{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 14 "f := x^2*y-1 ;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*&)%\"xG\"\"#\"\"\"%\"yGF*F*F *!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "g := x*y^2 -1 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,&*&%\"xG\"\"\")%\"yG\"\"#F(F( F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "L := [f,g];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7$,&*&)%\"xG\"\"#\"\"\"%\"yGF+F+ F+!\"\",&*&F)F+)F,F*F+F+F+F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "s := spoly(f,g,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG &-&%+term_orderG6#%'S-polyG6&7',&*&)%\"xG\"\"#\"\"\"%\"yGF2F2F2!\"\"\" \"$F2F.\"\"!7',&*&F0F2)F3F1F2F2F2F4F5F2F9F6*&F:F2F/F2F(6#F2" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"yG!\"\"%\"xG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG,&%\"yG!\"\"%\"xG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "L := [op(L),r];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"LG7%,&*&)%\"xG\"\"#\"\"\"%\"yGF+F+F+!\"\",&*&F)F+)F,F*F+F+F+F-,&F,F- F)F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "s := spoly(f,L[3],g rlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S- polyG6&7',&*&)%\"xG\"\"#\"\"\"%\"yGF2F2F2!\"\"\"\"$F2F.\"\"!7',&F3F4F0 F2F2F2F0F6F.F(6#F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"xG\"\"\")%\"yG\"\"#F&F&F&!\"\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"!" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 "s := spoly(g,L[3],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-polyG6&7',&*&%\"xG\"\"\")% \"yG\"\"#F0F0F0!\"\"\"\"$F0F.\"\"!7',&F2F4F/F0F0F0F/F6F.F(6#F0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&!\"\"\"\"\"*$)%\"yG\"\"$F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG,&!\"\"\"\"\"*$)%\"yG\"\"$F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "L := [op(L),r];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7&,&*&)%\"xG\"\"#\"\"\"%\"yGF+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 25 "s := spoly(f,L[4],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-polyG6&7',&*&)%\"xG\"\"#\" \"\"%\"yGF2F2F2!\"\"\"\"$F2F.\"\"!7',&F4F2*$)F3F5F2F2F5F2F9F6*&F:F2F/F 2F(6#F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,&*$)%\"yG\"\"#\"\"\"!\"\"*$)%\"xGF'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 25 "s := spoly(g,L[4],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG&-&%+term_orderG6#%'S-polyG6&7',&*&%\"xG\"\"\")% \"yG\"\"#F0F0F0!\"\"\"\"$F0F.\"\"!7',&F4F0*$)F2F5F0F0F5F0F9F6*&F:F0F/F 0F(6#F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,&%\"yG!\"\"%\"xG\"\"\"" }}}{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[4],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"sG&-&%+term_orderG6#%'S-polyG6&7',&%\"yG!\"\"%\"xG\"\"\"F1F1F0\"\"!7 ',&F/F1*$)F.\"\"$F1F1F7F1F5F2*&F6F1F0F1F(6#F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"yG \"\"%\"\"\"!\"\"%\"xGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " r := reduce(s,L,grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "L;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&,&*&)%\"xG\"\"#\"\"\"%\"yGF)F)F)!\"\",&*&F'F))F*F(F)F )F)F+,&F*F+F'F),&F+F)*$)F*\"\"$F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "gbasis([f,g],grlex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$,&%\"yG!\"\"%\"xG\"\"\",&F&F(*$)F%\"\"$F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "30 0 0" 0 }{VIEWOPTS 1 0 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }