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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Aufgabe 1" }}}{EXCHG {PARA 
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{MPLTEXT 1 0 6 "n:=10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"#5" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "q:=quo(x^n-a^n,x-a,x);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG,6*$)%\"xG\"\"*\"\"\"F**&%\"aGF
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25 "q:=n->quo(x^n-a^n,x-a,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"q
GR6#%\"nG6\"6$%)operatorG%&arrowGF(-%$quoG6%,&)%\"xG9$\"\"\")%\"aGF2!
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0 "" {MPLTEXT 1 0 5 "q(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Aufgabe 2, erstes Problem" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f := x^4-6*x^2+12*x-8;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,**$)%\"xG\"\"%\"\"\"F**&\"\"'F*
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{MPLTEXT 1 0 28 "g := 2*x^3 -10*x^2 +16*x -8;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"gG,**$)%\"xG\"\"$\"\"\"\"\"#*&\"#5F*)F(F+F*!\"\"*&
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{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\"#7\"\"\"*&\"#6F%)%\"xG\"\"#F%F%*&
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\"#i\"$@\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "r1;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&#!$C#\"$@\"\"\"\"*&#\"$%=F&F'%\"xGF'
F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "q2:=quo(r,r1,x,r2);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#q2G,&%\"xG#\"%J8\"$%=#\"%\"Q(\"%e
5!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "r2;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6##!$%[\"$H&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "q3:=quo(r1,r2,x,r3);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%#q3G,&#\"&C'H\"&TY\"\"\"\"*&#\"&MV#F(F)%\"xGF)!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "r3;" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Also ist r2 ein ggT. \+
Dann aber auch 1:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 
1 0 9 "gcd(f,g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "?gcdex" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "gcdex(f,g,x,a,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}{PARA 11 "" 
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{PARA 11 "" 1 "" {XPPMATH 20 "6#,*#\"#R\"\")\"\"\"*&#\"#^\"#;F'%\"xGF'
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "a*f+b*g;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*&,(!\"&\"\"\"*&#\"#()\"#;F'%\"xGF'F'*&#\"#BF+F'*$)F,
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> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Aufgabe 2, zweite
s Problem" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f := x^9 -1;" 
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" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "g := x^5 +x^3 -x^2 -1;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,**$)%\"xG\"\"&\"\"\"F**$)F(
\"\"$F*F**$)F(\"\"#F*!\"\"F*F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "gg := gcd(f,g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ggG,&*$)
%\"xG\"\"$\"\"\"F*F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
17 "gcdex(f,g,x,a,b);" }}{PARA 8 "" 1 "" {TEXT -1 60 "Error, (in gcdex
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0 "" {MPLTEXT 1 0 21 "gcdex(f,g,x,'a','b');" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*$)%\"xG\"\"$\"\"\"F(F(!\"\"" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 2 "a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "b;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,,\"\"\"F$%\"xG!\"\"*$)F%\"\"&F$F&*$)F%\"\"$F$F$*$)F%\"
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}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Aufgabe 2, drittes Problem" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f1 := x^3 + x^2 -4*x -4;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1G,**$)%\"xG\"\"$\"\"\"F**$)F(\"\"
#F*F**&\"\"%F*F(F*!\"\"F/F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
26 "f2 := x^3 - x^2 - 4*x +4 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f
2G,**$)%\"xG\"\"$\"\"\"F**$)F(\"\"#F*!\"\"*&\"\"%F*F(F*F.F0F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gg:=gcd(f1,f2);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%#ggG,&!\"%\"\"\"*$)%\"xG\"\"#F'F'" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 22 "Nun nur aus Interesse:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 24 "f3 := x^3 -2*x^2 -x + 2;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#f3G,**$)%\"xG\"\"$\"\"\"F**&\"\"#F*)F(F,F*!\"\"
F(F.F,F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "gcd(gg,f3);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"\"\"\"\"#!\"\"" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 9 "Aufgabe 3" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "f := x^5 -2*x^4 + 2*x^2 -x ;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fG,**$)%\"xG\"\"&\"\"\"F**&\"\"#F*)F(\"\"%F*!\"\"*&
F,F*)F(F,F*F*F(F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "g := x
^5 - x^4 -2*x^3 +2*x^2 +x -1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"g
G,.*$)%\"xG\"\"&\"\"\"F**$)F(\"\"%F*!\"\"*&\"\"#F*)F(\"\"$F*F.*&F0F*)F
(F0F*F*F(F*F*F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "solve(\{
f,g\},x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<#/%\"xG!\"\"<#/F%\"\"\"
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Wie kann man das \"zu Fuss\" \+
einsehen?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "f-g;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,**$)%\"xG\"\"%\"\"\"!\"\"*&\"\"#F(F&F(F)*&F
+F()F&\"\"$F(F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Rate die N
ullstelle 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eval(f-g,x=1
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 12 "eval(f,x=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "eval(g,x=1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "f1:=quo(f,x-1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%#f1G,**$)%\"xG\"\"%\"\"\"F**$)F(\"\"$F*!\"\"*$)F(\"\"#F*F.F(F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "g1:=quo(g,x-1,x);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#g1G,(*$)%\"xG\"\"%\"\"\"F**&\"\"#F*)F(F,F
*!\"\"F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "Die Nullstellen von
 g1 findet man als Loesungen einer biquadratischen Gleichung:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(y^2-2*y+1,y);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"F#" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 29 "Also nur -1 und 1 zu pruefen." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 14 "eval(f1,x=-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "eval(f1,x=1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}}{MARK "45 0 0" 17 }
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