Re: How do you define a polynomial? What is the official definition of a polynomial?


mzafrullah@xxxxxxx wrote:
> comtech wrote:
> > Hi all,
> >
> > How do you define a polynomial? What is the official definition of a
> > polynomial?
> >
> > What is the essential difference between a polynomial and some function
> > such as exp(x)?
> >
> > Can anybody give a precise definition of what is called a polynomial?
> >
> > Thanks a lot!
>
> A polynomial is essentially a finite sum of terms designed in some
> fashion. The terms could well be symbols representing constants. The
> following terminology may be helpful:
> A monomial is a single term such as "a", "b", "aX^{n}", "aX^{n}*y^{m}".
> A binomial is a sum of two terms such as "a+b", "aX^{m} +bX^{n}",
> "a+bX" etc.
> A trinomial is a sum of three terms etc.
> So it is fair to say that "a binomial raised to the power n, where n is
> a natural number, is a polynomial". (By "natural number" I mean really
> natural i.e. positive integer.)
> These days by a polynomial a lot of people mean a polynomial in a
> variable X (or in some variables X,Y,...'). If the context allows it is
> fine. So, if you are looking for a polynomial in X then you have an
> expression like: f(X) = a_0 +a_1 X + a_2 X^{2} + ...+a_n X^{n} where
> the coefficients come from your choice of an algebraic entity, that
> makes sense. So if a_i are real numbers the polynomial f(X) is a
> polynomial in a single variable X.
> I hope this helps.
> Muhammad

Please read:"So if a_i are real numbers the polynomial f(X) is a
polynomial in a single variable X" as
So if a_i are real numbers the polynomial f(X) is a polynomial in a
single variable X over real numbers.
Muhammad

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