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{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\"#<\"\"\"*$%\"xG\"#<!\"\"" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 66 "s := b(y) = b(y-2) + b(y-3), b, y, [b(0) = 1
, b(1) = 0, b(2) = 1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG6&/-%
\"bG6#%\"yG,&-F(6#,&F*\"\"\"!\"#F/F/-F(6#,&F*F/!\"$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,!#<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%F'7U/-F%6#\"
\"!F,/-F%6#F,F</-F%6#\"\"#F</-F%6#\"\"$F</-F%6#\"\"%F</-F%6#\"\"&F</-F
%6#\"\"'F</-F%6#\"\"(F</-F%6#\"\")F</-F%6#\"\"*F</-F%6#\"#5F</-F%6#\"#
6F</-F%6#\"#7F</-F%6#\"#8F</-F%6#\"#9F</-F%6#\"#:F</-F%6#\"#;F</-F%6#
\"#<\"#\\/-F%6#F.F</-F%6#\"#>F</-F%6#\"#?F</-F%6#\"#@F</-F%6#\"#AF</-F
%6#\"#BF</-F%6#\"#CF</-F%6#\"#DF</-F%6#\"#EF</-F%6#\"#FF</-F%6#\"#GF</
-F%6#\"#HF</-F%6#\"#IF</-F%6#\"#JF</-F%6#\"#KF</-F%6#\"#LF</-F%6#\"#M
\"%Ue/-F%6#\"#NF</-F%6#\"#OF</-F%6#\"#PF</-F%6#\"#QF</-F%6#\"#RF</-F%6
#\"#SF</-F%6#\"#TF</-F%6#\"#UF</-F%6#\"#VF</-F%6#\"#WF</-F%6#\"#XF</-F
%6#\"#YF</-F%6#\"#ZF</-F%6#\"#[F</-F%6#FjpF</-F%6#\"#]F<" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 27 "This gives the same result." }{MPLTEXT 1 
0 0 "" }}}}{MARK "9 0 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 }