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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" }}}{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
ent" }{TEXT 205 18 "\303\241ci\303\263" }}}{SECT 1 {PARA 3 "" 0 "" 
{TEXT 205 13 "4. Aritmetika" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 4 "5
. K" }{TEXT 205 8 "\303\255" }{TEXT 205 9 "nai marad" }{TEXT 205 8 "\3
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
ensel-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. Egyenletre
ndszerek" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 6 "10. Gr" }{TEXT 205 
27 "\303\266bner-b\303\241zisok" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 
10 "11. Racion" }{TEXT 205 8 "\303\241" }{TEXT 205 5 "lis t" }{TEXT 
205 8 "\303\266" }{TEXT 205 3 "rtf" }{TEXT 205 8 "\303\274" }{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 0 {PARA 3 "" 0 "" {TEXT 205 23 "12. A Risch-algoritmus
." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
134 "(x*(x+1)*((x^2*exp(2*x^2)-(log(x+1))^2)^2+2*x*exp(3*x^2)*(x-(2*x^
3+2*x^2+x+1)*log(x+1))))/((x+1)*(log(x+1))^2-(x^3+x^2)*exp(2*x^2))^2;"
 }}{PARA 11 "" 1 "" {XPPMATH 20 "**I\"xG6\"\"\"\",&F#F%F%F%F%,&*$),&*&
)F#\"\"#F%-I$expG6$%*protectedGI(_syslibGF$6#,$*&F-F%F,F%F%F%F%*$)-I#l
nGF06#F&F-F%!\"\"F-F%F%**F-F%F#F%-F/6#,$*&\"\"$F%F,F%F%F%,&F#F%*&,**&F
-F%)F#FAF%F%F5F%F#F%F%F%F%F8F%F;F%F%F%),&*&F&F%F7F%F%*&,&*$FFF%F%*$F,F
%F%F%F.F%F;F-F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(%,x);
" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,I\"xG6\"\"\"\"-I#lnG6$%*protectedG
I(_syslibGF$6#,&F#F%F%F%!\"\"**-I$expGF(6#*$)F#\"\"#F%F%F#F%F&F%,&*&F3
F%-F06#,$*&F4F%F3F%F%F%F%*$)F&F4F%F-F-F%*&#F%F4F%-F'6#,&*&F/F%F#F%F%F&
F%F%F%*&F>F%-F'6#,&FBF-F&F%F%F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 42 "int(1/(1+exp(x)),x); simplify(%,symbolic);" }}{PARA 11 "" 1 ""
 {XPPMATH 20 ",&-I#lnG6$%*protectedGI(_syslibG6\"6#,&\"\"\"F+-I$expGF%
6#I\"xGF(F+!\"\"-F$6#F,F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&-I#lnG6$%
*protectedGI(_syslibG6\"6#,&\"\"\"F+-I$expGF%6#I\"xGF(F+!\"\"F/F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "int(x/(1+exp(x)),x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",(*&#\"\"\"\"\"#F%)I\"xG6\"F&F%F%*&F(F%-
I#lnG6$%*protectedGI(_syslibGF)6#,&F%F%-I$expGF-6#F(F%F%!\"\"-I(polylo
gGF-6$F&,$F2F5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "int(1/(
1+x^2),x); convert(%,ln);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I'arctanG6
$%*protectedGI(_syslibG6\"6#I\"xGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "*
&*&#\"\"\"\"\"#F%^#F%F%F%,&-I#lnG6$%*protectedGI(_syslibG6\"6#,&F%F%*&
,$F'F%F%I\"xGF.F%!\"\"F%-F*6#,&F%F%*&F'F%F3F%F%F4F%" }}}{EXCHG {PARA 0
 "> " 0 "" {MPLTEXT 1 0 30 "int(cos(x),x); convert(%,exp);" }}{PARA 11
 "" 1 "" {XPPMATH 20 "-I$sinG6$%*protectedGI(_syslibG6\"6#I\"xGF'" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,$*&#\"\"\"\"\"#F'^#F'F'F'F',&-I$exp
G6$%*protectedGI(_syslibG6\"6#*&F)F'I\"xGF0F'F'*$F+!\"\"F5F'F5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "int(1/sqrt(1-x^2),x); conver
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yslibG6\"6#I\"xGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,$^#\"\"\"F&F&
-I#lnG6$%*protectedGI(_syslibG6\"6#,&*$),&F&F&*$)I\"xGF,\"\"#F&!\"\"#F
&F5F&F&*&F%F&F4F&F&F&F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "
int(arccosh(x),x); convert(arccosh(x),ln); int(%,x);" }}{PARA 11 "" 1 
"" {XPPMATH 20 ",&*&I\"xG6\"\"\"\"-I(arccoshG6$%*protectedGI(_syslibGF
%6#F$F&F&*&),&F$F&F&!\"\"#F&\"\"#F&),&F$F&F&F&F1F&F0" }}{PARA 11 "" 1 
"" {XPPMATH 20 "-I#lnG6$%*protectedGI(_syslibG6\"6#,&I\"xGF'\"\"\"*&),
&F*F+F+!\"\"#F+\"\"#F+),&F*F+F+F+F0F+F+" }}{PARA 11 "" 1 "" {XPPMATH 
20 ",&*&-I#lnG6$%*protectedGI(_syslibG6\"6#,&I\"xGF)\"\"\"*&),&F,F-F-!
\"\"#F-\"\"#F-),&F,F-F-F-F2F-F-F-F,F-F-F.F1" }}}{SECT 0 {PARA 4 "" 0 "
" {TEXT 206 9 "E 12.1. P" }{TEXT 206 12 "\303\251lda." }}{EXCHG {PARA 
0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
 1 0 38 "f:=exp(x)+exp(2*x)+exp(x/2); int(f,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",(-I$expG6$%*protectedGI(_syslibG6\"6#I\"xGF(\"\"\"-F$6#,
$*&\"\"#F+F*F+F+F+-F$6#,$*&#F+F0F+F*F+F+F+" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",(-I$expG6$%*protectedGI(_syslibG6\"6#I\"xGF(\"\"\"*&#F+
\"\"#F+-F$6#,$*&F.F+F*F+F+F+F+*&F.F+-F$6#,$*&F-F+F*F+F+F+F+" }}}}
{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 12.2. P" }{TEXT 206 12 "\303\25
1lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "g:=sqrt(log(x^2+3*x+2)*(log(x+1)+log(x+2)));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "*$)*&-I#lnG6$%*protectedGI(_syslibG6\"6#
,(*$)I\"xGF*\"\"#\"\"\"F1*&\"\"$F1F/F1F1F0F1F1,&-F&6#,&F/F1F1F1F1-F&6#
,&F/F1F0F1F1F1#F1F0F1" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 12.3
. P" }{TEXT 206 12 "\303\251lda." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 
0 "" "%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "h:=exp(ln(x)
/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$)I\"xG6\"#\"\"\"\"\"#F'" }}}}
{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 12.4. P" }{TEXT 206 12 "\303\25
1lda." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "g:=log(sqrt(x^2+1)+x)+log(sqrt(x^2+
1)-x); theta1:=sqrt(x^2+1);\n" }{MPLTEXT 1 0 56 "h:=(theta1-x)^k*(thet
a1+x)^k1; diff(h,x)/h; simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",
&-I#lnG6$%*protectedGI(_syslibG6\"6#,&*$),&*$)I\"xGF(\"\"#\"\"\"F2F2F2
#F2F1F2F2F0F2F2-F$6#,&F+F2F0!\"\"F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "*
$),&*$)I\"xG6\"\"\"#\"\"\"F*F*F*#F*F)F*" }}{PARA 11 "" 1 "" {XPPMATH 
20 "*&),&*$),&*$)I\"xG6\"\"\"#\"\"\"F-F-F-#F-F,F-F-F*!\"\"I\"kGF+F-),&
F%F-F*F-I#k1GF+F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,&*,),&*$),&*$)I
\"xG6\"\"\"#\"\"\"F/F/F/#F/F.F/F/F,!\"\"I\"kGF-F/F2F/,&*&F(F1F,F/F/F/F
1F/F&F1),&F'F/F,F/I#k1GF-F/F/*,F%F/F5F/F7F/,&F4F/F/F/F/F6F1F/F/F%F1F5F
1" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,&I\"kG6\"\"\"\"I#k1GF&!\"\"F')
,&*$)I\"xGF&\"\"#F'F'F'F'#F'F/F)F)" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 
206 9 "E 12.5. P" }{TEXT 206 12 "\303\251lda." }}{EXCHG {PARA 0 "" 0 "
" {XPPEDIT 2 0 "" "%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 
"exp(x^2+log(x)/2)/(2*(sqrt(x)-1))+exp(x^2+log(x)/2)/(2*(sqrt(x)+1));
\n" }{MPLTEXT 1 0 23 "diff(%,x); simplify(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",&*&-I$expG6$%*protectedGI(_syslibG6\"6#,&*$)I\"xGF)\"\"#
\"\"\"F0*&#F0F/F0-I#lnGF&6#F.F0F0F0,&*&F/F0)F.F2F0F0F/!\"\"F9F0*&F$F0,
&F7F0F/F0F9F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**(,&*&\"\"#\"\"\"I\"x
G6\"F'F'*&#F'F&F'F(!\"\"F'F'-I$expG6$%*protectedGI(_syslibGF)6#,&*$)F(
F&F'F'*&F+F'-I#lnGF/6#F(F'F'F',&*&F&F')F(F+F'F'F&F,F,F'*(F-F')F:F&F,F<
F,F,*(F$F'F-F',&F;F'F&F'F,F'*(F-F')F@F&F,F<F,F," }}{PARA 11 "" 1 "" 
{XPPMATH 20 "**-I$expG6$%*protectedGI(_syslibG6\"6#*$)I\"xGF(\"\"#\"\"
\"F.,(*&F-F.)F,\"\"$F.F.*&F-F.F+F.!\"\"F.F4F.),&*$)F,#F.F-F.F.F.F4F-F4
),&F7F.F.F.F-F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "int((2*x
^3-2*x^2-1)/(x-1)^2*exp(x^2),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,&
I\"xG6\"\"\"\"F&!\"\"F'F$F&-I$expG6$%*protectedGI(_syslibGF%6#*$)F$\"
\"#F&F&" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 12.6. P" }{TEXT 
206 12 "\303\251lda." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G"
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{PARA 11 "" 1 "" {XPPMATH 20 ",$-I#EiG6$%*protectedGI(_syslibG6\"6$\"
\"\",$-I#lnGF%6#I\"xGF(!\"\"F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 29 "resultant(1-z/x,theta,theta);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"*&,&I\"xG6\"\"\"\"I\"zGF%!\"\"F&F$F(" }}}}{SECT 0 {PARA 4 "" 0 "" 
{TEXT 206 9 "E 12.7. P" }{TEXT 206 12 "\303\251lda." }}{EXCHG {PARA 0 
"" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 17 "int(1/x/ln(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I#lnG6$%*p
rotectedGI(_syslibG6\"6#-F#6#I\"xGF'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "resultant(1/x-z/x,theta,theta);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",$*&,&\"\"\"!\"\"I\"zG6\"F%F%I\"xGF(F&F&" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "oR:=1-z;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",&\"\"\"F#I\"zG6\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "v1:=gcd(1/x-1/x,theta);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "I&thetaG6\"" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 9 "E 12.8. P" }
{TEXT 206 12 "\303\251lda." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "
%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "(x*(x+1)*((x^2*ex
p(2*x^2)-(log(x+1))^2)^2+2*x*exp(3*x^2)*(x-(2*x^3+2*x^2+x+1)*log(x+1))
))/((x+1)*(log(x+1))^2-(x^3+x^2)*exp(2*x^2))^2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "**I\"xG6\"\"\"\",&F#F%F%F%F%,&*$),&*&)F#\"\"#F%-I$expG6$%
*protectedGI(_syslibGF$6#,$*&F-F%F,F%F%F%F%*$)-I#lnGF06#F&F-F%!\"\"F-F
%F%**F-F%F#F%-F/6#,$*&\"\"$F%F,F%F%F%,&F#F%*&,**&F-F%)F#FAF%F%F5F%F#F%
F%F%F%F8F%F;F%F%F%),&*&F&F%F7F%F%*&,&*$FFF%F%*$F,F%F%F%F.F%F;F-F;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(%,x);" }}{PARA 11 "" 1 ""
 {XPPMATH 20 ",,I\"xG6\"\"\"\"-I#lnG6$%*protectedGI(_syslibGF$6#,&F#F%
F%F%!\"\"**-I$expGF(6#*$)F#\"\"#F%F%F#F%F&F%,&*&F3F%-F06#,$*&F4F%F3F%F
%F%F%*$)F&F4F%F-F-F%*&#F%F4F%-F'6#,&F&F%*&F#F%F/F%F-F%F-*&F>F%-F'6#,&F
BF%F&F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "subs(exp(x^2
)=theta1,%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "**I\"xG6\"\"\"\",&F#F%F
%F%F%,&*$),&*&)F#\"\"#F%-I$expG6$%*protectedGI(_syslibGF$6#,$*&F-F%F,F
%F%F%F%*$)-I#lnGF06#F&F-F%!\"\"F-F%F%**F-F%F#F%-F/6#,$*&\"\"$F%F,F%F%F
%,&F#F%*&,**&F-F%)F#FAF%F%F5F%F#F%F%F%F%F8F%F;F%F%F%),&*&F&F%F7F%F%*&,
&*$FFF%F%*$F,F%F%F%F.F%F;F-F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 28 "subs(exp(2*x^2)=theta1^2,%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "**
I\"xG6\"\"\"\",&F#F%F%F%F%,&*$),&*&)F#\"\"#F%)I'theta1GF$F-F%F%*$)-I#l
nG6$%*protectedGI(_syslibGF$6#F&F-F%!\"\"F-F%F%**F-F%F#F%-I$expGF46#,$
*&\"\"$F%F,F%F%F%,&F#F%*&,**&F-F%)F#F?F%F%*&F-F%F,F%F%F#F%F%F%F%F2F%F8
F%F%F%),&*&F&F%F1F%F%*&,&*$FDF%F%*$F,F%F%F%F.F%F8F-F8" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "subs(exp(3*x^2)=theta1^3,%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "**I\"xG6\"\"\"\",&F#F%F%F%F%,&*$),&*&)F#
\"\"#F%)I'theta1GF$F-F%F%*$)-I#lnG6$%*protectedGI(_syslibGF$6#F&F-F%!
\"\"F-F%F%**F-F%F#F%)F/\"\"$F%,&F#F%*&,**&F-F%)F#F;F%F%*&F-F%F,F%F%F#F
%F%F%F%F2F%F8F%F%F%),&*&F&F%F1F%F%*&,&*$F@F%F%*$F,F%F%F%F.F%F8F-F8" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "f:=subs(ln(x+1)=theta2,%);"
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)F#\"\"#F%)I'theta1GF$F-F%F%*$)I'theta2GF$F-F%!\"\"F-F%F%**F-F%F#F%)F/
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "a:=(2*x^2+1)*theta1*theta2-x/(x+1)*
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}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "b:=theta2^2-x^2*theta1^2;" 
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31 "oR:=4*z^2-1; c1:=1/2; c2:=-1/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",
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