{VERSION 5 0 "IBM INTEL NT" "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 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 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 "" {TEXT -1 3 "01." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 19 "a:=x^2+2*x:\nb:=x-c:" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 3 "02." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "result ant(a,b,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%\"cG\"\"\",&\"\"#! \"\"F%F)F&F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "03." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 268 "resultant1:=proc(a,b,x)\nlocal n,m ,r;\nn:=degree(a,x);\nm:=degree(b,x);\nif m=0\n then return(b^n)\n e lif n " 0 "" {MPLTEXT 1 0 18 "resultant1(a,b ,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"#\"\"\"%\"cGF&F&*$)F'F %F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "res:=resultant((x-y)^2-2,y^3-5,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG,.*$)%\"xG\"\"'\"\"\"F**&\"#7F*)F(\" \"#F*F**&F)F*)F(\"\"%F*!\"\"\"# " 0 " " {MPLTEXT 1 0 12 "factor(res);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.* $)%\"xG\"\"'\"\"\"F(*&\"#7F()F&\"\"#F(F(*&F'F()F&\"\"%F(!\"\"\"# " 0 "" {MPLTEXT 1 0 35 "res:=resultan t1((x-y)^2-2,y^3-5,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG,.*$) %\"xG\"\"'\"\"\"F**&\"#7F*)F(\"\"#F*F**&F)F*)F(\"\"%F*!\"\"\"# " 0 "" {MPLTEXT 1 0 455 "with(ListTools):\nSy lvesterMatrix:=proc(a,b,x)\nlocal n,m,alist,blist,amat,bmat;\nn:=degre e(a,x);\nm:=degree(b,x);\nalist:=[seq(coeff(a,x,n-i),i=0..n),seq(0,i=1 ..m-1)];\nblist:=[seq(coeff(b,x,m-i),i=0..m),seq(0,i=1..n-1)];\nif m=0 \n then amat:=NULL\n else amat:=seq(Rotate(alist,-i),i=0..m-1)\nend \+ if;\nif n=0\n then bmat:=NULL\n else bmat:=seq(Rotate(blist,-i),i=0. .n-1)\nend if;\nif nargs>3 \n then [amat,bmat] \n else matrix(n+m,n+ m,[amat,bmat])\nend if;\nend proc:" }}{PARA 7 "" 1 "" {TEXT -1 58 "War ning, the assigned name Group now has a global binding\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "10." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "a:=sum((k+1)^3*x^k,k=0..7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"aG,2\"\"\"F&*&\"\")F&%\"xGF&F&*&\"#FF&)F)\"\"#F&F&*&\"#kF&)F)\"\" $F&F&*&\"$D\"F&)F)\"\"%F&F&*&\"$;#F&)F)\"\"&F&F&*&\"$V$F&)F)\"\"'F&F&* &\"$7&F&)F)\"\"(F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "11." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "b:=sum(k^2*x^k,k=0..5);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG,,%\"xG\"\"\"*&\"\"%F')F&\"\"#F' F'*&\"\"*F')F&\"\"$F'F'*&\"#;F')F&F)F'F'*&\"#DF')F&\"\"&F'F'" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "12." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "S:=SylvesterMatrix(a,b,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG-%'matrixG6#7.7.\"$7&\"$V$\"$;#\"$D\"\"#k\"#F\"\" )\"\"\"\"\"!F2F2F27.F2F*F+F,F-F.F/F0F1F2F2F27.F2F2F*F+F,F-F.F/F0F1F2F2 7.F2F2F2F*F+F,F-F.F/F0F1F27.F2F2F2F2F*F+F,F-F.F/F0F17.\"#D\"#;\"\"*\" \"%F1F2F2F2F2F2F2F27.F2F8F9F:F;F1F2F2F2F2F2F27.F2F2F8F9F:F;F1F2F2F2F2F 27.F2F2F2F8F9F:F;F1F2F2F2F27.F2F2F2F2F8F9F:F;F1F2F2F27.F2F2F2F2F2F8F9F :F;F1F2F27.F2F2F2F2F2F2F8F9F:F;F1F2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "13." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "linalg[det](S) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!+L)yeQ#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "14." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "resul tant(a,b,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!+L)yeQ#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "15." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "r:=rem(a,b,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG,,\"\" \"F&*&#\"'G86\"&Dc\"F&%\"xGF&F&*&#\"'7wNF*F&*$)F+\"\"#F&F&F&*&#\"'_'=& F*F&*$)F+\"\"$F&F&F&*&#\"')>o$F*F&*$)F+\"\"%F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "16." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "S:=SylvesterMatrix(a,b,x,opt):\nT:=matrix(12,12,subs(\{512=0,343=0,21 6=0,125=368198/15625,64=518652/15625,27=357612/15625,8=111328/15625\}, S));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TG-%'matrixG6#7.7.\"\"!F*F *#\"')>o$\"&Dc\"#\"'_'=&F-#\"'7wNF-#\"'G86F-\"\"\"F*F*F*F*7.F*F*F*F*F+ F.F0F2F4F*F*F*7.F*F*F*F*F*F+F.F0F2F4F*F*7.F*F*F*F*F*F*F+F.F0F2F4F*7.F* F*F*F*F*F*F*F+F.F0F2F47.\"#D\"#;\"\"*\"\"%F4F*F*F*F*F*F*F*7.F*F:F;F \+ " 0 "" {MPLTEXT 1 0 15 "linalg[det](T);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!+L)yeQ#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }