{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 "" 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 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 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 0 224 "reducepol:=proc(p,x,redp)\nlocal n,m,rules,po l;\npol:=p;\nn:=degree(redp,x);\nm:=degree(p,x);\nrules:=seq(map(y->y* x^i,x^n=-redp+lcoeff(redp)*x^n),i=0..m-n);\nwhile degree(pol,x)>=n do \n pol:=subs(rules,pol);\nend do;\npol\nend proc:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "02." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "F:=sum('expand'(c[k]*(alpha+beta)^k),k=0..6):\nF:=reducepol(F,alpha,a lpha^2-2):\nF:=reducepol(F,beta,beta^3-5);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"FG,X**\"#C\"\"\"&%\"cG6#\"\"'F(%&alphaGF(%%betaGF(F (**\"\")F(&F*6#\"\"%F(F-F(F.F(F(**\"#IF(F)F(F-F()F.\"\"#F(F(**\"#DF(&F *6#\"\"&F(F-F(F.F(F(**\"\"$F(&F*6#F>F(F-F(F6F(F(**F7F(&F*6#F7F(F-F(F.F (F(**\"#?F(F:F(F-F(F6F(F(*&FBF(F6F(F(*&&F*6#F(F(F.F(F(*&FHF(F-F(F(*&F< F(F?F(F(*&F3F(F1F(F(*&\"$+\"F(F:F(F(*&\"#LF(F)F(F(&F*6#\"\"!F(*&F7F(FB F(F(*(\"#7F(F1F(F6F(F(*(F,F(F?F(F.F(F(*(F7F(F?F(F-F(F(*(\"#gF(F)F(F6F( F(*(FEF(F:F(F.F(F(*(F3F(F:F(F-F(F(*(FEF(F1F(F-F(F(*(\"$+#F(F)F(F-F(F(* (F " 0 "" {MPLTEXT 1 0 56 "sol:=solve(\{coeffs(F,[alpha,beta])\},\{seq(c[k],k=0..6)\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG<)/&%\"cG6#\"\"%,$*&\"\"'\"\"\" &F(6#F-F.!\"\"/&F(6#\"\"!,$*&\"# " 0 "" {MPLTEXT 1 0 47 "F:=subs(c[6]=1,subs(sol,sum(c[k]*x^k,k=0..6)));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG,.\"#<\"\"\"*&\"#gF'%\"xGF'!\"\" *&\"#7F')F*\"\"#F'F'*&\"#5F')F*\"\"$F'F+*&\"\"'F')F*\"\"%F'F+*$)F*F5F' F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(F);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,. \"#<\"\"\"*&\"#gF%%\"xGF%!\"\"*&\"#7F%)F(\"\"#F%F%*&\"#5F%)F(\"\"$F%F) *&\"\"'F%)F(\"\"%F%F)*$)F(F3F%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "06." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "alpha:=RootOf(x^2 -2,x,2):\nbeta:=RootOf(x^3-5,x,1):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "07." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "result:=evala( alpha+beta);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'resultG,&-%'RootOfG 6$,&*$)%#_ZG\"\"#\"\"\"F.F-!\"\"F-F.-F'6$,&*$)F,\"\"$F.F.\"\"&F/F.F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "08." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "09." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evala(alpha*beta);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%'RootOfG6$,&*$)%#_ZG\"\"#\"\"\"F,F+!\"\" F+F,-F%6$,&*$)F*\"\"$F,F,\"\"&F-F,F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "10." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "evala(1/(alpha +beta));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,.*&#\"\"%\"#<\"\"\"-%'Roo tOfG6$,&*$)%#_ZG\"\"#F(F(F0!\"\"F0F(F1*&#\"\"&F'F(*&F)F(-F*6$,&*$)F/\" \"$F(F(F4F1F(F(F(F1*&#F0F'F(*&F)F()F6F0F(F(F1*&#F&F'F(F6F(F(*&#F4F'F(* $F?F(F(F(#\"#5F'F(" }}}{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 }