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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 203 29 "Komputeralgebrai algorit
musok" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 204 18 "J\303\241rai Antal" }}
}{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" }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 
3 "" 0 "" {TEXT 205 18 "2. Algebrai alapok" }}{PARA 0 "" 0 "" {TEXT 
201 0 "" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 0 {PARA 4 "" 0 "" 
{TEXT 206 5 "2.1. " }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 
"" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 
4 "2.2." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}
}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 3 "
" 0 "" {TEXT 205 7 "3. Norm" }{TEXT 205 8 "\303\241" }{TEXT 205 6 "l f
orm" }{TEXT 205 8 "\303\241" }{TEXT 205 12 "k, reprezent" }{TEXT 205 
18 "\303\241ci\303\263" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 13 "4. Ar
itmetika" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 4 "5. K" }{TEXT 205 8 "
\303\255" }{TEXT 205 9 "nai marad" }{TEXT 205 8 "\303\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 ", Hensel-felemel" }
{TEXT 205 8 "\303\251" }{TEXT 205 1 "s" }}}{SECT 1 {PARA 3 "" 0 "" 
{TEXT 205 15 "7. Legnagyobb k" }{TEXT 205 8 "\303\266" }{TEXT 205 1 "z
" }{TEXT 205 8 "\303\266" }{TEXT 205 6 "s oszt" }{TEXT 205 8 "\303\263
" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 11 "8. Faktoriz" }{TEXT 205 8 "
\303\241" }{TEXT 205 1 "l" }{TEXT 205 8 "\303\241" }{TEXT 205 1 "s" }}
}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 21 "9. Egyenletrendszerek" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT 205 6 "10. Gr" }{TEXT 205 27 "\303\266bn
er-b\303\241zisok" }}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 29 "E 10.1. Lex
ikografikus rendez" }{TEXT 206 10 "\303\251s." }}{PARA 0 "" 0 "" {TEXT
 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "p:=x+y+z+x^2+z^3
+x*y+y^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",0I\"xG6\"\"\"\"I\"yGF$F%I
\"zGF$F%*$)F#\"\"#F%F%*$)F'\"\"$F%F%*&F#F%F&F%F%*$)F&F*F%F%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "sort(p,[x,y,z],plex);" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",0*$)I\"xG6\"\"\"#\"\"\"F(*&F%F(I\"yGF&F
(F(F%F(*$)F*F'F(F(F*F(*$)I\"zGF&\"\"$F(F(F/F(" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "sort(p,[z,y,x],plex);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",0*$)I\"zG6\"\"\"$\"\"\"F(F%F(*$)I\"yGF&\"\"#F(F(*&F+F(I
\"xGF&F(F(F+F(*$)F.F,F(F(F.F(" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 
13 "E 10.2. Foksz" }{TEXT 206 26 "\303\241m rendez\303\251s." }}{PARA 
0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "s
ort(p,[x,y,z]);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",0*$)I\"zG6\"\"\"$\"
\"\"F(*$)I\"xGF&\"\"#F(F(*&F+F(I\"yGF&F(F(*$)F.F,F(F(F+F(F.F(F%F(" }}}
{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 
0 "" {TEXT 206 9 "E 10.3. P" }{TEXT 206 12 "\303\251lda." }}{PARA 0 ""
 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "p:=-2
*x^2*y*z+x^2*y^2+x^2*z^2+x^2*y+2*x*y^2*z^2-3*x*y*z^3-x*y+y*z+z^2+5;" }
}{PARA 11 "" 1 "" {XPPMATH 20 ",6**\"\"#\"\"\")I\"xG6\"F$F%I\"yGF(F%I
\"zGF(F%!\"\"*&F&F%)F)F$F%F%*&F&F%)F*F$F%F%*&F&F%F)F%F%**F$F%F'F%F-F%F
/F%F%**\"\"$F%F'F%F)F%)F*F3F%F+*&F'F%F)F%F+*&F)F%F*F%F%*$F/F%F%\"\"&F%
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sort(p,[x,y,z]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",6**\"\"#\"\"\"I\"xG6\"F%)I\"yGF'F$F%)I
\"zGF'F$F%F%**\"\"$F%F&F%F)F%)F+F-F%!\"\"*&)F&F$F%F(F%F%**F$F%F1F%F)F%
F+F%F/*&F1F%F*F%F%*&F1F%F)F%F%*&F&F%F)F%F/*&F)F%F+F%F%*$F*F%F%\"\"&F%"
 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "op(1,p); lcoeff(%,[x,y,z
],'t'); t;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**\"\"#\"\"\"I\"xG6\"F%)
I\"yGF'F$F%)I\"zGF'F$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}
{PARA 11 "" 1 "" {XPPMATH 20 "*(I\"xG6\"\"\"\")I\"yGF$\"\"#F%)I\"zGF$F
(F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "collect(p,[x,y]);" }
}{PARA 11 "" 1 "" {XPPMATH 20 ",,*&,(*$)I\"yG6\"\"\"#\"\"\"F**&,&*&F)F
*I\"zGF(F*!\"\"F*F*F*F'F*F**$)F.F)F*F*F*)I\"xGF(F)F*F**&,&*(F)F*F&F*F1
F*F**&,&F*F/*&\"\"$F*)F.F:F*F/F*F'F*F*F*F3F*F*F0F*\"\"&F**&F'F*F.F*F*"
 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "pp:=collect(p,[x,y],`dis
tributed`);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",2*$)I\"zG6\"\"\"#\"\"\"F
(\"\"&F(**F'F(I\"xGF&F()I\"yGF&F'F(F$F(F(*(,&F(!\"\"*&\"\"$F()F%F2F(F0
F(F+F(F-F(F(*&)F+F'F(F,F(F(*(,&*&F'F(F%F(F0F(F(F(F5F(F-F(F(*&F-F(F%F(F
(*&F5F(F$F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "sort(pp,[x
,y]);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",2*&)I\"xG6\"\"\"#\"\"\")I\"yGF
&F'F(F(*(,&*&F'F(I\"zGF&F(!\"\"F(F(F(F$F(F*F(F(**F'F()F.F'F(F%F(F)F(F(
*&F1F(F$F(F(*(,&F(F/*&\"\"$F()F.F6F(F/F(F%F(F*F(F(*&F.F(F*F(F(*$F1F(F(
\"\"&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "op(1,p); lcoeff(
%,[x,y],'t'); t;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**\"\"#\"\"\")I\"z
G6\"F$F%I\"xGF(F%)I\"yGF(F$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&
\"\"#\"\"\")I\"zG6\"F$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&)I\"yG6
\"\"\"#\"\"\"I\"xGF%F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "w
ith(Groebner);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7:I&BasisG6\"I%FGLMGF$
I1HilbertDimensionGF$I2HilbertPolynomialGF$I.HilbertSeriesGF$I,InterRe
duceGF$I)IsProperGF$I2IsZeroDimensionalGF$I3LeadingCoefficientGF$I0Lea
dingMonomialGF$I,LeadingTermGF$I.MonomialOrderGF$I5MultiplicationMatri
xGF$I+NormalFormGF$I*NormalSetGF$I'ReduceGF$I.RememberBasisGF$I,SPolyn
omialGF$I&SolveGF$I*TestOrderGF$I0ToricIdealBasisGF$I5UnivariatePolyno
mialGF$I%WalkGF$I*fglm_algoGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 38 "LeadingTerm(p,tdeg(x,y,z)); %[1]*%[2];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"\"#*(I\"xG6\"\"\"\")I\"yGF&F#F')I\"zGF&F#F'" }}{PARA 
11 "" 1 "" {XPPMATH 20 ",$**\"\"#\"\"\"I\"xG6\"F%)I\"yGF'F$F%)I\"zGF'F
$F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "LeadingMonomial(p,
tdeg(x,y,z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(I\"xG6\"\"\"\")I\"yGF
$\"\"#F%)I\"zGF$F(F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Lea
dingCoefficient(p,tdeg(x,y,z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#
" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 
4 "" 0 "" {TEXT 206 9 "E 10.4. P" }{TEXT 206 12 "\303\251lda." }}
{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 38 "p:=6*x^4+13*x^3-6*x+1; q:=3*x^2+5*x-1;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",**&\"\"'\"\"\")I\"xG6\"\"\"%F%F%*&\"#8F%)F'\"\"$F%F%*&F$
F%F'F%!\"\"F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&\"\"$\"\"\")I\"xG
6\"\"\"#F%F%*&\"\"&F%F'F%F%F%!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "p-2*x^2*q;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*&\"\"'
\"\"\")I\"xG6\"\"\"%F%F%*&\"#8F%)F'\"\"$F%F%*&F$F%F'F%!\"\"F%F%*(\"\"#
F%)F'F1F%,(*&F-F%F2F%F%*&\"\"&F%F'F%F%F%F/F%F/" }}}{EXCHG {PARA 0 "> "
 0 "" {MPLTEXT 1 0 18 "expand(p-2*x^2*q);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",**&\"\"$\"\"\")I\"xG6\"F$F%F%*&\"\"'F%F'F%!\"\"F%F%*&\"
\"#F%)F'F-F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "expand(p-
13/3*x*q);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&\"\"'\"\"\")I\"xG6\"\"
\"%F%F%*&#\"\"&\"\"$F%F'F%!\"\"F%F%*&#\"#lF-F%)F'\"\"#F%F." }}}{EXCHG 
{PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" 
{TEXT 206 9 "E 10.5. P" }{TEXT 206 12 "\303\251lda." }}{PARA 0 "" 0 ""
 {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "p:=2*y^2*z
-x*z^2; q1:=7*y^2+y*z-4; q2:=2*y*z-3*x+1;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",&*(\"\"#\"\"\")I\"yG6\"F$F%I\"zGF(F%F%*&I\"xGF(F%)F)F$F%
!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&\"\"(\"\"\")I\"yG6\"\"\"#F%
F%*&F'F%I\"zGF(F%F%\"\"%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*(\"
\"#\"\"\"I\"yG6\"F%I\"zGF'F%F%*&\"\"$F%I\"xGF'F%!\"\"F%F%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "sort(p,[x,y,z]); sort(q1,[x,y,z]); \+
sort(q2,[x,y,z]);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&I\"xG6\"\"\"\")
I\"zGF%\"\"#F&!\"\"*(F)F&)I\"yGF%F)F&F(F&F&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",(*&\"\"(\"\"\")I\"yG6\"\"\"#F%F%*&F'F%I\"zGF(F%F%\"\"%!
\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*(\"\"#\"\"\"I\"yG6\"F%I\"zGF'
F%F%*&\"\"$F%I\"xGF'F%!\"\"F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 35 "expand(p-2/7*z*q1); expand(p-y*q2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",(*&I\"xG6\"\"\"\")I\"zGF%\"\"#F&!\"\"*(#F)\"\"(F&I\"yGF%
F&F'F&F**&#\"\")F-F&F(F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&I\"xG6
\"\"\"\")I\"zGF%\"\"#F&!\"\"*(\"\"$F&F$F&I\"yGF%F&F&F-F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(%+1/7*q2);" }}{PARA 11 "" 1 
"" {XPPMATH 20 ",.*&I\"xG6\"\"\"\")I\"zGF%\"\"#F&!\"\"*(\"\"$F&F$F&I\"
yGF%F&F&F-F**(#F)\"\"(F&F-F&F(F&F&*&#F,F0F&F$F&F*#F&F0F&" }}}{EXCHG 
{PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" 
{TEXT 206 19 "A 10.1. Algoritmus." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "reducers:=proc(p,Q,ord) loca
l phmonom,qhmonom,q,R;\n" }{MPLTEXT 1 0 43 "  R:=[]; phmonom:=LeadingM
onomial(p,ord);\n" }{MPLTEXT 1 0 17 "  for q in Q do\n" }{MPLTEXT 1 0 
18 "    if q<>0 then\n" }{MPLTEXT 1 0 40 "      qhmonom:=LeadingMonomi
al(q,ord);\n" }{MPLTEXT 1 0 57 "      if divide(phmonom,qhmonom) then \+
R:=[op(R),q]; fi;\n" }{MPLTEXT 1 0 9 "    fi;\n" }{MPLTEXT 1 0 10 "  o
d; R;\n" }{MPLTEXT 1 0 6 "end;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%
I\"pG6\"I\"QGF%I$ordGF%6&I(phmonomGF%I(qhmonomGF%I\"qGF%I\"RGF%F%F%C&>
F,7\">F)-_I)GroebnerG6$%*protectedGI(_syslibGF%I0LeadingMonomialGF%6$F
$F'?&F+F&I%trueGF5@$0F+\"\"!C$>F*-F26$F+F'@$-I'divideGF56$F)F*>F,7$-I#
opGF56#F,F+F,F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "Q:=[
q1,q2]; QQ:=reducers(p,Q,tdeg(x,y,z));" }}{PARA 11 "" 1 "" {XPPMATH 20
 "7$,(*&\"\"(\"\"\")I\"yG6\"\"\"#F&F&*&F(F&I\"zGF)F&F&\"\"%!\"\",(*(F*
F&F(F&F,F&F&*&\"\"$F&I\"xGF)F&F.F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "
7$,(*&\"\"(\"\"\")I\"yG6\"\"\"#F&F&*&F(F&I\"zGF)F&F&\"\"%!\"\",(*(F*F&
F(F&F,F&F&*&\"\"$F&I\"xGF)F&F.F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "reducer:=proc(p,Q,ord) Q[1] end;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "f*6%I\"pG6\"I\"QGF%I$ordGF%F%F%F%&F&6#\"\"\"F%F%F%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "reducer(p,QQ,tdeg(x,y,z));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&\"\"(\"\"\")I\"yG6\"\"\"#F%F%*&F'F
%I\"zGF(F%F%\"\"%!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "m
yreduce:=proc(p,Q,ord) local QQ,q,pp,ppp,lpp,lq,t;\n" }{MPLTEXT 1 0 
18 "  pp:=p; ppp:=0;\n" }{MPLTEXT 1 0 18 "  while pp<>0 do\n" }
{MPLTEXT 1 0 29 "    QQ:=reducers(pp,Q,ord);\n" }{MPLTEXT 1 0 20 "    \+
if QQ<>[] then\n" }{MPLTEXT 1 0 29 "      q:=reducer(p,QQ,ord);\n" }
{MPLTEXT 1 0 47 "      t:=LeadingTerm(pp,ord); lpp:=t[1]*t[2];\n" }
{MPLTEXT 1 0 45 "      t:=LeadingTerm(q,ord); lq:=t[1]*t[2];\n" }
{MPLTEXT 1 0 32 "      pp:=expand(pp-lpp*q/lq);\n" }{MPLTEXT 1 0 10 " \+
   else\n" }{MPLTEXT 1 0 44 "      LeadingTerm(pp,ord); lpp:=%[1]*%[2]
;\n" }{MPLTEXT 1 0 21 "      ppp:=ppp+lpp;\n" }{MPLTEXT 1 0 19 "      \+
pp:=pp-lpp;\n" }{MPLTEXT 1 0 9 "    fi;\n" }{MPLTEXT 1 0 12 "  od; ppp
;\n" }{MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%I\"pG6
\"I\"QGF%I$ordGF%6)I#QQGF%I\"qGF%I#ppGF%I$pppGF%I$lppGF%I#lqGF%I\"tGF%
F%F%C&>F+F$>F,\"\"!?(F%\"\"\"F5F%0F+F3C$>F)-I)reducersGF%6%F+F&F'@%0F)
7\"C(>F*-I(reducerGF%6%F$F)F'>F/-_I)GroebnerG6$%*protectedGI(_syslibGF
%I,LeadingTermGF%6$F+F'>F-*&&F/6#F5F5&F/6#\"\"#F5>F/-FF6$F*F'>F.FN>F+-
I'expandGFI6#,&F+F5*(F-F5F*F5F.!\"\"FhnC&FE>F-*&&I\"%GF%FPF5&F]oFRF5>F
,,&F,F5F-F5>F+,&F+F5F-FhnF,F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "myreduce(p,Q,tdeg(x,y,z));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",(*&I\"xG6\"\"\"\")I\"zGF%\"\"#F&!\"\"*(#\"\"$\"\"(F&F(F&
F$F&F**&#\"\"*F.F&F(F&F&" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%
#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 10.6. P" }{TEXT 206 
12 "\303\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 ">
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^2+y^2; q2:=7*x*y^2-2*y^3+1;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**(\"\"
$\"\"\")I\"xG6\"F$F%I\"yGF(F%F%*(\"\"#F%)F'F+F%)F)F+F%F%*(F$F%F'F%F)F%
!\"\"*&\"\"&F%F'F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&)I\"xG6\"\"
\"#\"\"\"I\"yGF&F(F(*&\"\"&F(F$F(F(*$)F)F'F(F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",(*(\"\"(\"\"\"I\"xG6\"F%)I\"yGF'\"\"#F%F%*&F*F%)F)\"\"$F
%!\"\"F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(p-3*x*
q1);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*(\"\"#\"\"\")I\"xG6\"F$F%)I\"
yGF(F$F%F%*(\"\"$F%F'F%F*F%!\"\"*&\"\"&F%F'F%F%*&\"#:F%)F'F,F%F-*(F,F%
F'F%F)F%F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(%-2*y*
q1);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.*(\"\"$\"\"\"I\"xG6\"F%I\"yGF'
F%!\"\"*&\"\"&F%F&F%F%*&\"#:F%)F&F$F%F)*(F$F%F&F%)F(\"\"#F%F)*(\"#5F%)
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16 "expand(%+10*q1);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",0*(\"\"$\"\"\"I
\"xG6\"F%I\"yGF'F%!\"\"*&\"\"&F%F&F%F%*&\"#:F%)F&F$F%F)*(F$F%F&F%)F(\"
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(%+3/7*q2);" }}{PARA 11 "" 1 
"" {XPPMATH 20 ",0*(\"\"$\"\"\"I\"xG6\"F%I\"yGF'F%!\"\"*&\"\"&F%F&F%F%
*&\"#:F%)F&F$F%F)*&#\"#?\"\"(F%)F(F$F%F)*&\"#]F%)F&\"\"#F%F%*&\"#5F%)F
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{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 10.7. P" }{TEXT 206 12 "\303\25
1lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "q1:=x^3*y*z-x*z^2; q2:=x*y^2*z-x*y*z; q3:=x^2*y^2-z^2
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{PARA 11 "" 1 "" {XPPMATH 20 ",&*()I\"xG6\"\"\"$\"\"\"I\"yGF&F(I\"zGF&
F(F(*&F%F()F*\"\"#F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*(I\"xG6
\"\"\"\")I\"yGF%\"\"#F&I\"zGF%F&F&*(F$F&F(F&F*F&!\"\"" }}{PARA 11 "" 1
 "" {XPPMATH 20 ",&*&)I\"xG6\"\"\"#\"\"\")I\"yGF&F'F(F(*$)I\"zGF&F'F(!
\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*()I\"xG6\"\"\"#\"\"\")I\"yGF&
F'F(I\"zGF&F(F(*$)F+\"\"$F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*(
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "expand(p1-z*q3); expand(p2+x
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" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"zG6\"\"
\"$\"\"\"!\"\"*()I\"xGF&\"\"#F(I\"yGF&F(F%F(F(" }}}{EXCHG {PARA 0 "" 0
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" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "G:=[q1,q2,q3,x^2*y*z-z^3
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z^5-z^4];" }}{PARA 11 "" 1 "" {XPPMATH 20 "7+,&*()I\"xG6\"\"\"$\"\"\"I
\"yGF'F)I\"zGF'F)F)*&F&F))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)F9F/,&*(F&F)F*F)F-F)F)F,F/,&*&F6F)F-F)F)*$)F+\"
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57 "myreduce(p1,G,tdeg(x,y,z)); myreduce(p2,G,tdeg(x,y,z));\n" }
{MPLTEXT 1 0 30 "myreduce(p1-p2,G,tdeg(x,y,z));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 
"" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" 
"%#%?G" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 9 "E 10.9. P" }{TEXT 
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{SECT 1 {PARA 4 "" 0 "" {TEXT 206 10 "E 10.10. P" }{TEXT 206 12 "\303
\251lda." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 19 "A 10.3. Algoritmus.
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\303\251lda." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 19 "A 10.4. Algorit
mus." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 
{PARA 4 "" 0 "" {TEXT 206 10 "E 10.12. P" }{TEXT 206 12 "\303\251lda."
 }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 4 
"" 0 "" {TEXT 206 10 "E 10.13. P" }{TEXT 206 12 "\303\251lda." }}
{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 4 "" 
0 "" {TEXT 206 10 "E 10.14. P" }{TEXT 206 12 "\303\251lda." }}{EXCHG 
{PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT 206 10 "E 10.15. P" }{TEXT 206 12 "\303\251lda." }}{EXCHG {PARA 
0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 
206 10 "E 10.16. P" }{TEXT 206 12 "\303\251lda." }}{EXCHG {PARA 0 "" 0
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A 10.5. Algoritmus." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" 
}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 10 "E 10.17. P" }{TEXT 206 12 "
\303\251lda." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}
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{TEXT 206 10 "E 10.18. P" }{TEXT 206 12 "\303\251lda." }}{EXCHG {PARA 
0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 
206 19 "A 10.7. Algoritmus." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" 
"%#%?G" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 206 10 "E 10.19. P" }{TEXT 
206 12 "\303\251lda." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G"
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\303\251lda." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}
{SECT 1 {PARA 4 "" 0 "" {TEXT 206 10 "E 10.21. P" }{TEXT 206 12 "\303
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{PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 3 "" 0 "" 
{TEXT 205 10 "11. Racion" }{TEXT 205 8 "\303\241" }{TEXT 205 5 "lis t"
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{TEXT 205 3 "ggv" }{TEXT 205 8 "\303\251" }{TEXT 205 11 "nyek integr" 
}{TEXT 205 8 "\303\241" }{TEXT 205 1 "l" }{TEXT 205 8 "\303\241" }
{TEXT 205 2 "sa" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 23 "12. A Risch-
algoritmus." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 12 "13. \305\221" }}
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 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}}
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