{VERSION 5 0 "HP RISC UNIX" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "M aple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "helvetica" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 262 "" 0 "" {TEXT -1 29 "L\366sung von Aufgabe 2, Blatt 6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 176 "restart:\nordn e := gl -> collect(map(simplify, gl), [w, x, y, z]):\nLK := proc(gl1, \+ gl2, c)\nprintf(\"Addiere %a mal %a zu %a\\n\", c, gl1, gl2);\nordne(e val(gl1) + c*eval(gl2));\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "gl1 := x + y - z = 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$gl 1G/,(%\"xG\"\"\"%\"yGF(%\"zG!\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "gl2 := 3*w + a*x - y + z = 2*a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$gl2G/,**&\"\"$\"\"\"%\"wGF)F)*&%\"aGF)%\"xGF)F)%\"yG !\"\"%\"zGF),$*&\"\"#F)F,F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "gl3 := w - y + z = 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$gl3G /,(%\"wG\"\"\"%\"yG!\"\"%\"zGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "gl4 := a*w - x -a*y + 3*z = 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$gl4G/,**&%\"aG\"\"\"%\"wGF)F)%\"xG!\"\"*&F(F)%\"yGF) F,*&\"\"$F)%\"zGF)F)F)" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 251 "Da w in der ersten Gleichung nicht vorkommt, sortieren wir um; die dritte \+ Gleichung kommt dabei an die zweite Stelle, da eine Gleichung ohne w m it einem isolierten x als erster Variablen die x-Elimination aus den w eiteren Gleichungen sehr erleichtert." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "g1 := gl3; g2 := gl1; g3 := gl2; g4 := gl4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g1G/,(%\"wG\"\"\"%\"yG! \"\"%\"zGF(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g2G/,(%\"xG\"\"\"% \"yGF(%\"zG!\"\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g3G/,**&\"\"$ \"\"\"%\"wGF)F)*&%\"aGF)%\"xGF)F)%\"yG!\"\"%\"zGF),$*&\"\"#F)F,F)F)" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g4G/,**&%\"aG\"\"\"%\"wGF)F)%\"xG! \"\"*&F(F)%\"yGF)F,*&\"\"$F)%\"zGF)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "h3 := LK('g3', 'g1', - 3);" }}{PARA 6 "" 1 "" {TEXT -1 23 "Addiere -3 mal g3 zu g1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h 3G/,(*&%\"aG\"\"\"%\"xGF)F)*&\"\"#F)%\"yGF)F)*&F,F)%\"zGF)!\"\",&*&F,F )F(F)F)\"\"$F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "h4 := LK( 'g4', 'g1', -a);" }}{PARA 6 "" 1 "" {TEXT -1 23 "Addiere -a mal g4 zu \+ g1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h4G/,&%\"xG!\"\"*&,&\"\"$\"\" \"%\"aGF(F,%\"zGF,F,,&F,F,F-F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "g1 := g1; g2 := g2; h3 := h3; h4 := h4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g1G/,(%\"wG\"\"\"%\"yG!\"\"%\"zGF(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g2G/,(%\"xG\"\"\"%\"yGF(%\"zG!\"\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h3G/,(*&%\"aG\"\"\"%\"xGF)F)*&\"\"#F)%\"y GF)F)*&F,F)%\"zGF)!\"\",&*&F,F)F(F)F)\"\"$F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h4G/,&%\"xG!\"\"*&,&\"\"$\"\"\"%\"aGF(F,%\"zGF,F,,&F ,F,F-F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "k3 := LK('h3', ' g2', -a);" }}{PARA 6 "" 1 "" {TEXT -1 23 "Addiere -a mal h3 zu g2" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k3G/,&*&,&\"\"#\"\"\"%\"aG!\"\"F*% \"yGF*F**&,&F)F,F+F*F*%\"zGF*F*,&F+F*\"\"$F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "k4 := LK('h4', 'g2', 1);" }}{PARA 6 "" 1 "" {TEXT -1 22 "Addiere 1 mal h4 zu g2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#k4G/,&%\"yG\"\"\"*&,&\"\"#F(%\"aG!\"\"F(%\"zGF(F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "g1 := g1; g2 := g2; k3:= k3; k4 := \+ k4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g1G/,(%\"wG\"\"\"%\"yG!\"\"% \"zGF(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g2G/,(%\"xG\"\"\"%\"yGF (%\"zG!\"\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k3G/,&*&,&\"\"#\" \"\"%\"aG!\"\"F*%\"yGF*F**&,&F)F,F+F*F*%\"zGF*F*,&F+F*\"\"$F," }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k4G/,&%\"yG\"\"\"*&,&\"\"#F(%\"aG! \"\"F(%\"zGF(F(F*" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 85 "Da die let zte Gleichung angenehmer ist als die vorletzte, vertauschen wir die be iden:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "g1 := g1; g2 := g2; k4 := k4; k3:= k3; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g1G/,(%\"wG\"\"\"%\"yG!\"\"%\"zGF(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g2G/,(%\"xG\"\"\"%\"yGF(%\"zG!\"\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k4G/,&%\"yG\"\"\"*&,&\"\"#F(%\"aG!\"\"F(%\"zGF( F(F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k3G/,&*&,&\"\"#\"\"\"%\"aG! \"\"F*%\"yGF*F**&,&F)F,F+F*F*%\"zGF*F*,&F+F*\"\"$F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "l3 := LK('k3', 'k4', a-2);" }}{PARA 6 "" 1 "" {TEXT -1 25 "Addiere -2+a mal k3 zu k4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l3G/*&,(\"\"'!\"\"*&\"\"&\"\"\"%\"aGF,F,*$)F-\"\"#F, F)F,%\"zGF,,(*&F+F,F-F,F,\"\"(F)F.F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "z_Koeff := coeff(lhs(l3), z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(z_KoeffG,(\"\"'!\"\"*&\"\"&\"\"\"%\"aGF*F**$)F+\"\"# F*F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Nullstellen := solv e(z_Koeff);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,NullstellenG6$\"\"# \"\"$" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 98 "Einsetzen dieser Nulls tellen in die rechte Seite (wenn man nicht gleich so sieht, was heraus kommt)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "subs(a = 2, rhs(l3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "subs(a = 3, rhs(l3));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 101 "F\374r a=2 und a=3 ist das Gleichungssystem somit unl \366sbar. F\374r alle sonstigen a k\366nnen wir z berechnen:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "z := sort(-rhs(l3))/sort(-z_ Koeff);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG*&,(*$)%\"aG\"\"#\"\" \"F+*&\"\"&F+F)F+!\"\"\"\"(F+F+,(F'F+*&F-F+F)F+F.\"\"'F+F." }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 34 "Das l\344\337t sich besser schreiben al s" }{MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "z := 1 + 1/((a-2)*(a-3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,&\"\"\"F&*&F&F&*&,&\"\"#!\"\"%\"aGF&F&,&F,F&\"\" $F+F&F+F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "k3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&,&\"\"#\"\"\"%\"aG!\"\"F(%\"yGF(F(*&,&F 'F*F)F(F(,&F(F(*&F(F(*&F-F(,&F)F(\"\"$F*F(F*F(F(F(F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "konst_term_links := simplify(subs(y=0, lh s(k3)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%1konst_term_linksG*&,(*$ )%\"aG\"\"#\"\"\"F+*&\"\"&F+F)F+!\"\"\"\"(F+F+,&F)F+\"\"$F.F." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "sort(simplify(k3 + (-konst_t erm_links = -konst_term_links)), a);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/,$*&,&%\"aG\"\"\"\"\"#!\"\"F(%\"yGF(F*,$*&F&F(,&F'F(\"\"$F*F*F*" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "simplify(%/(2-a));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG*&\"\"\"F&,&%\"aGF&\"\"$!\"\"F* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "y := 1/(a-3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG*&\"\"\"F&,&%\"aGF&\"\"$!\"\"F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "g2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,*%\"xG\"\"\"*&F&F&,&%\"aGF&\"\"$!\"\"F+F&F&F+*&F&F&*& ,&F)F&\"\"#F+F&F(F&F+F+F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "x := solve(g2, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG*&,&*& \"\"#\"\"\"%\"aGF)F)\"\"&!\"\"F),&F*F)F(F,F," }}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 8 "Sch\366ner:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "x : = 2 + sort(simplify(x-2), a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"x G,&\"\"#\"\"\"*&F'F',&%\"aGF'F&!\"\"F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "g1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,*%\"wG\"\"\"* &F&F&,&%\"aGF&\"\"$!\"\"F+F+F&F&*&F&F&*&,&F)F&\"\"#F+F&F(F&F+F&F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "w := solve(g1, w);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG*&\"\"\"F&,&%\"aGF&\"\"#!\"\"F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "L\366sungsmenge := \{[w, x, \+ y, z]\}; # nur fuer a<>2 und a<> 3; fuer a=2 und a=3 ist sie leer" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%-L|azsungsmengeG<#7&*&\"\"\"F(,&%\"a GF(\"\"#!\"\"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 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 9 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }