{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 }{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 }} {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);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "03." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "sol:=sol ve(\{coeffs(F,[alpha,beta])\},\{seq(c[k],k=0..6)\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "F:=subs(c[6]=1,subs(sol,sum(c[k]*x^k,k=0..6)));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(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:=Ro otOf(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);" }}}{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);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "10." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "evala(1/(alpha+beta));" }}}}{MARK "1 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }