{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 34 "with(Ore_algebra): with(Groebner): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A:=poly_algebra(x,y,z); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG%,Ore_algebraG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "M:=[[1,1,1],[1,0,0],[0,1,0]];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG7%7%\"\"\"F'F'7%F'\"\"!F)7%F)F'F )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "grlex:=termorder(A,'ma trix'(M,[x,y,z]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&grlexG%+term_ orderG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f := x - z^4;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&%\"xG\"\"\"*$)%\"zG\"\"%F'!\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "g := y - z^5;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,&%\"yG\"\"\"*$)%\"zG\"\"&F'!\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "L := [f,g];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7$,&%\"xG\"\"\"*$)%\"zG\"\"%F(!\"\",&% \"yGF(*$)F+\"\"&F(F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "s : = spoly(f,g,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term _orderG6#%'S-polyG6&7',&%\"xG\"\"\"*$)%\"zG\"\"%F/!\"\"F/F4F0\"\"!7',& %\"yGF/*$)F2\"\"&F/F4F/F4F9F5F9F(6#F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"zG\"\"\"% \"xGF&!\"\"%\"yGF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r := \+ reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG,&*&%\"zG \"\"\"%\"xGF(!\"\"%\"yGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "L := [op(L),r];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7%,&%\"xG \"\"\"*$)%\"zG\"\"%F(!\"\",&%\"yGF(*$)F+\"\"&F(F-,&*&F+F(F'F(F-F/F(" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[1],L[3],grlex );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-poly G6&7',&%\"xG\"\"\"*$)%\"zG\"\"%F/!\"\"F/F4F0\"\"!7',&*&F2F/F.F/F4%\"yG F/\"\"#F4F8F5*&F.F/F1F/F(6#F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"#\"\"\"!\"\"* &)%\"zG\"\"$F(%\"yGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " r := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG,&*$) %\"xG\"\"#\"\"\"!\"\"*&)%\"zG\"\"$F*%\"yGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "L := [op(L),r];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7&,&%\"xG\"\"\"*$)%\"zG\"\"%F(!\"\",&%\"yGF(*$)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 28 "s := spoly(L[2],L[3],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-polyG6&7',&%\"yG\"\"\" *$)%\"zG\"\"&F/!\"\"F/F4F0\"\"!7',&*&F2F/%\"xGF/F4F.F/\"\"#F4F8F5*&F9F /F1F/F(6#F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"xG\"\"\"%\"yGF&!\"\"*&)%\"zG\"\"%F&F' F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grl ex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[1],L[4],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-polyG6&7',&%\"xG\" \"\"*$)%\"zG\"\"%F/!\"\"F/F4F0\"\"!7',&*$)F.\"\"#F/F4*&)F2\"\"$F/%\"yG F/F/F:F/F;F5*&F1F/F>F/F(6#F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"xG\"\"\"%\"yGF&F&*&% \"zGF&)F%\"\"#F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r \+ := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[2],L[4],grle x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-pol yG6&7',&%\"yG\"\"\"*$)%\"zG\"\"&F/!\"\"F/F4F0\"\"!7',&*$)%\"xG\"\"#F/F 4*&)F2\"\"$F/F.F/F/F;F/F " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"yG\" \"#\"\"\"F(*&)%\"zGF'F()%\"xGF'F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s := s poly(L[3],L[4],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+t erm_orderG6#%'S-polyG6&7',&*&%\"zG\"\"\"%\"xGF0!\"\"%\"yGF0\"\"#F2F.\" \"!7',&*$)F1F4F0F2*&)F/\"\"$F0F3F0F0F4F0F:F5*(F;F0F3F0F1F0F(6#F0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&)%\"zG\"\"#\"\"\")%\"yGF'F(F(*$)%\"xG\"\"$F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG,&*&)%\"zG\"\"#\"\"\")%\"yGF)F *F**$)%\"xG\"\"$F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " L := [op(L),r];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7',&%\"xG\"\" \"*$)%\"zG\"\"%F(!\"\",&%\"yGF(*$)F+\"\"&F(F-,&*&F+F(F'F(F-F/F(,&*$)F' \"\"#F(F-*&)F+\"\"$F(F/F(F(,&*&)F+F8F()F/F8F(F(*$)F'F;F(F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[1],L[5],grlex);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-polyG6&7', &%\"xG\"\"\"*$)%\"zG\"\"%F/!\"\"F/F4F0\"\"!7',&*&)F2\"\"#F/)%\"yGF:F/F /*$)F.\"\"$F/F4F?F/F8F5*&F;F/F1F/F(6#F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&)%\"yG\"\"# \"\"\"%\"xGF(F(*&)%\"zGF'F()F)\"\"$F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 23 "r := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[2],L[5],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"sG&-&%+term_orderG6#%'S-polyG6&7',&%\"yG\"\"\"*$)%\"zG\"\"&F/!\"\"F/ F4F0\"\"!7',&*&)F2\"\"#F/)F.F:F/F/*$)%\"xG\"\"$F/F4F?F/F8F5*&F;F/F1F/F (6#F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"yG\"\"$\"\"\"F(*&)%\"zGF'F()%\"xGF'F(!\"\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"!" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[3],L[5],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-polyG6&7',&*&%\"zG\"\"\" %\"xGF0!\"\"%\"yGF0\"\"#F2F.\"\"!7',&*&)F/F4F0)F3F4F0F0*$)F1\"\"$F0F2F =F0F8F5*(F9F0F:F0F1F0F(6#F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"zG\"\"\")%\"yG\"\"$F&F &*$)%\"xG\"\"%F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r \+ := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG,&*&%\" zG\"\"\")%\"yG\"\"$F(F(*$)%\"xG\"\"%F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "L := [op(L),r];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"LG7(,&%\"xG\"\"\"*$)%\"zG\"\"%F(!\"\",&%\"yGF(*$)F+\"\"&F(F-,&*&F +F(F'F(F-F/F(,&*$)F'\"\"#F(F-*&)F+\"\"$F(F/F(F(,&*&)F+F8F()F/F8F(F(*$) F'F;F(F-,&*&F+F()F/F;F(F(*$)F'F,F(F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[4],L[5],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-polyG6&7',&*$)%\"xG\"\"#\" \"\"!\"\"*&)%\"zG\"\"$F2%\"yGF2F2F1F2F4\"\"!7',&*&)F6F1F2)F8F1F2F2*$)F 0F7F2F3F7F2FF2F5F2F(6#F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"yG\"\"\")%\"xG\"\" #F&!\"\"*&%\"zGF&)F(\"\"$F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"r G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[1],L [6],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6 #%'S-polyG6&7',&%\"xG\"\"\"*$)%\"zG\"\"%F/!\"\"F/F4F0\"\"!7',&*&F2F/)% \"yG\"\"$F/F/*$)F.F3F/F4F3F4F " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[2],L[6],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"sG&-&%+term_orderG6#%'S-polyG6&7',&%\"yG\"\"\"*$)%\"zG\"\"&F/!\"\"F/ F4F0\"\"!7',&*&F2F/)F.\"\"$F/F/*$)%\"xG\"\"%F/F4F>F4F;F5*&F " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"!" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[3],L[6],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-polyG6&7',&*&%\"zG\"\" \"%\"xGF0!\"\"%\"yGF0\"\"#F2F.\"\"!7',&*&F/F0)F3\"\"$F0F0*$)F1\"\"%F0F 2F=F2F;F5*&F " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[4],L[ 6],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6# %'S-polyG6&7',&*$)%\"xG\"\"#\"\"\"!\"\"*&)%\"zG\"\"$F2%\"yGF2F2F1F2F4 \"\"!7',&*&F6F2)F8F7F2F2*$)F0\"\"%F2F3F@F3F>F9*(F?F2F5F2F8F2F(6#F2" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s := spoly(L[5],L[6],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-polyG6&7',&*&)%\"zG\"\"#\" \"\")%\"yGF1F2F2*$)%\"xG\"\"$F2!\"\"F8F2F.\"\"!7',&*&F0F2)F4F8F2F2*$)F 7\"\"%F2F9FAF9F?F:*(F@F2F/F2F3F2F(6#F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "L;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7(,&%\"xG\"\"\"*$)%\"zG\"\"%F&!\"\",&% \"yGF&*$)F)\"\"&F&F+,&*&F)F&F%F&F+F-F&,&*$)F%\"\"#F&F+*&)F)\"\"$F&F-F& F&,&*&)F)F6F&)F-F6F&F&*$)F%F9F&F+,&*&F)F&)F-F9F&F&*$)F%F*F&F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "gbasis([f,g],grlex);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7',&*&%\"zG\"\"\"%\"xGF'F'%\"yG!\"\",& F(F**$)F&\"\"%F'F',&*$)F(\"\"#F'F**&)F&\"\"$F'F)F'F',&*&)F&F2F')F)F2F' F'*$)F(F5F'F*,&*&F&F')F)F5F'F**$)F(F.F'F'" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "54 0 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