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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 thedefinition be replaced with "generalized Laurent 'polynomial' function".In this situation, one must specify the two degrees (nonnegative andnonpositive over which the summation is occurring); the input domain ofthe function and the steps of summation (is it natural numbers? What ifthe degree is √2?) should be specified in the definition too. The goodnews is that we now would have a very general function/mathematical toolthat has a robustly defined name (outside of English usages if"polynomial" but simple generalizations really) and which is exact andclearly different from "formal polynomial" (which is not the case inEnglish).I think that this word is a good one, but the definition needs to bemathematically more exact and correct.
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