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Sitzung" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 364 "Die folgende Aufgabe so ll geloest und zur Korrektur abgeliefert werden (ihre erfolgreiche Bea rbeitung zaehlt als Teilkriterium fuer die Vergabe des Praktikumsschei ns zu diesem Kurs). Ergaenze dazu dieses Worksheet mit den MAPLE-Befeh len, die die Loesung der Aufgabe liefern. Trage Namen und (falls vorha nden) die flcaXX-Nummer ein. Raeume auf: entferne mittels " }{TEXT 279 19 "Edit, Remove Output" }{TEXT -1 88 " eventuelle Ausgaben aus d em Worksheet. Speichere das Worksheet, etwa unter dem Namen " }{TEXT 264 11 "Loesung.mws" }{TEXT -1 53 " , dann schicke diese Datei per el ectronic mail an " }{TEXT 268 26 "flca00@rz.uni-frankfurt.de" }{TEXT -1 39 " . Auf UNIX-Ebene wird dies z.B. durch" }}{PARA 0 "" 0 "" {TEXT -1 6 " " }{TEXT 266 47 "elm flca00@rz.uni-frankfurt.de < \+ Loesung.mws" }}{PARA 0 "" 0 "" {TEXT -1 17 "erledigt (wobei " } {TEXT 283 3 "elm" }{TEXT -1 67 " einige Directories anzulegen versuch t, was man zulassen sollte). " }{TEXT 278 57 "Die Abgabe hat bis zum F reitag, den 23.5.97, zu erfolgen" }{TEXT -1 27 ". Nach diesem Datum w ird in" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 267 23 "/home/fb12 /kurse/flca00" }}{PARA 0 "" 0 "" {TEXT -1 15 "das Worksheet " }{TEXT 265 18 "Musterloesung7.mws" }{TEXT -1 130 " lesbar gemacht. Korrigier te Versionen der eingesandten Loesungen werden individuell per electro nic mail zurueckgeschickt werden." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 269 10 "Trage ein:" }{TEXT -1 1 " " }}{PARA 0 " " 0 "" {TEXT -1 24 "Name und Vorname: " }{TEXT 280 19 "Musterman n, Hermann" }}{PARA 0 "" 0 "" {TEXT -1 25 "flcaXX-Nummer : " }{TEXT 270 6 "flca??" }}{PARA 0 "" 0 "" {TEXT -1 33 "oder email \+ : " }{TEXT 275 26 "flca??@rz.uni-frankfurt.de" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 11 "Aufgabe 1. " }{TEXT -1 84 " In der Kombinatorik von Gr aphen wird bewiesen, dass mit den ganzzahligen Werten " }{XPPEDIT 18 0 "a[p]" "&%\"aG6#%\"pG" }{TEXT -1 47 " , welche die kombinatorische \+ Interpretation " }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "a[p] " "&%\"aG6#% \"pG" }{TEXT -1 43 " = ``Anzahl aller gewurzelten Baeume mit " } {XPPEDIT 18 0 "p" "I\"pG6\"" }{TEXT -1 9 " Knoten''" }}{PARA 0 "" 0 " " {TEXT -1 51 "haben, die folgende formale Potenzreihenidentitaet " }} {PARA 0 "" 0 "" {TEXT -1 3 " " }{XPPEDIT 18 0 "sum(a[p+1]*x^p , p=0. .infinity)*product( (1-x^p)^a[p],p=1..infinity) = 1" "/*&-%$sumG6$*&&% \"aG6#,&%\"pG\"\"\"\"\"\"F-F-)%\"xGF,F-/F,;\"\"!%)infinityGF--%(produc tG6$),&\"\"\"F-)F0F,!\"\"&F)6#F,/F,;\"\"\"F4F-\"\"\"" }{TEXT -1 2 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 22 "in einer Unbestimmten " }{XPPEDIT 18 0 "x" "I\"xG6\"" }{TEXT -1 15 " erfuellt ist. " }{TEXT 256 18 "Bestimm e hieraus " }{XPPEDIT 18 0 "a[1], `` .. ``, a[51]" "6%&%\"aG6#\"\"\"; %!GF(&F$6#\"#^" }{TEXT -1 2 " " }{TEXT 276 1 "!" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 259 9 "Anleitung" }{TEXT 260 2 ": " }{TEXT -1 6 " Sei " }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{XPPEDIT 18 0 "A[N](x) = sum(a[p+1 ]*x^p , p=0..N)*` `,` `*B[N] (x)= product( (1-x^p)^a[p],p=1..N)*` ,` " "6$/-&%\"AG6#%\"NG6#%\"xG*&-%$sumG6$*&&%\"aG6#,&%\"pG\"\"\"\"\"\"F5F 5)F*F4F5/F4;\"\"!F(F5%\"~GF5/*&F;F5-&%\"BG6#F(6#F*F5*&-%(productG6$),& \"\"\"F5)F*F4!\"\"&F16#F4/F4;\"\"\"F(F5%$~~,GF5" }{TEXT -1 2 " " }} {PARA 0 "" 0 "" {TEXT -1 4 "also" }}{PARA 0 "" 0 "" {TEXT -1 2 " " } {XPPEDIT 18 0 "A[infinity](x)=A[N](x)+O(x^(N+1))*` `,``" "6$/-&%\"AG6# %)infinityG6#%\"xG,&-&F&6#%\"NG6#F*\"\"\"*&-%\"OG6#)F*,&F/F1\"\"\"F1F1 %\"~GF1F1%!G" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{XPPEDIT 18 0 "B[infi nity](x)=B[N](x)*(1+x^(N+1))^(a[N+1])*(`...`)*` = `*B[N](x)+O(x^(N+1)) *` .`" "/-&%\"BG6#%)infinityG6#%\"xG,&*,-&F%6#%\"NG6#F)\"\"\"),&\"\"\" F1)F),&F/F1\"\"\"F1F1&%\"aG6#,&F/F1\"\"\"F1F1%$...GF1%$~=~GF1-&F%6#F/6 #F)F1F1*&-%\"OG6#)F),&F/F1\"\"\"F1F1%#~.GF1F1" }{MPLTEXT 1 0 0 "" }} {PARA 0 "" 0 "" {TEXT -1 6 "Mit " }{XPPEDIT 18 0 " A[infinity](x)*B[ infinity](x) = 1 " "/*&-&%\"AG6#%)infinityG6#%\"xG\"\"\"-&%\"BG6#F(6#F *F+\"\"\"" }{TEXT -1 10 " folgt " }}{PARA 0 "" 0 "" {TEXT -1 2 " \+ " }{XPPEDIT 18 0 "t[N](x):= A[N](x)*B[N](x)-1*` = `*A[infinity]*B[infi nity]+O(x^(N+1)) -1 *` = `*O(x^(N+1))" ">-&%\"tG6#%\"NG6#%\"xG,**&-&% \"AG6#F'6#F)\"\"\"-&%\"BG6#F'6#F)F1F1**\"\"\"F1%$~=~GF1&F.6#%)infinity GF1&F46#F(" }{TEXT -1 9 " , ... ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "Trage hier die no etigen MAPLE-Befehle (mit Erlaeuterungen!!!) ein !" }}}}{MARK "1 2 2" 2 }{VIEWOPTS 1 1 0 3 2 1804 }