x -> x^2 + x + 1:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "g := m1(x) * m3(x) * m5(x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"gG*(,(*$)%\"xG\"\"%\"\"\"F+F)F+F+F+F+,,F'F+*$)F)\"
\"$F+F+*$)F)\"\"#F+F+F)F+F+F+F+,(F0F+F)F+F+F+F+" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 19 "g := unapply(g, x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*(,(*$)9$\"\"%
\"\"\"F2F0F2F2F2F2,,F.F2*$)F0\"\"$F2F2*$)F0\"\"#F2F2F0F2F2F2F2,(F7F2F0
F2F2F2F2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "r := x ->
 1 + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^10:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 19 "syn := vector(2*t);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$synG-%&arrayG6$;\"\"\"\"\"'7\"" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 22 "for i from 1 to 2*t do" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "    syn[i] := Rem(r(a^i), p(a), a) mod 2:" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 31 "    syn[i] := ftable[ syn[i] ];" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 "evalm(syn);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7(*$)
%\"aG\"\"$\"\"\"*$)F)\"\"'F+F,*$)F)\"#7F+*$)F)\"#5F+F/" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "syn[5];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*$)%\"aG\"#5\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 96 "A := matrix( [ [syn[1], syn[2], syn[3]], [syn[2], syn
[3], syn[4]], [syn[3], syn[4], syn[5]] ] );" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%*$)%\"aG\"\"$\"\"\"*$)F,\"\"'F.F/
7%F/F/*$)F,\"#7F.7%F/F3*$)F,\"#5F." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "b := vector( [syn[4], syn[5], syn[6]] );" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"bG-%'vectorG6#7%*$)%\"aG\"#7\"\"\"*$)F+\"#5
F-F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "d := det(A);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG,,*$)%\"aG\"#>\"\"\"F**$)F(\"#FF
*!\"\"*$)F(\"#AF*F.*&\"\"#F*)F(\"#CF*F**$)F(\"#=F*F." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 32 "d := Rem(det(A), p(a), a) mod 2;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG,**$)%\"aG\"\"$\"\"\"F**$)F(\"\"
#F*F*F(F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "d := ftabl
e[d];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG*$)%\"aG\"#7\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "col(A, 2);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#-%'vectorG6#7%*$)%\"aG\"\"'\"\"\"F'*$)F)\"#7F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A1 := augment(b, col(A,2), c
ol(A,3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G-%'matrixG6#7%7%*$)
%\"aG\"#7\"\"\"*$)F,\"\"'F.F/7%*$)F,\"#5F.F/F*7%F*F*F3" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "dA1 := ftable[ Rem(det(A1), p(a), a
) mod 2 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dA1G*$)%\"aG\"#9\"\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sigma3 := dA1/d;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigma3G*$)%\"aG\"\"#\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A2 := augment(col(A,1), b, c
ol(A,3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G-%'matrixG6#7%7%*$)
%\"aG\"\"$\"\"\"*$)F,\"#7F.*$)F,\"\"'F.7%F2*$)F,\"#5F.F/7%F2F/F6" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "dA2 := ftable[ Rem(det(A2), \+
p(a), a) mod 2 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dA2G*$)%\"aG\"
#5\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sigma2 := dA2/d
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigma2G*&\"\"\"F&*$)%\"aG\"\"#
F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "sigma2 := sigma2
 * a^(fs-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigma2G*$)%\"aG\"#8
\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A3 := augment(col
(A,1), col(A,2), b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A3G-%'matri
xG6#7%7%*$)%\"aG\"\"$\"\"\"*$)F,\"\"'F.*$)F,\"#7F.7%F/F/*$)F,\"#5F.7%F
/F2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "dA3 := ftable[ Rem
(det(A3), p(a), a) mod 2 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dA3G
*$)%\"aG\"#:\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sigma
1 := dA3/d;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigma1G*$)%\"aG\"\"$
\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "EL := z^3 + sigma
1*z^2 + sigma2*z + sigma3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ELG,*
*$)%\"zG\"\"$\"\"\"F**&)%\"aGF)F*)F(\"\"#F*F**&)F-\"#8F*F(F*F**$)F-F/F
*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "EL := unapply(EL, z)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ELGf*6#%\"zG6\"6$%)operatorG%&
arrowGF(,**$)9$\"\"$\"\"\"F1*&)%\"aGF0F1)F/\"\"#F1F1*&)F4\"#8F1F/F1F1*
$)F4F6F1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "for i f
rom 1 to fs-1 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "    if Rem(EL(a
^i), p(a), a) mod 2 = 0 then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "   \+
    print(a^i, `  is a root of EL(z) =  `, EL(z));" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 7 "    fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%*$)%\"aG\"\"&\"\"\"%9~~is~a~root~of~EL
(z)~=~~G,**$)%\"zG\"\"$F'F'*&)F%F-F')F,\"\"#F'F'*&)F%\"#8F'F,F'F'*$)F%
F1F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%*$)%\"aG\"#7\"\"\"%9~~is~a~r
oot~of~EL(z)~=~~G,**$)%\"zG\"\"$F'F'*&)F%F-F')F,\"\"#F'F'*&)F%\"#8F'F,
F'F'*$)F%F1F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%*$)%\"aG\"#:\"\"\"%
9~~is~a~root~of~EL(z)~=~~G,**$)%\"zG\"\"$F'F'*&)F%F-F')F,\"\"#F'F'*&)F
%\"#8F'F,F'F'*$)F%F1F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 
"e := x -> 1 + x^5 + x^12:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "c := (r(x) + e(x)) mod 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"c
G,0*$)%\"xG\"\"#\"\"\"F**$)F(\"\"$F*F**$)F(\"\"%F*F**$)F(\"\"'F*F**$)F
(\"\"(F*F**$)F(\"#5F*F**$)F(\"#7F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "(Factor(c) mod 2)/g(x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*$)%\"xG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
45 "r := x -> 1 + x^3 + x^7 + x^10 + x^11 + x^13:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 22 "for i from 1 to 2*t do" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "    syn[i] := Rem(r(a^i), p(a), a) mod 2:" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 31 "    syn[i] := ftable[ syn[i] ];" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 "evalm(syn);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7(*$)
%\"aG\"\"&\"\"\"*$)F)\"#5F+*$)F)\"\"#F+F'*$)F)\"#:F+*$)F)\"\"%F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "A := matrix( [ [syn[1], syn[
2], syn[3]], [syn[2], syn[3], syn[4]], [syn[3], syn[4], syn[5]] ] );" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%*$)%\"aG\"\"&
\"\"\"*$)F,\"#5F.*$)F,\"\"#F.7%F/F2F*7%F2F**$)F,\"#:F." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "b := vector( [syn[4], syn[5], syn[6
]] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%'vectorG6#7%*$)%\"aG
\"\"&\"\"\"*$)F+\"#:F-*$)F+\"\"%F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "d := Rem(det(A), p(a), a) mod 2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"dG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
22 "A := delrows(A, 3..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%
'matrixG6#7$7%*$)%\"aG\"\"&\"\"\"*$)F,\"#5F.*$)F,\"\"#F.7%F/F2F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "b := col(A, 3);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"bG-%'vectorG6#7$*$)%\"aG\"\"#\"\"\"*$)F+\"
\"&F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "A := delcols(A, 3.
.3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7$7$*$)%\"aG
\"\"&\"\"\"*$)F,\"#5F.7$F/*$)F,\"\"#F." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "d := ftable[ Rem(det(A), p(a), a) mod 2 ];" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"dG*$)%\"aG\"#8\"\"\"" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 27 "A1 := augment(b, col(A,2));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#A1G-%'matrixG6#7$7$*$)%\"aG\"\"#\"\"\"*$)F,\"#5
F.7$*$)F,\"\"&F.F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "dA1 :
= ftable[ Rem(det(A1), p(a), a) mod 2 ];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$dA1G%\"aG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sigma
2 := dA1/d;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigma2G*&\"\"\"F&*$)
%\"aG\"#7F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "sigma2 \+
:= sigma2 * a^(fs-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigma2G*$)
%\"aG\"\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "A2 := a
ugment(col(A,1), b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G-%'matri
xG6#7$7$*$)%\"aG\"\"&\"\"\"*$)F,\"\"#F.7$*$)F,\"#5F.F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "dA2 := ftable[ Rem(det(A2), p(a), a
) mod 2 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dA2G*$)%\"aG\"\"$\"\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sigma1 := dA2/d;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigma1G*&\"\"\"F&*$)%\"aG\"#5F&!\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "sigma1 := sigma1 * a^
(fs-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigma1G*$)%\"aG\"\"&\"\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "EL := z^2 + sigma1*z \+
+ sigma2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ELG,(*$)%\"zG\"\"#\"\"
\"F**&)%\"aG\"\"&F*F(F*F**$)F-\"\"$F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "EL := unapply(EL, z);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#ELGf*6#%\"zG6\"6$%)operatorG%&arrowGF(,(*$)9$\"\"#\"\"\"F1*&)
%\"aG\"\"&F1F/F1F1*$)F4\"\"$F1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "for i from 1 to fs-1 do" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "    if Rem(EL(a^i), p(a), a) mod 2 = 0 then" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 53 "       print(a^i, `  is a root of EL(z) =
  `, EL(z));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "    fi:" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%\"aG%
9~~is~a~root~of~EL(z)~=~~G,(*$)%\"zG\"\"#\"\"\"F**&)F#\"\"&F*F(F*F**$)
F#\"\"$F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%*$)%\"aG\"\"#\"\"\"%9~~
is~a~root~of~EL(z)~=~~G,(*$)%\"zGF&F'F'*&)F%\"\"&F'F,F'F'*$)F%\"\"$F'F
'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "e := x -> x + x^2:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "c := (r(x) + e(x)) mod 2;" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG,2\"\"\"F&*$)%\"xG\"\"$F&F&*$)
F)\"\"(F&F&*$)F)\"#5F&F&*$)F)\"#6F&F&*$)F)\"#8F&F&F)F&*$)F)\"\"#F&F&" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sort(c);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,2*$)%\"xG\"#8\"\"\"F(*$)F&\"#6F(F(*$)F&\"#5F(F(*$)F
&\"\"(F(F(*$)F&\"\"$F(F(*$)F&\"\"#F(F(F&F(F(F(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 23 "(Factor(c) mod 2)/g(x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"F)F'F)F)F)F),&F'F)F)F)F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }
{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }