{VERSION 2 3 "SUN SPARC SOLARIS" "2.3" } {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 "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 13 "with(linalg):" }} {PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }} {PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "M := matrix([[16,8,4,2,1],[8 1,27,9,3,1],[256,64,16,4,1],[625,125,25,5,1],[1296,216,36,6,1]]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'MATRIXG6#7'7'\"#;\"\")\"\"%\" \"#\"\"\"7'\"#\")\"#F\"\"*\"\"$F.7'\"$c#\"#kF*F,F.7'\"$D'\"$D\"\"#D\" \"&F.7'\"%'H\"\"$;#\"#O\"\"'F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "v := vector([2,4,8,16,31]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"vG-%'VECTORG6#7'\"\"#\"\"%\"\")\"#;\"#J" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "multiply(M^(-1),v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'VECTORG6#7'#\"\"\"\"#C#!\"\"\"\"%#\"#BF)#!\"$F,F(" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "f := x -> 1/24*x^4 - 1/4*x ^3 + 23/24*x^2 - 3/4*x +1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6 #%\"xG6\"6$%)operatorG%&arrowGF(,,*$9$\"\"%#\"\"\"\"#C*$F.\"\"$#!\"\"F /*$F.\"\"##\"#BF2F.#!\"$F/F1F1F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(4) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 5 "f(5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#J" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "Need to ch eck whether 7 points will lead to the line being divided into 57 secti ons:" }}{PARA 0 "" 0 "" {TEXT -1 86 "If so, then it looks promising th at the number of sections is given by the polynomial." }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#d" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} }{MARK "10 1 0" 86 }{VIEWOPTS 1 1 0 1 1 1803 }