{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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 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 9 "with(MS):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "Consider the example of the Padovan numbe rs defined in \\cite\{Stewart\} \\Label\{defn:Padovan\}. Let " } {XPPEDIT 18 0 "s(x) = sum(b[i]*x^i/i!,i = 0 .. infinity);" "6#/-%\"sG6 #%\"xG-%\$sumG6\$*(&%\"bG6#%\"iG\"\"\")F'F/F0-%*factorialG6#F/!\"\"/F/; \"\"!%)infinityG" }{TEXT -1 8 ", where " }{XPPEDIT 18 0 "b[i] = b[i-2] +b[i-3];" "6#/&%\"bG6#%\"iG,&&F%6#,&F'\"\"\"\"\"#!\"\"F,&F%6#,&F'F,\" \"\$F.F," }{TEXT -1 5 " and " }{XPPEDIT 18 0 "b[0] = 1;" "6#/&%\"bG6#\" \"!\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "b[1] = 0;" "6#/&%\"bG6#\" \"\"\"\"!" }{TEXT -1 6 ", and " }{XPPEDIT 18 0 "b[2] = 1;" "6#/&%\"bG6 #\"\"#\"\"\"" }{TEXT -1 0 "" }{TEXT -1 102 " . Consider multisectioni ng this by 17 at 0. This example will do this by computing the result ant of" }{TEXT -1 13 " P^s(y) with " }{XPPEDIT 18 0 "y^17-x^17;" "6#,& *\$%\"yG\"#<\"\"\"*\$%\"xG\"# " 0 "" {MPLTEXT 1 0 66 "s := b(y) = b(y-2) + b(y-3), b, y, [b(0) = 1 , b(1) = 0, b(2) = 1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG6&/-% \"bG6#%\"yG,&-F(6#,&F*\"\"\"!\"#F/F/-F(6#,&F*F/!\"\$F/F/F(F*7%/-F(6#\" \"!F//-F(6#F/F9/-F(6#\"\"#F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "poly := convert_poly(s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%p olyG,(*\$)%\"yG\"\"\$\"\"\"\"\"\"F(!\"\"F,F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 36 "poly := resultant(y^17-x^17,poly,y);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%polyG,**\$)%\"xG\"#<\"\"\"!#=!\"\"\"\"\"*\$)F( \"#MF*!\$>\"*\$)F(\"#^F*F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "convert_rec(poly, f, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"fG6# %\"xG,(-F%6#,&F'\"\"\"!#MF,\"#=-F%6#,&F'F,!#^F,F,-F%6#,&F'F,!# \"" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 62 "There is a command in Maple to do this called `egf/ms/r esult`." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "`egf/ms/result`( s,17,0);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6&/-%\"bG6#%\"yG,(-F%6#,&F' \"\"\"!#MF,\"#=-F%6#,&F'F,!#^F,F,-F%6#,&F'F,!#\"F%F'7U/-F%6#\" \"!F,/-F%6#F,FF