{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 
{CSTYLE "" -1 -1 "" 0 1 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 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "# Gauss-eg\351szek" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "with(GaussInt): # Gauss-e
g\351szek csomag" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "with(pl
ots): conformal(z, z=-10-10*I..10+10*I); # a komplex sik" }}{PARA 13 "
" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "68-%'CURVESG6$777$$!#5\"\"!F
(7$F($!\"*F*7$F($!\")F*7$F($!\"(F*7$F($!\"'F*7$F($!\"&F*7$F($!\"%F*7$F
($!\"$F*7$F($!\"#F*7$F($!\"\"F*7$F(F*7$F($\"\"\"F*7$F($\"\"#F*7$F($\"
\"$F*7$F($\"\"%F*7$F($\"\"&F*7$F($\"\"'F*7$F($\"\"(F*7$F($\"\")F*7$F($
\"\"*F*7$F($\"#5F*-%'COLOURG6&%$RGBG$F^oFEF*F*-F$6$777$F/F(7$F/F,7$F/F
/7$F/F27$F/F57$F/F87$F/F;7$F/F>7$F/FA7$F/FD7$F/F*7$F/FH7$F/FK7$F/FN7$F
/FQ7$F/FT7$F/FW7$F/FZ7$F/Fgn7$F/Fjn7$F/F]oF_o-F$6$777$F5F(7$F5F,7$F5F/
7$F5F27$F5F57$F5F87$F5F;7$F5F>7$F5FA7$F5FD7$F5F*7$F5FH7$F5FK7$F5FN7$F5
FQ7$F5FT7$F5FW7$F5FZ7$F5Fgn7$F5Fjn7$F5F]oF_o-F$6$777$F;F(7$F;F,7$F;F/7
$F;F27$F;F57$F;F87$F;F;7$F;F>7$F;FA7$F;FD7$F;F*7$F;FH7$F;FK7$F;FN7$F;F
Q7$F;FT7$F;FW7$F;FZ7$F;Fgn7$F;Fjn7$F;F]oF_o-F$6$777$FAF(7$FAF,7$FAF/7$
FAF27$FAF57$FAF87$FAF;7$FAF>7$FAFA7$FAFD7$FAF*7$FAFH7$FAFK7$FAFN7$FAFQ
7$FAFT7$FAFW7$FAFZ7$FAFgn7$FAFjn7$FAF]oF_o-F$6$777$F*F(7$F*F,7$F*F/7$F
*F27$F*F57$F*F87$F*F;7$F*F>7$F*FA7$F*FD7$F*F*7$F*FH7$F*FK7$F*FN7$F*FQ7
$F*FT7$F*FW7$F*FZ7$F*Fgn7$F*Fjn7$F*F]oF_o-F$6$777$FKF(7$FKF,7$FKF/7$FK
F27$FKF57$FKF87$FKF;7$FKF>7$FKFA7$FKFD7$FKF*7$FKFH7$FKFK7$FKFN7$FKFQ7$
FKFT7$FKFW7$FKFZ7$FKFgn7$FKFjn7$FKF]oF_o-F$6$777$FQF(7$FQF,7$FQF/7$FQF
27$FQF57$FQF87$FQF;7$FQF>7$FQFA7$FQFD7$FQF*7$FQFH7$FQFK7$FQFN7$FQFQ7$F
QFT7$FQFW7$FQFZ7$FQFgn7$FQFjn7$FQF]oF_o-F$6$777$FWF(7$FWF,7$FWF/7$FWF2
7$FWF57$FWF87$FWF;7$FWF>7$FWFA7$FWFD7$FWF*7$FWFH7$FWFK7$FWFN7$FWFQ7$FW
FT7$FWFW7$FWFZ7$FWFgn7$FWFjn7$FWF]oF_o-F$6$777$FgnF(7$FgnF,7$FgnF/7$Fg
nF27$FgnF57$FgnF87$FgnF;7$FgnF>7$FgnFA7$FgnFD7$FgnF*7$FgnFH7$FgnFK7$Fg
nFN7$FgnFQ7$FgnFT7$FgnFW7$FgnFZ7$FgnFgn7$FgnFjn7$FgnF]oF_o-F$6$777$F]o
F(7$F]oF,7$F]oF/7$F]oF27$F]oF57$F]oF87$F]oF;7$F]oF>7$F]oFA7$F]oFD7$F]o
F*7$F]oFH7$F]oFK7$F]oFN7$F]oFQ7$F]oFT7$F]oFW7$F]oFZ7$F]oFgn7$F]oFjn7$F
]oF]oF_o-F$6$77F'7$F,F(Fgo7$F2F(F_q7$F8F(Fgr7$F>F(F_t7$FDF(Fgu7$FHF(F_
w7$FNF(Fgx7$FTF(F_z7$FZF(Fg[l7$FjnF(F_]l-F`o6&FboF*FcoF*-F$6$77F.7$F,F
/Fio7$F2F/Faq7$F8F/Fir7$F>F/Fat7$FDF/Fiu7$FHF/Faw7$FNF/Fix7$FTF/Faz7$F
ZF/Fi[l7$FjnF/Fa]lFa_l-F$6$77F47$F,F5F[p7$F2F5Fcq7$F8F5F[s7$F>F5Fct7$F
DF5F[v7$FHF5Fcw7$FNF5F[y7$FTF5Fcz7$FZF5F[\\l7$FjnF5Fc]lFa_l-F$6$77F:7$
F,F;F]p7$F2F;Feq7$F8F;F]s7$F>F;Fet7$FDF;F]v7$FHF;Few7$FNF;F]y7$FTF;Fez
7$FZF;F]\\l7$FjnF;Fe]lFa_l-F$6$77F@7$F,FAF_p7$F2FAFgq7$F8FAF_s7$F>FAFg
t7$FDFAF_v7$FHFAFgw7$FNFAF_y7$FTFAFgz7$FZFAF_\\l7$FjnFAFg]lFa_l-F$6$77
FF7$F,F*Fap7$F2F*Fiq7$F8F*Fas7$F>F*Fit7$FDF*Fav7$FHF*Fiw7$FNF*Fay7$FTF
*Fiz7$FZF*Fa\\l7$FjnF*Fi]lFa_l-F$6$77FJ7$F,FKFcp7$F2FKF[r7$F8FKFcs7$F>
FKF[u7$FDFKFcv7$FHFKF[x7$FNFKFcy7$FTFKF[[l7$FZFKFc\\l7$FjnFKF[^lFa_l-F
$6$77FP7$F,FQFep7$F2FQF]r7$F8FQFes7$F>FQF]u7$FDFQFev7$FHFQF]x7$FNFQFey
7$FTFQF][l7$FZFQFe\\l7$FjnFQF]^lFa_l-F$6$77FV7$F,FWFgp7$F2FWF_r7$F8FWF
gs7$F>FWF_u7$FDFWFgv7$FHFWF_x7$FNFWFgy7$FTFWF_[l7$FZFWFg\\l7$FjnFWF_^l
Fa_l-F$6$77Ffn7$F,FgnFip7$F2FgnFar7$F8FgnFis7$F>FgnFau7$FDFgnFiv7$FHFg
nFax7$FNFgnFiy7$FTFgnFa[l7$FZFgnFi\\l7$FjnFgnFa^lFa_l-F$6$77F\\o7$F,F]
oF[q7$F2F]oFcr7$F8F]oF[t7$F>F]oFcu7$FDF]oF[w7$FHF]oFcx7$FNF]oF[z7$FTF]
oFc[l7$FZF]oF[]l7$FjnF]oFc^lFa_l" 1 2 0 1 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "GI
norm(2+13*I); # norma\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$t\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 99 "GInearest(-2.34+6.87*I), GInearest((2+8*I)/(3-7*I)); \+
# egy komplex szamhoz legkozelebbi Gauss-egesz" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$,&!\"#\"\"\"%\"IG\"\"(,&!\"\"F%F&F%" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 50 "GInormal(3-2*I); # az elso negyedbeli asszo
cialt\n\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"#\"\"\"%\"IG\"\"$" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "GIgcd(-345+515*I,1574+368
*I); # lnko " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"#T\"\"\"%\"IG\"$<
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "GIgcdex(-345+515*I,1
574+368*I,'u','v'), u, v; # lnko(z,t) az euklideszi algoritmussal es o
lyan u,v megadasa, amelyekre (z,t)=uz+vt" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6%,&\"#T\"\"\"%\"IG\"$<\",&\"\"&F%F&!\"#,$F&F*" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 72 "GIquo(6+12*I,-8+4*I,'r'), r; # maradekos os
ztas hanyadosa es r=maradeka " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$%\"
IG!\"\",&\"\"#\"\"\"F$\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
72 "GIrem(6+12*I,-8+4*I,'q'), q; # maradekos osztas maradeka es q=hany
adosa " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&\"\"#\"\"\"%\"IG\"\"%,$F&!
\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "GIlcm(1+2*I,-3+5*I,
14+3*I); # lkkt" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"#h\"\"\"%\"IG\"
#d" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "GIprime(751), GIprime
(4+9*I),GIprime(-3+4*I); # Gauss-prim teszt" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%%%trueGF#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "GIfactor(12101-15295*I); # primtenyezokre bontas " }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*.-%!G6#!\"\"\"\"\"-F%6#,&F(F(%\"IGF(F
(-F%6#,&F(F(F,\"\"%F(-F%6#,&\"\"&F(F,\"\")F(-F%6#,&\"\"*F(F,\"#;F(-F%6
#,&!\"(F(F,!#=F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " expand
(%); # visszaalakitas" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"&,@\"\"\"
\"%\"IG!&&H:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 " GIsieve(10
); # GIsieve(m) megadja azokat az x+yI Gauss-primeket, amelyek normaja
 <= m^2 es 0<y<=x" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"#970,&\"\"\"F
'%\"IGF',&F'F'F(\"\"#\"\"$,&F*F'F(F+,&F'F'F(\"\"%,&F*F'F(\"\"&,&F'F'F(
\"\"',&F.F'F(F0\"\"(,&F*F'F(F4,&F0F'F(F2,&F+F'F(\"\"),&F0F'F(F8,&F.F'F
(\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " GIdivisor(161+24
0*I); # az elso negyedbeli osztok" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<
'\"\"\",&\"\"%F$%\"IGF$,&\"$h\"F$F'\"$S#,&\"#_F$F'\"#Z,&\"#:F$F'\"\")
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 " GInodiv(10-2*I); # a n
emasszocialt osztok szama " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "GIphi(-21+5*I); # GIphi(m)
 egy mod m redukalt maradekrendszer elemeinek a szama" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"$K#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}}{MARK "18 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }