{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 }{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 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{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 "" {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;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG*$),&-%$cosG6#%\"tG\"\"\"-%$sinGF*F,\"#5F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "02." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "q:=expand(p);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"qG,8*$)-% $cosG6#%\"tG\"#5\"\"\"F-*(F,F-)F(\"\"*F--%$sinGF*F-F-*(\"#XF-)F(\"\")F -)F1\"\"#F-F-*(\"$?\"F-)F(\"\"(F-)F1\"\"$F-F-*(\"$5#F-)F(\"\"'F-)F1\" \"%F-F-*(\"$_#F-)F(\"\"&F-)F1FHF-F-*(F@F-)F(FDF-)F1FBF-F-*(F:F-)F(F>F- )F1F " 0 "" {MPLTEXT 1 0 10 "factor(q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),&-% $cosG6#%\"tG\"\"\"-%$sinGF(F*\"#5F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "indets(q);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<%%\"tG-%$cosG6#F$-%$sinGF'" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "collect(expand(reducepol(expand(p),cos(t),sin(t)^2+co s(t)^2-1)),cos(t));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,.*&,,*&\"#!)\" \"\")-%$sinG6#%\"tG\"\"$F(F(*&\"#5F(F*F(F(*&\"#[F()F*\"\"&F(!\"\"*&\"# kF()F*\"\"(F(F5*&\"#KF()F*\"\"*F(F(F(-%$cosGF,F(F(F(F(*&\"#SF()F*\"\"# F(F(*&F'F()F*\"\")F(F(*&FAF()F*\"\"%F(F(*&\"$g\"F()F*\"\"'F(F5" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "06." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "rem((x+y)^10,x^2+y^2-1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.*&,,*&\"#K\"\"\")%\"yG\"\"*F(F(*&\"#kF()F*\"\"(F(!\" \"*&\"#[F()F*\"\"&F(F0*&\"#!)F()F*\"\"$F(F(*&\"#5F(F*F(F(F(%\"xGF(F(*& F6F()F*\"\")F(F(*&\"$g\"F()F*\"\"'F(F0*&\"#SF()F*\"\"%F(F(*&FDF()F*\" \"#F(F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "07." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "combine(expand(p),trig);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.*&#\"\"\"\"#;F&-%$sinG6#,$*&\"#5F&%\"tGF&F &F&F&*&#\"\"&\"\")F&-%$cosG6#,$*&F2F&F.F&F&F&F&*&#\"#:\"\"#F&-F46#,$*& \"\"%F&F.F&F&F&!\"\"*&#\"#XF'F&-F)6#,$*&\"\"'F&F.F&F&F&FA*&#\"$0\"F2F& -F)6#,$*&F;F&F.F&F&F&F&#\"#jF2F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }