{VERSION 3 0 "SGI MIPS 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 "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 9 "with(MS):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 155 "This example determines what deg^d(s(x)) and deg^P(s(x)) are for various s(x). This example uses the automate d code described in appendix \\ref\{apnd:outl\}." }}{PARA 0 "" 0 "" {TEXT -1 62 "First consider the function from Example \\ref\{ex:chap 1 ex 1\}." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "s[1] := x + x * exp(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"sG6#\"\"\",&%\"xGF'*& F)F'-%$expG6#F)F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "pe/ metric/d(s[1],x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Recalls that$P^\{s_1\}(x) = x^4 - 2 x^3 + x^2$." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "pe/metri c/P(s[1],x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Next, consider the Fibonacci numbers from Example \\ref\{ex:chap 1 ex 2\}." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "s[2] := b(x) = b(x-1)+b(x-2),b,x, [b(0)=0,b(1)=1];" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"sG6#\"\"#6&/-%\"bG6#%\"xG,&-F+6# ,&F-\"\"\"!\"\"F2F2-F+6#,&F-F2!\"#F2F2F+F-7$/-F+6#\"\"!F " 0 "" {MPLTEXT 1 0 21 "egf/metric/d(s[2]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "egf/metric/P(s[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}}{MARK "1 0 0" 48 }{VIEWOPTS 1 1 0 1 1 1803 }