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0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 24 "factor(x^5+x^4+x^2+x+2);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"\"\"\"F'F*F*F*F*,(*$)F'\"\"$F)
F*F'!\"\"F(F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "expand((
x^5+x^4+x^2+x+2) * (x^7-x^6+x^5-2*x^4+2*x^3-4*x^2+7*x));" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,.%\"xG\"#9*$)F$\"\"&\"\"\"\"\"**$)F$\"\"%F)!\"'
*$)F$\"\"#F)!\"\"*$)F$\"\"$F)\"\"(*$)F$\"#7F)\"\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 56 "expand((x^5+x^4+x^2+x+2) * (-4*x^4+3*x^3-
2*x^2+2*x-4));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,4!\")\"\"\"*$)%\"
xG\"\"&\"\"\"!\"$*$)F(\"\"%F*!#6*$)F(\"\"#F*!\"'*$)F(\"\"$F*\"\"'*$)F(
\"\"(F*F%*$)F(F7F*!\"%*$)F(\"\"*F*F=*$)F(\"\")F*!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "expand((x^5+x^4+x^2+x+2) * (x^4-x^3
+x^2-2*x+2));\n" }}{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 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 171 "rest
art;\nwith (linalg):\n\nR := matrix(5,5,[ 1,0,1,1,0,   0,0,1,1,2,   0,
0,0,2,2,   0,1,1,0,1,   0,0,2,1,0 ]);\nc := vector(5,[ b[0],b[1],b[2],
b[3],b[4] ]);\n\nevalm( R &* c);\n" }}{PARA 7 "" 1 "" {TEXT -1 32 "War
ning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning,
 new definition for trace" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG-%'
matrixG6#7'7'\"\"\"\"\"!F*F*F+7'F+F+F*F*\"\"#7'F+F+F+F-F-7'F+F*F*F+F*7
'F+F+F-F*F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG-%'vectorG6#7'&%
\"bG6#\"\"!&F*6#\"\"\"&F*6#\"\"#&F*6#\"\"$&F*6#\"\"%" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#-%'vectorG6#7',(&%\"bG6#\"\"!\"\"\"&F)6#\"\"#F,&F)6#
\"\"$F,,(F-F,F0F,&F)6#\"\"%F/,&F0F/F4F/,(&F)6#F,F,F-F,F4F,,&F-F/F0F," 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "b[0] := 0;\nb[4] := 1;\nb
[3] := 1;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"bG6#\"\"!F'" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"bG6#\"\"%\"\"\"" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>&%\"bG6#\"\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 88 "vector([b[0]+b[2]+b[3], b[2]+b[3]+2*b[4], 2*b[3]+2*b[
4], b[1]+b[2]+b[4], 2*b[2]+b[3]]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#-%'vectorG6#7',&\"\"\"F(&%\"bG6#\"\"#F(,&F)F(\"\"$F(\"\"%,(&F*6#F(F(
F)F(F(F(,&F)F,F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "expa
nd((x^5+x^4+x^2+x+2)*(x^15-x^14+x^13-2*x^12+2*x^11-4*x^10+7*x^9-9*x^8+
15*x^7-22*x^6+32*x^5-52*x^4+77*x^3-117*x^2+181*x-270));\n" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,.*$)%\"xG\"\"%\"\"\"!$9%*$)F&\"\"#F(!$B$*$)F&
\"\"$F(\"$=#*$)F&\"#?F(\"\"\"!$S&F5F&\"##*" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 135 "expand((x^5+x^4+x^2+x+2)*(x^15-x^14+x^13-2*x^12+2*
x^11-4*x^10+7*x^9-9*x^8+15*x^7-22*x^6+32*x^5-52*x^4+77*x^3-117*x^2+181
*x-270)) mod 5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"xG\"\"%\"\"
\"\"\"\"*$)F&\"\"#F(F,*$)F&\"\"$F(F/*$)F&\"#?F(F)F&F," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 170 "restart;\nwith (linalg):\n\nR := matrix(5,5,[ 1,3,2,
4,2,   0,4,0,3,0,   0,4,4,0,2,   0,0,2,0,3,   0,4,3,2,1 ]);\nc := vect
or(5,[ b[0],b[1],b[2],b[3],b[4] ]);\n\nevalm( R &* c);" }}{PARA 7 "" 
1 "" {TEXT -1 32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" 
{TEXT -1 33 "Warning, new definition for trace" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"RG-%'matrixG6#7'7'\"\"\"\"\"$\"\"#\"\"%F,7'\"\"!F-F
/F+F/7'F/F-F-F/F,7'F/F/F,F/F+7'F/F-F+F,F*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"cG-%'vectorG6#7'&%\"bG6#\"\"!&F*6#\"\"\"&F*6#\"\"#&
F*6#\"\"$&F*6#\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7',
,&%\"bG6#\"\"!\"\"\"&F)6#F,\"\"$&F)6#\"\"#F2&F)6#F/\"\"%&F)6#F5F2,&F-F
5F3F/,(F-F5F0F5F6F2,&F0F2F6F/,*F-F5F0F/F3F2F6F," }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 19 "evalm( R &* c = c);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%'vectorG6#7',,&%\"bG6#\"\"!\"\"\"&F*6#F-\"\"$&F*6#\"
\"#F3&F*6#F0\"\"%&F*6#F6F3,&F.F6F4F0,(F.F6F1F6F7F3,&F1F3F7F0,*F.F6F1F0
F4F3F7F--F%6#7'F)F.F1F4F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 194 "restart;\nwith (linalg):\n\nR := matrix(4,4,[
 3,0,3,0,   4,3,0,2,   0,2,4,3,   4,3,2,0 ]);\nc := vector(4,[ b[0],b[
1],b[2],b[3] ]);\nd := vector(4,[ 0,0,0,0 ] );\n\nevalm( R &* c = d);
\nlinsolve( R,d );" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new defini
tion for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition \+
for trace" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG-%'matrixG6#7&7&\"
\"$\"\"!F*F+7&\"\"%F*F+\"\"#7&F+F.F-F*7&F-F*F.F+" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"cG-%'vectorG6#7&&%\"bG6#\"\"!&F*6#\"\"\"&F*6#\"\"#&
F*6#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG-%'vectorG6#7&\"\"!
F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%'vectorG6#7&,&&%\"bG6#\"
\"!\"\"$&F*6#\"\"#F-,(F)\"\"%&F*6#\"\"\"F-&F*6#F-F0,(F3F0F.F2F6F-,(F)F
2F3F-F.F0-F%6#7&F,F,F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG
6#7&\"\"!F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "expand ((x^3+x+2)*(x^2-x+1))
 mod 5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.*$)%\"xG\"\"&\"\"\"\"\"\"
*$)F&\"\"%F(F,*$)F&\"\"$F(\"\"#*$)F&F0F(F)F&F,F0F)" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 24 "factor(x^5+x^4+x^2+x+2);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"\"\"\"F'F*F*F*F*,(*$)F'\"\"$F)
F*F'!\"\"F(F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "expand((x+y)^2);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"\"\"\"*&F&F)%\"yGF)F'*$)F+F'F(F)
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gcd (x^5+x^4+x^2+x+2, x
^2+x+1) mod 3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"
\"\"\"\"F&F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "rem (x^
5+x^4+x^2+x+2, x^2+x+3,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&!#5\"
\"\"%\"xG\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "q;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"$\"\"\"\"\"\"F&!\"\"\"\"
#F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "divide (x^2-1,x^2-2*
x+1,'pq');" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "p
q;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#pqG" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}}{MARK "25 0 0" 3 }{VIEWOPTS 1 1 0 1 1 1803 }