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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 203 29 "Komputeralgebrai algorit
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}{EXCHG {PARA 19 "" 0 "" {TEXT 201 69 "Ezek a programok csak szeml\303
\251ltet\303\251sre szolg\303\241lnak." }}}{SECT 1 {PARA 3 "" 0 "" 
{TEXT 205 4 "1. T" }{TEXT 205 18 "\303\266rt\303\251" }{TEXT 205 3 "ne
t" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 18 "2. Algebrai alapok" }}}
{SECT 1 {PARA 3 "" 0 "" {TEXT 205 7 "3. Norm" }{TEXT 205 8 "\303\241" 
}{TEXT 205 6 "l form" }{TEXT 205 8 "\303\241" }{TEXT 205 12 "k, reprez
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{TEXT 205 13 "4. Aritmetika" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 4 "5
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03\251" }{TEXT 205 3 "kol" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "s" }}
}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 14 "6. Newton-iter" }{TEXT 205 8 "
\303\241" }{TEXT 205 2 "ci" }{TEXT 205 8 "\303\263" }{TEXT 205 16 ", H
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{PARA 3 "" 0 "" {TEXT 205 15 "7. Legnagyobb k" }{TEXT 205 8 "\303\266"
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{TEXT 205 1 "s" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> "
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19 "A 8.1. Algoritmus. " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%
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0 18 "  z:=quo(w,y,x);\n" }{MPLTEXT 1 0 17 "  out:=out*z^i;\n" }
{MPLTEXT 1 0 11 "  i:=i+1;\n" }{MPLTEXT 1 0 24 "  w:=y; c:=quo(c,y,x);
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{XPPMATH 20 "f*6$I\"aG6\"I\"xGF%6)I\"iGF%I$outGF%I\"bGF%I\"cGF%I\"yGF%
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03\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "a:=x^8-2*x^6+2*x^2-1;" }}{PARA 11 "" 1 "" {XPPMATH 
20 ",**$)I\"xG6\"\"\")\"\"\"F(*&\"\"#F()F%\"\"'F(!\"\"*&F*F()F%F*F(F(F
(F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "debug(SquareFree); S
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{PARA 9 "" 1 "" {TEXT 207 51 "\{--> enter SquareFree, args = x^8-2*x^6
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" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&\"\")\"\"\"
)I\"xG6\"\"\"(F%F%*&\"#7F%)F'\"\"&F%!\"\"*&\"\"%F%F'F%F%" }}{PARA 11 "
" 1 "" {XPPMATH 20 ",(*$)I\"xG6\"\"\"%\"\"\"F(*&\"\"#F()F%F*F(!\"\"F(F
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}}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"\"#\"\"\"F(F(!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"\"#\"\"\"F(F(F(" }}{PARA 
11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"\"#\"\"\"F(F(F(" }}{PARA 11 "" 
1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"
\"\"#\"\"\"F(F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"
\"#\"\"\"F(F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"\"#
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{XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"\"#
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 1 "" {XPPMATH 20 "*&,&*$)I\"xG6\"\"\"#\"\"\"F)F)F)F)),&F$F)F)!\"\"\"
\"$F)" }}{PARA 9 "" 1 "" {TEXT 207 60 "<-- exit SquareFree (now at top
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I\"xG6\"\"\"#\"\"\"F)F)F)F)),&F$F)F)!\"\"\"\"$F)" }}}{EXCHG {PARA 0 ""
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%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "a:=x^13+1; diff(a,
x) mod 13;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"#8\"\"\"F(F
(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 34 "(x+1)^13 mod 13; expand(%) mod 13;" }}{PARA 11 "" 1
 "" {XPPMATH 20 "*$),&I\"xG6\"\"\"\"F'F'\"#8F'" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",&*$)I\"xG6\"\"#8\"\"\"F(F(F(" }}}}{SECT 0 {PARA 4 "" 0 "
" {TEXT 206 19 "A 8.3. Algoritmus. " }}{EXCHG {PARA 0 "" 0 "" 
{XPPEDIT 2 0 "" "%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "S
quareFreeFF:=proc(a,x,p) local i,out,b,c,y,z,w;" }}}}{SECT 0 {PARA 4 "
" 0 "" {TEXT 206 8 "E 8.4. P" }{TEXT 206 12 "\303\251lda." }}{EXCHG 
{PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "a:=x^11+2*x^9+2*x^8+x^6+x^5+2*x^3+2*x^2+1;" }}{PARA 
11 "" 1 "" {XPPMATH 20 ",2*$)I\"xG6\"\"#6\"\"\"F(*&\"\"#F()F%\"\"*F(F(
*&F*F()F%\"\")F(F(*$)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 20 "ap:=diff(a
,x) mod 3;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"xG6\"\"#5\"\"\"!\"
\"*$)F%\"\"(F(F(*$)F%\"\"%F(F)F%F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "c:=Gcd(a,ap) mod 3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
,**$)I\"xG6\"\"\"*\"\"\"F(*$)F%\"\"'F(!\"\"*$)F%\"\"$F(F(F(F," }}}
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"" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 8 "E 8.6. P" }{TEXT 
206 12 "\303\251lda." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 19 "A 8.4. \+
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{SECT 1 {PARA 4 "" 0 "" {TEXT 206 8 "E 8.7. P" }{TEXT 206 12 "\303\251
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 
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{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 8 "E 8.9.
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{PARA 4 "" 0 "" {TEXT 206 9 "E 8.10. P" }{TEXT 206 12 "\303\251lda." }
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1 {PARA 4 "" 0 "" {TEXT 206 9 "E 8.12. P" }{TEXT 206 12 "\303\251lda."
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}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 19 "A 8.7. Algoritmus. " }}
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0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 8.14
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0 "" "%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "a:=x^63+1;" 
}}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"#j\"\"\"F(F(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "a1:=Gcd(a,x^2-x) mod 2; a:=Q
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%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",jr\"\"\"F#*$)I\"xG6\"\"#6F#F#*$)F&
\"#5F#F#*$)F&\"\"%F#F#*$)F&\"\"$F#F#*$)F&\"\"(F#F#*$)F&\"\"&F#F#*$)F&
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F&\"\"*F#F#*$)F&\"#]F#F#*$)F&\"#_F#F#*$)F&\"#`F#F#*$)F&\"#aF#F#*$)F&\"
#bF#F#*$)F&\"#cF#F#*$)F&\"#dF#F#*$)F&\"#eF#F#*$)F&\"#fF#F#*$)F&\"#gF#F
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#[F#F#*$)F&\"#\\F#F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "a2:
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{XPPMATH 20 ",(*$)I\"xG6\"\"\"#\"\"\"F(F%F(F(F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",L*$)I\"xG6\"\"#g\"\"\"F(*$)F%\"#dF(F(*$)F%\"#aF(F(*$)F%
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0*$)I\"xG6\"\"\"'\"\"\"F(*$)F%\"\"&F(F(*$)F%\"\"%F(F(*$)F%\"\"$F(F(*$)
F%\"\"#F(F(F%F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ",X\"\"\"F#*$)I\"x
G6\"\"#6F#F#*$)F&\"\"%F#F#*$)F&\"\"$F#F#F&F#*$)F&\"#7F#F#*$)F&\"\")F#F
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "a4:=Gcd(a,x^16-x) mod 2; a:=Quo(a,a
4,x) mod 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "
" {XPPMATH 20 ",X\"\"\"F#*$)I\"xG6\"\"#6F#F#*$)F&\"\"%F#F#*$)F&\"\"$F#
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