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{SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT -1 35 "\334bungsblatt 3 - Diskret
e Mathematik" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "Martin Klossek - \+
klossek@informatik.uni-frankfurt.de" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 
-1 25 "Aufgabe 12 - Kontinuanten" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 76 "Berechnen wir die Rekursion f\374r
 die Bestimmungsbr\374che mal per Hand bis z[8]:" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 442 "z[1] := x[
1]*z[0] + z[-1];\nz[2] := collect(simplify(x[2]*z[1] + z[0]), [z[0],z[
-1]]);\nz[3] := collect(simplify(x[3]*z[2] + z[1]), [z[0],z[-1]]);\nz[
4] := collect(simplify(x[4]*z[3] + z[2]), [z[0],z[-1]]);\nz[5] := coll
ect(simplify(x[5]*z[4] + z[3]), [z[0],z[-1]]);  \nz[6] := collect(simp
lify(x[6]*z[5] + z[4]), [z[0],z[-1]]);\nz[7] := collect(simplify(x[7]*
z[6] + z[5]), [z[0],z[-1]]);\nz[8] := collect(simplify(x[8]*z[7] + z[4
]), [z[0],z[-1]]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"zG6#\"\"
\",&*&&%\"xGF&F'&F%6#\"\"!F'F'&F%6#!\"\"F'" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"zG6#\"\"#,&*&,&*&&%\"xGF&\"\"\"&F-6#F.F.F.F.F.F.&F
%6#\"\"!F.F.*&F,\"\"\"&F%6#!\"\"F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>&%\"zG6#\"\"$,&*&,(&%\"xGF&\"\"\"&F,6#F-F-*(F+F-&F,6#\"\"#F-F.F-F-F
-&F%6#\"\"!F-F-*&,&F-F-*&F+\"\"\"F1F:F-F-&F%6#!\"\"F-F-" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>&%\"zG6#\"\"%,&*&,,*&&%\"xGF&\"\"\"&F-6#\"\"$F.
F.**F,\"\"\"F/F3&F-6#\"\"#F.&F-6#F.F.F.*&F4F3F7F3F.F.F.*&F,F3F7F3F.F.&
F%6#\"\"!F.F.*&,(F,F.*(F,F3F/F3F4F3F.F4F.F.&F%6#!\"\"F.F." }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>&%\"zG6#\"\"&,&*&,2*(&%\"xGF&\"\"\"&F-6#\"\"%F
.&F-6#\"\"$F.F.*(F,\"\"\"&F-6#\"\"#F.&F-6#F.F.F.F,F.*,F,F6F/F6F2F6F7F6
F:F6F.F:F.*(F2F6F7F6F:F6F.*(F,F6F/F6F:F6F.F2F.F.&F%6#\"\"!F.F.*&,,*&F,
F6F/F6F.**F,F6F/F6F2F6F7F6F.*&F,F6F7F6F.*&F2F6F7F6F.F.F.F.&F%6#!\"\"F.
F." }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%\"zG6#\"\"',&*&,<**&%\"xGF&\"
\"\"&F-6#\"\"&F.&F-6#\"\"%F.&F-6#\"\"$F.F.*&F,\"\"\"&F-6#F.F.F.**F,F9F
5F9&F-6#\"\"#F.F:F9F.**F,F9F/F9F2F9F:F9F.*.F,F9F/F9F2F9F5F9F=F9F:F9F.*
&F2F9F5F9F.**F2F9F5F9F=F9F:F9F.*&F=F9F:F9F.*&F,F9F5F9F.*&F2F9F:F9F.**F
,F9F/F9F=F9F:F9F.*&F,F9F/F9F.F.F.F.&F%6#\"\"!F.F.*&,2*(F,F9F/F9F2F9F.*
,F,F9F/F9F2F9F5F9F=F9F.*(F2F9F5F9F=F9F.*(F,F9F/F9F=F9F.*(F,F9F5F9F=F9F
.F2F.F,F.F=F.F.&F%6#!\"\"F.F." }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%\"
zG6#\"\"(,&*&,L&%\"xG6#\"\"\"F.*(&F,F&F.&F,6#\"\"'F.F+F.F.&F,6#\"\"&F.
*(F0\"\"\"&F,6#\"\"#F.F+F8F.*(F0F8&F,6#\"\"%F.F+F8F.*(&F,6#\"\"$F.F9F8
F+F8F.*(F4F.F=F8F+F8F.*(F4F8F9F8F+F8F.*(F0F8F1F8F4F8F.*(F0F8F1F8FAF8F.
*0F0F8F1F8F4F8F=F8FAF8F9F8F+F8F.*(F0F8F=F8FAF8F.*,F0F8F1F8F4F8F=F8FAF8
F.*,F0F8F1F8F4F8F=F8F+F8F.FAF.*,F0F8F1F8F4F8F9F8F+F8F.*(F4F8F=F8FAF8F.
*,F0F8F1F8FAF8F9F8F+F8F.*,F4F8F=F8FAF8F9F8F+F8F.*,F0F8F=F8FAF8F9F8F+F8
F.F0F.F.&F%6#\"\"!F.F.*&,<*&FAF8F9F8F.*&F0F8F1F8F.*&F4F8F9F8F.F.F.*&F0
F8F9F8F.**F0F8F1F8FAF8F9F8F.**F4F8F=F8FAF8F9F8F.**F0F8F=F8FAF8F9F8F.**
F0F8F1F8F4F8F9F8F.*&F0F8F=F8F.**F0F8F1F8F4F8F=F8F.*.F0F8F1F8F4F8F=F8FA
F8F9F8F.*&F4F8F=F8F.F.&F%6#!\"\"F.F." }}{PARA 12 "" 1 "" {XPPMATH 20 "
6#>&%\"zG6#\"\"),&*&,V\"\"\"F+*&&%\"xG6#\"\"#F+&F.6#F+F+F+**&F.F&F+&F.
6#\"\"$F+F-\"\"\"F1F8F+**F4F8&F.6#\"\"&F+&F.6#\"\"%F+F1F8F+**F4F8F:F8F
-F8F1F8F+**F4F8&F.6#\"\"(F+&F.6#\"\"'F+F:F8F+**F4F8FBF8FEF8F5F8F+**F4F
8FBF8FEF8F1F8F+**F4F8FBF8F=F8F5F8F+**F4F8FBF8F-F8F1F8F+**F4F8FBF8F=F8F
1F8F+**F4F8F:F8F=F8F5F8F+*&F=F8F1F8F+*&F=F8F5F8F+**F=F8F5F8F-F8F1F8F+*
&F4F8F5F8F+*&F4F8FBF8F+*&F4F8F:F8F+*&F4F8F1F8F+*.F4F8F:F8F=F8F5F8F-F8F
1F8F+*2F4F8FBF8FEF8F:F8F=F8F5F8F-F8F1F8F+*.F4F8FBF8FEF8F:F8F=F8F5F8F+*
.F4F8FBF8FEF8F:F8F=F8F1F8F+*.F4F8FBF8FEF8F:F8F-F8F1F8F+*.F4F8FBF8FEF8F
5F8F-F8F1F8F+*.F4F8FBF8F=F8F5F8F-F8F1F8F+F+&F%6#\"\"!F+F+*&,B*(F=F8F5F
8F-F8F+*,F4F8FBF8F=F8F5F8F-F8F+*(F4F8F:F8F-F8F+*(F4F8F5F8F-F8F+*,F4F8F
:F8F=F8F5F8F-F8F+*(F4F8FBF8FEF8F+*(F4F8FBF8F=F8F+F-F+*(F4F8F:F8F=F8F+*
(F4F8FBF8F-F8F+F4F+*0F4F8FBF8FEF8F:F8F=F8F5F8F-F8F+F=F+*,F4F8FBF8FEF8F
5F8F-F8F+*,F4F8FBF8FEF8F:F8F=F8F+*,F4F8FBF8FEF8F:F8F-F8F+F+&F%6#!\"\"F
+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 80 "Die Kontinuanten bis f[8] habe ich aus obigen Ausdruck per Hand
 rausgeschrieben:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 1325 "f[1] := x[1];\nf[2] := x[2]*x[1]+1;\nf[3] \+
:= x[3]+x[1]+x[3]*x[2]*x[1];\nf[4] := x[4]*x[3]+x[4]*x[3]*x[2]*x[1]+x[
2]*x[1]+1+x[4]*x[1];\nf[5] := x[5]*x[4]*x[3]+x[5]*x[2]*x[1]+x[5]+x[5]*
x[4]*x[3]*x[2]*x[1]+x[1]+x[3]*x[2]*x[1]+x[5]*x[4]*x[1]+x[3];\nf[6] := \+
x[6]*x[5]*x[4]*x[3]+x[6]*x[1]+x[6]*x[3]*x[2]*x[1]+x[6]*x[5]*x[4]*x[1]+
x[6]*x[5]*x[4]*x[3]*x[2]*x[1]+x[4]*x[3]+x[4]*x[3]*x[2]*x[1]+x[2]*x[1]+
x[6]*x[3]+x[4]*x[1]+x[6]*x[5]*x[2]*x[1]+x[6]*x[5]+1;\nf[7] := \nx[1]+x
[7]*x[6]*x[1]+x[5]+x[7]*x[2]*x[1]+x[7]*x[4]*x[1]+x[3]*x[2]*x[1]+x[5]*x
[4]*x[1]+x[5]*x[2]*x[1]+x[7]*x[6]*x[5]+x[7]*x[6]*x[3]+x[7]*x[6]*x[5]*x
[4]*x[3]*x[2]*x[1]+x[7]*x[4]*x[3]+x[7]*x[6]*x[5]*x[4]*x[3]+x[7]*x[6]*x
[5]*x[4]*x[1]+x[3]+x[7]*x[6]*x[5]*x[2]*x[1]+x[5]*x[4]*x[3]+x[7]*x[6]*x
[3]*x[2]*x[1]+x[5]*x[4]*x[3]*x[2]*x[1]+x[7]*x[4]*x[3]*x[2]*x[1]+x[7];
\nf[8] := 1+x[2]*x[1]+x[8]*x[3]*x[2]*x[1]+x[8]*x[5]*x[4]*x[1]+x[8]*x[5
]*x[2]*x[1]+x[8]*x[7]*x[6]*x[5]+x[8]*x[7]*x[6]*x[3]+x[8]*x[7]*x[6]*x[1
]+x[8]*x[7]*x[4]*x[3]+x[8]*x[7]*x[2]*x[1]+x[8]*x[7]*x[4]*x[1]+x[8]*x[5
]*x[4]*x[3]+x[4]*x[1]+x[4]*x[3]+x[4]*x[3]*x[2]*x[1]+x[8]*x[3]+x[8]*x[7
]+x[8]*x[5]+x[8]*x[1]+x[8]*x[5]*x[4]*x[3]*x[2]*x[1]+x[8]*x[7]*x[6]*x[5
]*x[4]*x[3]*x[2]*x[1]+x[8]*x[7]*x[6]*x[5]*x[4]*x[3]+x[8]*x[7]*x[6]*x[5
]*x[4]*x[1]+x[8]*x[7]*x[6]*x[5]*x[2]*x[1]+x[8]*x[7]*x[6]*x[3]*x[2]*x[1
]+x[8]*x[7]*x[4]*x[3]*x[2]*x[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&
%\"fG6#\"\"\"&%\"xGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"
#,&*&&%\"xGF&\"\"\"&F+6#F,F,F,F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>&%\"fG6#\"\"$,(&%\"xGF&\"\"\"&F*6#F+F+*(F)F+&F*6#\"\"#F+F,F+F+" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"%,,*&&%\"xGF&\"\"\"&F+6#
\"\"$F,F,**F*\"\"\"F-F1&F+6#\"\"#F,&F+6#F,F,F,*&F2F1F5F1F,F,F,*&F*F1F5
F1F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"&,2*(&%\"xGF&\"\"
\"&F+6#\"\"%F,&F+6#\"\"$F,F,*(F*\"\"\"&F+6#\"\"#F,&F+6#F,F,F,F*F,*,F*F
4F-F4F0F4F5F4F8F4F,F8F,*(F0F4F5F4F8F4F,*(F*F4F-F4F8F4F,F0F," }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"',<**&%\"xGF&\"\"\"&F+6#\"\"&F,
&F+6#\"\"%F,&F+6#\"\"$F,F,*&F*\"\"\"&F+6#F,F,F,**F*F7F3F7&F+6#\"\"#F,F
8F7F,**F*F7F-F7F0F7F8F7F,*.F*F7F-F7F0F7F3F7F;F7F8F7F,*&F0F7F3F7F,**F0F
7F3F7F;F7F8F7F,*&F;F7F8F7F,*&F*F7F3F7F,*&F0F7F8F7F,**F*F7F-F7F;F7F8F7F
,*&F*F7F-F7F,F,F," }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"(,L&
%\"xG6#\"\"\"F,*(&F*F&F,&F*6#\"\"'F,F)F,F,&F*6#\"\"&F,*(F.\"\"\"&F*6#
\"\"#F,F)F6F,*(F.F6&F*6#\"\"%F,F)F6F,*(&F*6#\"\"$F,F7F6F)F6F,*(F2F,F;F
6F)F6F,*(F2F6F7F6F)F6F,*(F.F6F/F6F2F6F,*(F.F6F/F6F?F6F,*0F.F6F/F6F2F6F
;F6F?F6F7F6F)F6F,*(F.F6F;F6F?F6F,*,F.F6F/F6F2F6F;F6F?F6F,*,F.F6F/F6F2F
6F;F6F)F6F,F?F,*,F.F6F/F6F2F6F7F6F)F6F,*(F2F6F;F6F?F6F,*,F.F6F/F6F?F6F
7F6F)F6F,*,F2F6F;F6F?F6F7F6F)F6F,*,F.F6F;F6F?F6F7F6F)F6F,F.F," }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"),V\"\"\"F)*&&%\"xG6#\"\"
#F)&F,6#F)F)F)**&F,F&F)&F,6#\"\"$F)F+\"\"\"F/F6F)**F2F6&F,6#\"\"&F)&F,
6#\"\"%F)F/F6F)**F2F6F8F6F+F6F/F6F)**F2F6&F,6#\"\"(F)&F,6#\"\"'F)F8F6F
)**F2F6F@F6FCF6F3F6F)**F2F6F@F6FCF6F/F6F)**F2F6F@F6F;F6F3F6F)**F2F6F@F
6F+F6F/F6F)**F2F6F@F6F;F6F/F6F)**F2F6F8F6F;F6F3F6F)*&F;F6F/F6F)*&F;F6F
3F6F)**F;F6F3F6F+F6F/F6F)*&F2F6F3F6F)*&F2F6F@F6F)*&F2F6F8F6F)*&F2F6F/F
6F)*.F2F6F8F6F;F6F3F6F+F6F/F6F)*2F2F6F@F6FCF6F8F6F;F6F3F6F+F6F/F6F)*.F
2F6F@F6FCF6F8F6F;F6F3F6F)*.F2F6F@F6FCF6F8F6F;F6F/F6F)*.F2F6F@F6FCF6F8F
6F+F6F/F6F)*.F2F6F@F6FCF6F3F6F+F6F/F6F)*.F2F6F@F6F;F6F3F6F+F6F/F6F)" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}}{MARK 
"1 0 0" 52 }{VIEWOPTS 1 1 0 1 1 1803 }