{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 -1 ;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"\",**$)%\"xG\"\"#F'F'*$)%\"yGF,F'F'
*$)%\"zGF,F'F'F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f[
2] := x^2 + z^2 - y ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#\"\"
#,(*$)%\"xGF'\"\"\"F,*$)%\"zGF'F,F,%\"yG!\"\"" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 12 "f[3] := x-z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>&%\"fG6#\"\"$,&%\"xG\"\"\"%\"zG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "G := gbasis([f[1],f[2],f[3]],plex(x,y,z));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"GG7%,(*$)%\"zG\"\"#\"\"\"F*F+!\"\"*&\"\"
%F+)F)F.F+F+,&%\"yGF+*&F*F+F(F+F,,&%\"xGF+F)F," }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 5 "G[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%
\"zG\"\"#\"\"\"F'F(!\"\"*&\"\"%F()F&F+F(F(" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "S := [solve(G[1],z)];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"SG7&,$*$-%%sqrtG6#,&!\"\"\"\"\"*$-F)6#\"\"&F-F-F-#F,\"\"#,$F
'#F-F3,$*$-F)6#,&F,F-F.F,F-F2,$F7F5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "z := S[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,
$*$-%%sqrtG6#,&!\"\"\"\"\"*$-F(6#\"\"&F,F,F,#F+\"\"#" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "x := z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%\"xG,$*$-%%sqrtG6#,&!\"\"\"\"\"*$-F(6#\"\"&F,F,F,#F+\"\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "y := 2*z^2;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"yG,&#!\"\"\"\"#\"\"\"*&#F)F(F)-%%sqrtG6#\"\"&F
)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f[2];" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 1 0" 0 }{VIEWOPTS 1 
1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }