{VERSION 5 0 "IBM INTEL LINUX" "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 "Maple 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(Groebner):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f[1] := x^2 + y^2 + z^2 - 4;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"\",**$)%\"xG\"\"#F'F'*$)%\"yGF,F'F' *$)%\"zGF,F'F'\"\"%!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f[2] := x^2 + 2*y^2 - 5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6# \"\"#,(*$)%\"xGF'\"\"\"F,*&F'F,)%\"yGF'F,F,\"\"&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f[3] := x*z - 1;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>&%\"fG6#\"\"$,&*&%\"xG\"\"\"%\"zGF+F+F+!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "F := convert(f,list);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG7%,**$)%\"xG\"\"#\"\"\"F+*$)%\"y GF*F+F+*$)%\"zGF*F+F+\"\"%!\"\",(F'F+*&F*F+F-F+F+\"\"&F3,&*&F)F+F1F+F+ F+F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "G := gbasis(F,plex( x,y,z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"GG7%,(\"\"\"F'*&\"\"#F ')%\"zG\"\"%F'F'*&\"\"$F')F+F)F'!\"\",(*$)%\"yGF)F'F'*$F/F'F0F'F0,(%\" xGF'*&F)F')F+F.F'F'*&F.F'F+F'F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "S := [solve(G[1],z)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"S G7&!\"\"\"\"\",$*$-%%sqrtG6#\"\"#F'#F'F-,$F)#F&F-" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 10 "z := S[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"zG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(G[3] ,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(G[2],y);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6$*$-%%sqrtG6#\"\"#\"\"\",$F#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "z := S[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG \"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(G[3],x);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(G[2],y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$- %%sqrtG6#\"\"#\"\"\",$F#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "z := S[3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,$*$-%%sqrtG 6#\"\"#\"\"\"#F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve (G[3],x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(G[2],y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*$-%%sqrtG6#\"\"'\"\"\"#F)\"\"#,$F$#!\"\"F +" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "z := S[4];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,$*$-%%sqrtG6#\"\"#\"\"\"#!\"\"F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(G[3],x);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,$*$-%%sqrtG6#\"\"#\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(G[2],y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*$-%%sqrtG6#\"\"'\"\"\"#F)\"\"#,$F$#!\"\"F+" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "Man sieht also: Keine der 8 Loesun gen ist rational, die Varietaet ist leer !" }}}}{MARK "20 0 0" 76 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }