{VERSION 3 0 "DEC ALPHA UNIX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {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 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 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 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 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 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "A:=x^n:\nB:=x^2-2*co s(phi)*x+1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "rem(A,B,x); " }}{PARA 8 "" 1 "" {TEXT -1 50 "Error, (in quo) arguments must be pol ynomial in, x" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for n to 5 do \n collect(rem(A,B,x),x,readlib(`combine/trig`))\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&! \"\"\"\"\"*&-%$cosG6#%$phiGF%%\"xGF%\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&,&\"\"\"F&-%$cosG6#,$%$phiG\"\"#F,F&%\"xGF&F&-F(6#F +!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&,&-%$cosG6#%$phiG\"\"#-F' 6#,$F)\"\"$F*\"\"\"%\"xGF/F/!\"\"F/-F'6#,$F)F*!\"#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,(*&,(\"\"\"F&-%$cosG6#,$%$phiG\"\"#F,-F(6#,$F+\"\"%F ,F&%\"xGF&F&-F(6#F+!\"#-F(6#,$F+\"\"$F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "for n to 5 do \n collect(rem(A,B,x),x,expand)\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&!\"\"\"\"\"*&-%$cosG6#%$phiGF%%\"xGF%\"\"#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,&-%$cosG6#%$phiG!\"#*&,&!\"\"\"\"\"*$)F$\"\"#\"\"\" \"\"%F,%\"xGF,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\"\"\"F$*$)-%$co sG6#%$phiG\"\"#\"\"\"!\"%*&,&F'F-*$)F'\"\"$F,\"\")F$%\"xGF$F$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,(-%$cosG6#%$phiG\"\"%*$)F$\"\"$\"\"\" !\")*&,(\"\"\"F0*$)F$\"\"#F,!#7*$)F$F(F,\"#;F0%\"xGF0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "n:='n':" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 61 "solve(\{cos(n*phi)=a*cos(phi)+b,sin(n*phi)=a*sin(ph i)\},\{a,b\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"bG,$*&,&*&-%$c osG6#*&%\"nG\"\"\"%$phiGF/F/-%$sinG6#F0F/!\"\"*&-F2F,F/-F+F3F/F/\"\"\" F1!\"\"F4/%\"aG*&F6F8F1F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "map(combine,%,trig);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"bG,$ *&-%$sinG6#,&*&%\"nG\"\"\"%$phiGF.F.F/!\"\"\"\"\"-F)6#F/!\"\"F0/%\"aG* &-F)6#F,F1F2F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "for n fro m 0 to 4 do\n orthopoly[U](n,cos(phi))\nod; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$cosG6#%$ phiG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)-%$cosG6#%$phiG\"\"# \"\"\"\"\"%!\"\"\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)-%$cosG 6#%$phiG\"\"$\"\"\"\"\")F&!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\" \"\"F$*$)-%$cosG6#%$phiG\"\"#\"\"\"!#7*$)F'\"\"%F,\"#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "8 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }