{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 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 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "reducepol:=proc(p,x, redp)\n" }{MPLTEXT 1 0 21 "local n,m,rules,pol;\n" }{MPLTEXT 1 0 8 "po l:=p;\n" }{MPLTEXT 1 0 19 "n:=degree(redp,x);\n" }{MPLTEXT 1 0 16 "m:= degree(p,x);\n" }{MPLTEXT 1 0 63 "rules:=seq(map(y->y*x^i,x^n=-redp+lc oeff(redp)*x^n),i=0..m-n);\n" }{MPLTEXT 1 0 26 "while degree(pol,x)>=n do\n" }{MPLTEXT 1 0 24 " pol:=subs(rules,pol);\n" }{MPLTEXT 1 0 8 "e nd do;\n" }{MPLTEXT 1 0 4 "pol\n" }{MPLTEXT 1 0 9 "end proc:" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "01." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "p:=(cos(t)+sin(t))^10;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "02." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "q:=expan d(p);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "03." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(q);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "indets(q);" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "collect(expand(reducepol(expand(p),cos(t),sin(t)^2+co s(t)^2-1)),cos(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "06." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "rem((x+y)^10,x^2+y^2-1,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "07." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 24 "combine(expand(p),trig);" }}}}{MARK "0 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }