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== Imprecise definition of polynomial ==
The definition of polynomial is more complex that needed, repeated twice (in introduction and not-so-formal definition) and not really well defined: "... polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables."
What is a coefficient and what is its role in the polynomial?. They are mentioned to exists and then not "used" in the definition. I think it is better to be pragmatical and start with an example, then try to make it clear what the operations allowed to variables and what is the meaning of "coefficients x (variable exponentiation)". What "a·x²" means in practice. "x²" is vector and "a" a transposed constact vector (sort of escalar product)? Not clear at all from the definition. Or maybe the coefficient are SU matrices and the result is of evaluation the polynomial is just another vector? Or maybe "a·x²" must just be interpreted as another new variable?
"Indeterminates" does not even appear in my English dictionary. "Variable" is well known and understood. "Indeterminates" distract attentions without providing any meaningful information.
== Polynomial functions ==
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