The convert(f, 'horner', x) command converts the input to horner form with respect to x, or the names in x if this argument is a list or set.

If x is omitted, it is taken as indets(f,name).

If x is given as a list or set of names, the conversion is applied recursively to the coefficients of f in the first variable given.  A list allows for control over the order of the conversions.

If f is a set, list or relation, the result is map(convert, f, 'horner', x).

Any subexpressions of f which are not either polynomials or rational functions in x are frozen via a call to frontend prior to conversion.