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Discussion of "polynomial function"
[parent] [root]
Comment #1: Issues
Curtis W Franks (Tue Jan 21 19:14:03 2014)

A polynomial is not really a summation of powers, technically the powers
must be natural numbers or zero, you do not specify what "in" means (is it
the coefficient ring or the indeterminant/variable? If the latter, which
one?). The interpretation rule is a good idea in this case. I suggest that
this definition be specified to be for a polynomial /function/, that is: a
polynomial whereïn the indeterminant is replaced by values and then the
output is evaluated according to certain rules, the mapping from the input
to the output of this process is the polynomial function.

Comment #2: Re: Issues
Curtis W Franks (Tue Jan 21 19:20:30 2014)

Based on the vagueness of the power term too, I suggest further that the
definition be replaced with "generalized Laurent 'polynomial' function".
In this situation, one must specify the two degrees (nonnegative and
nonpositive over which the summation is occurring); the input domain of
the function and the steps of summation (is it natural numbers? What if
the degree is √2?) should be specified in the definition too. The good
news is that we now would have a very general function/mathematical tool
that has a robustly defined name (outside of English usages if
"polynomial" but simple generalizations really) and which is exact and
clearly different from "formal polynomial" (which is not the case in
English).

I think that this word is a good one, but the definition needs to be
mathematically more exact and correct.

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