{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 2 0 0 0 0 0 0 0 1 }{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 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" -1 257 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" -1 258 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" -1 259 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 " -1 260 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 "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 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" -1 263 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 -1 47 "Beispiel 20.19 (b) Ein Zer f\344llungsk\366rper f\374r " }{XPPEDIT 18 0 "f = x^6+1;" "6#/%\"fG, &*$%\"xG\"\"'\"\"\"F)F)" }{TEXT -1 40 " \374ber dem K\366rper der ra tionale Zahlen." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 37 "(Einf \374hrung in die Algebra SoSe 2004)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "restart: f := x^6 + 1 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*$)%\"xG\"\"'\"\"\"F*F*F*" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 21 " Sprachregelungen :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 101 " faktorisiere_:=factor:Nullstelle:=RootOf:Qu otient:=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,.%#a1G\"\"\"%\"xGF'*& F&F')F(\"\"#F'!\"\"*$)F(\"\"$F'F,*&F&F')F(\"\"%F'F'*$)F(\"\"&F'F'" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 11 " Probe :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " berechne_( f1 * ( x-a1 ) - f ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 114 "----------------------------------- -------------- SCHRITT 2 --------------------------------- ---------" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " faktorisiere_ ( f1 , a1 ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(,(*$)%\"xG\"\"#\" \"\"!\"\"*&%#a1GF*F(F*F*F*F*F*,(F&F*F,F*F*F+F*,&F(F*F-F*F*F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " g1 := x^2 + a1 * x \+ - 1 :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " sei_( a2 = Nullst elle( g1 ) ) :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 " f2:= bere chne_( Quotient( f1 , x - a2 , x ) ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2G,.\"\"\"F&*&%#a2GF&%#a1GF&!\"\"*&F)F&)%\"xG\"\"$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'%#a2GF'F',&F&F 'F)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 -1 163 "Hier kann man abbrech en, da ja alle Faktoren linear sind. Zusammen mit den bereits abgespa ltenen 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,$*.,(%\"xG\"\"\"%#a1GF)%#a2GF)F),&F(F) F+F)F),(F(!\"\"F*F)F+F)F),&F(F.F+F)F),&F(F.F*F)F),&F(F)F*F)F)F." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Zur Probe rechnen wir dieses Produ kt noch einmal aus:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " berechne_( expand(Zerf) );" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"'\"\"\"F(F(F(" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 123 "------------------------------------------------- ---------------------------------------------------------------------- ----" }}{PARA 0 "" 0 "" {TEXT -1 70 "Zum Vergleich die Berechnung ei ner Zerf\344llung von f durch MAPLE :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " faktorisiere_( f , \{a1,a2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*.,(%\"xG\"\"\"%#a1GF '%#a2GF'F',&F&F'F)F'F',(F&!\"\"F(F'F)F'F',&F&F,F)F'F',&F&F,F(F'F',&F&F 'F(F'F'F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "Sinnvollerweise wurd en unsere Abk\374rzungen benutzt. Ohne diese erh\344lt man:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " \+ sei_(a1=a1,a2=a2): evala(AFactor( f ));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#*.,(%\"xG\"\"\"-%'RootOfG6#,(*$)%#_ZG\"\"#F&!\"\"*$)F- \"\"%F&F&F&F&F&*$)F'\"\"$F&F/F&,&F%F&F'F/F&,&F%F&F'F&F&,(F%F&F'F/F3F&F &,&F%F&F3F/F&,&F%F&F3F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 17 }{VIEWOPTS 1 0 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }