{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 0 597 "DivAlg := proc(f,F: :list,LT::procedure) \nlocal p,r,s,a,divoccurred,i,g,q; \n (p,r) := ( f,0); \n s := nops(F); \n a := Array(1..s); # Arrays are automatical ly initialized to 0\n while p <> 0 do \n divoccurred := false; \n for i from 1 to s while not divoccurred do \n if divide(LT (p),LT(F[i])) then # if LT(F[i]) | LT(p) then \n q := LT(p)/ LT(F[i]);\n p := expand( p - q*F[i] ); \n a[i] := \+ a[i]+q; \n divoccurred := true;\n fi;\n end do;\n if not divoccurred then\n r := r+LT(p);\n p := p-LT (p);\n fi;\n end do;\n a,r;\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "f := x^3*y^2+x^3*y^2-y+1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,(*(\"\"#\"\"\")%\"xG\"\"$F()%\"yGF'F(F(F-!\"\"F( F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "F := [x*y^2-x,x-y^2]; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG7$,&*&%\"xG\"\"\")%\"yG\"\"# F)F)F(!\"\",&F(F)*$F*F)F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "X := x,y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG6$%\"xG%\"yG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "LTlex := proc(f) local c,m; \+ c := lcoeff(f,order=plex(X),'m'); c*m; end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "a,r := DivAlg( f, F, LTlex );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%\"aG%\"rG6$-%'RTABLEG6%\"*#>2'\\\"-%'VECTORG6#7$,(* &\"\"#\"\"\")%\"xGF2F3F3*&F2F3F5F3F3F2F3F0%&ArrayG,(%\"yG!\"\"F3F3*&F2 F3)F9F2F3F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "expand( f-a[ 1]*F[1]-a[2]*F[2]-r );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Groebner[NormalForm](f,F,ple x(X));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"yG!\"\"\"\"\"F&*&\"\"#F &)F$F(F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "LTgrlex := pr oc(f) local c,m; c := lcoeff(f,order=grlex(X),'m'); c*m; end:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "DivAlg( f, F, LTgrlex );" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$-%'RTABLEG6%\"*WQN^\"-%'VECTORG6#7$,$* &\"\"#\"\"\")%\"xGF-F.F.\"\"!%&ArrayG,(%\"yG!\"\"F.F.*&F-F.)F0\"\"$F.F ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Groebner[NormalForm](f ,F,grlex(X));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"yG!\"\"\"\"\"F&* &\"\"#F&)%\"xG\"\"$F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{MARK "11 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 149607192 151353844 } {RTABLE M7R0 I6RTABLE_SAVE/149607192X*%)anythingG6"6"[gl!!%!!!"#"#,(*$%"xG""#F*F)F*F*"""F'F& } {RTABLE M7R0 I6RTABLE_SAVE/151353844X*%)anythingG6"6"[gl!!%!!!"#"#,$*$%"xG""#F*""!F& }