specific form of Horner's scheme



Hi all,

is there any command (flag to be used with horner()-command, e.g.) or 
other procedure (or even trick) to force Maxima not only to 
recursively extract the powers of a variable from a series, but the 
corresponding coeffients, too? I'd really appreciate a result like 
A*x*(1+B*X*(1+C*X*(1+D*X))) , e.g., instead of x*(A+x*(F+x*(G+x*H))), 
which is of the kind that horner() gives me.

BTW: when searching the web for an answer to the question above, I 
found Mr. Fateman's remarks on numerical problems in case of 
evaluating Legendre's polynomials in Horner()-form as floats. I 
(fortunately unseccessfully, i.e., LP(20,1.0)=1.0) tried to reproduce 
Mr. Fateman's results. But indeed, I encountered numerical problems 
when "rat" was involved automatically: (wx)Maxima told me that "rat" 
had (quite pathetically!!, i.e., only to 10 significant digits or so) 
tried to rationalize floats by listing the original float together 
with the automatically derived fraction of integer numbers as well as 
the float that fraction represents. Is it meanwhile common sense, that
these problems described by Mr. Fateman were caused by "rat" rather 
than by "horner"?

Kind regards
Dragan Stoikovitch