{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "MS Sans Serif" 1 8 0 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "Tahoma" 1 8 0 0 0 1 2 2 2 0 0 2 0 0 0 1 } {CSTYLE "Roter Text" -1 256 "Tahoma" 0 0 255 0 0 1 2 1 1 0 0 2 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Norm al" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 9 0 0 0 1 2 1 2 2 2 2 1 1 1 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 \+ Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 9 128 0 128 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 8 0 128 128 1 1 2 2 0 0 0 0 0 0 1 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Seitenumbruch" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 0 2 1 2 0 0 2 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 1 0 -1 0 }{PSTYLE "Normal" -1 259 1 {CSTYLE "" -1 -1 "Ti mes" 1 10 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 1" -1 260 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 261 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 0" -1 262 1 {CSTYLE "" -1 -1 "Helvetica" 1 9 128 0 128 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 263 1 {CSTYLE "" -1 -1 "Courier" 1 8 0 128 128 1 1 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Seitenumbruch" -1 264 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 1 2 0 1 }{PSTYLE "Normal" -1 265 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 266 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 0" -1 267 1 {CSTYLE "" -1 -1 "Helvetica" 1 8 128 0 128 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 268 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 257 18 "Beispiel 15.3 (b)" } {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 28 "Ein Zerf\344llungsk\366r per f\374r " }{XPPEDIT 18 0 "f = x^6+1;" "6#/%\"fG,&*$%\"xG\"\"'\"\" \"F)F)" }{TEXT -1 40 " \374ber dem K\366rper der rationale Zahlen." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "restart: f := x^6 + 1 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"fG,&*$)%\"xG\"\"'\"\"\"F*F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 " Sprachregelungen :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 101 " \+ faktorisiere_:=factor:Nullstelle:=RootOf:Quotient:=quo:berechne _:=evala:sei_:=alias: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 114 "------------------------------------ ------------- SCHRITT 1 ---------------------------------- --------" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " faktorisiere_( f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&\"\"\"F%*$)%\"xG\"\"#F%F%F% ,(*$)F(\"\"%F%F%F&!\"\"F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " g := x^2 + 1 :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " \+ sei_( a1=Nullstelle( g )) :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 " f1:=berechne_( Quotient( f , x - a1 , x ) ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1G,.*$)%\"xG\"\"&\"\"\"F**&%#a1GF*)F(\" \"%F*F**$)F(\"\"$F*!\"\"*&F,F*)F(\"\"#F*F2F(F*F,F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 " Probe :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " berechne_( f1 * ( x-a1 ) - f ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 114 "---------------------------------------------- --- SCHRITT 2 ------------------------------------------" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " faktorisiere_( f1 , a1 ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(,(*$)%\"xG\"\"#\"\"\"F**&%#a 1GF*F(F*F*F*!\"\"F*,(F&F-F+F*F*F*F*,&F(F*F,F*F*F-" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 33 " g1 := x^2 + a1 * x - 1 :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " sei_( a2 = Nullstelle( g1 ) ) : " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 " f2:= berechne_( Quotien t( f1 , x - a2 , x ) ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2G,.\" \"\"F&*&%#a2GF&%#a1GF&!\"\"*&F)F&)%\"xG\"\"$F&F&*&F,F&F(F&F&*$)F-\"\"% F&F&*&F)F&F-F&F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 " Probe :" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " berechne_( f2 * ( x - a2 ) - f1 ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 118 "---------------- ------------------------------------ SCHRITT 3 ---------- --------------------------------" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " faktorisiere_( f2 , [ a1 , a2 ] ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**,&%\"xG\"\"\"%#a1GF'F',(F&!\"\"F(F'%#a2GF'F',(F&F'F (F'F+F'F',&F&F'F+F'F'F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 " " }} {PARA 0 "" 0 "" {TEXT -1 59 "Hier kann man abbrechen, da ja alle Fakto ren linear sind. " }}{PARA 0 "" 0 "" {TEXT -1 104 "Zusammen mit den b ereits abgespaltenen Linearfaktoren ergibt sich nun folgende \"Zerf \344llung von f \" :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 49 " Zerf:= faktorisiere_( f , [ a1 , a2 ] \+ ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ZerfG*.,&%\"xG\"\"\"%#a1GF(F (,&F'!\"\"F)F(F(,&F'F(%#a2GF+F(,(F'F(F)F(F-F(F(,(F'F+F)F(F-F(F(,&F'F(F -F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Zur Probe rechnen wir di eses Produkt noch einmal aus:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " berechne_( expand(Zerf) ); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"'\"\"\"F(F(F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 123 "--------------------------------- ---------------------------------------------------------------------- --------------------" }}{PARA 0 "" 0 "" {TEXT -1 70 "Zum Vergleich d ie Berechnung einer Zerf\344llung von f durch MAPLE :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " faktorisiere_( f ,\{a1,a2\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*.,&%\"xG\"\"\"%#a1GF&F&,&F%!\"\"F'F&F &,&F%F&%#a2GF)F&,(F%F&F'F&F+F&F&,(F%F)F'F&F+F&F&,&F%F&F+F&F&" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "Sinnvollerweise wurden unsere Abk \374rzungen benutzt. Ohne diese erh\344lt man:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 27 "restart: f := x^6 + 1 :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " evala(AFactor( f ));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*.,&%\"xG\"\"\"-%'RootOfG6#,&F&F&*$)%#_ZG\" \"#F&F&!\"\"F&,&F%F&F'F&F&,&F%F&-F(6#,(F+F&*&F'F&F-F&F/F&F/F/F&,(F%F&F 'F/F2F&F&,(F%F&F'F&F2F/F&,&F%F&F2F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 1 0" 0 }{VIEWOPTS 1 0 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }