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Bj\366rnstjern e Zindler, M.Sc." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT 257 58 "Erstellt: 07. Januar 2013 - Letzte Revision: 30. Juni 20 14" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 808 "Mit Hilfe von Maple sollen alle Zahlen ermittelt werden, welche durch die Summe von drei Quadraten dargestellt werden \+ k\366nnen bis zu einem gew\344hlten Maximalwert. Da die Reihenfolge de r Quadrate nicht eindeutig ist, k\366nnen f\374r eine betrachtete Zahl mehrere L\366sungen m\366glich sein z. B. f\374r 6 = [1,1,2] , [1,2,1 ] , [2,1,1] oder 14 = [1,2,3] , [1,3,2] , [2,1,3] , [2,3,1] , [3,1,2] , [3,2,1] oder 101 = [9,4,2] , [9,2,4] , [4,9,2] , [4,2,9] , [2,9,4] \+ , [2,4,9] , [8,6,1] , [8,1,6] , [6,8,1] , [6,1,8] , [1,8,6] , [1,6,8] \+ , [7,6,4] , [7,4,6] , [6,7,4] , [6,4,7] , [4,7,6] , [4,6,7]. Die L\366 sungen sind jedoch nicht nach n sortiert, sondern aufsteigend nach den Basen der Quadrate. Gegebenenfalls ist bei Bedarf ein Sortierverfahre n zu implementieren, ist jedoch nicht Inhalt der hier vorliegenden Auf gabenstellung." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 4 "EA 4" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "allsum3sqr:=proc(nmax) # Ausgabe all er L\366sungen von sum3sqr(n) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 " # Definit ion der Locals " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 " \+ local a,b,c,d,n,z: # Hilfsvariable d,z Laufvariable a,b,c" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 " \+ # L\366sung von sum3sqr(n) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "######################################## Eingabekontrollen und ggf . Korrektur " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " \+ #" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "if nm ax<3 then print(Fehler) else # Kleine Minimalkontrolle der Eingab e" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " \+ #" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "if sqrt(nmax)=floor(s qrt(nmax)) then # Aussieben von Quadratzahlen" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " n:=nmax-1 else # " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " n:=nmax #" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "fi: \+ #" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " \+ #" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "################ ######################## Berechnung der maximal m\366glichen Base" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " \+ #" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "d:=floor(sqrt(n)): \+ # Maximal m\366glicher Wert einer Base" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " #" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "######################################## \+ Beginn Berechnung sum3sqr(n)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " \+ #" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "for a from 1 to d+1 do # Beginn Schleife der Bas e a" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "for b from 1 to d+1 do \+ # Beginn Schleife der Base b" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "for c from 1 to d+1 do # Beginn Schleife der B ase c" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " \+ #" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "################# ####################### Beginn Ausgabe der berechneten Werte" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " # " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 " z:=a^2+b ^2+c^2: # Rekonstruktion der Quadratsummenzahl" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 " # Aussieben de r Zahlen gr\366\337er nmax" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "if z< nmax+1 then print(z,a,b,c); fi: # Format: n = a , b , c " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " # " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "############################### ######### Ende Ausgabe der berechneten Werte" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " #" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 65 "od: # End e Schleife der Base c" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "od: \+ # Ende Schleife der Base b" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 65 "od: # Ende \+ Schleife der Base a" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " \+ #" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "### ##################################### Ende Berechnung sum3sqr(n)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " \+ #" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "fi: \+ # Ende der ersten Sprunganweisung" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " #" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 56 "######################################## End e Berechnung" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " \+ #" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "end: \+ # Ende der Prozedur allsum3sqr" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 14 "allsum3sqr(6);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "allsum 3sqr(9);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "allsum3sqr(100);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}}{MARK "9" 0 }{VIEWOPTS 1 1 0 1 1 1803 }