I was trying to convert a rational function R(X) to a polynomial of type R|X,X−1| but I failed. I searched internet and R|X,X−1| has its own name!: "Laurent polynomials". a. Every Laurent polynomial is a combination of rational functions. Is every Laurent polynomial possible to be equal to a single rational function? b. Are there methods to convert rational functions to Laurent polynomials? How are they?

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I was trying to convert a rational function R(X) to a polynomial of type R|X,X−1| but I failed. I searched internet and R|X,X−1| has its own name!: &quot;Laurent polynomials&quot;.    a. Every Laurent polynomial is a combination of rational functions. Is every Laurent polynomial possible to be equal to a single rational function?    b. Are there methods to convert rational functions to Laurent polynomials? How are they?

jorgegalar0xk · Accepted Answer

a. Yes. A Laurent polynomial is an expression of the typeanXn+an+1Xn+1+…+an+kXn+k,   (1)with n∈Z and k∈N. This is a polynomial (and therefore a rational function) is n≥0. Otherwise(1)=an+an+1Xn+…+an+kXkX−nwhich is a rational function.2. No. For instance, 11+X is a rational function, but you can&#039;t express it as an element of R[X,X−1].

Vikki Chapman · Accepted Answer

A rational function f(X) can be a Laurent polynomial if and only if Xmf(x) is an ordinary polynomial for some positive integer m.    Clearly one can find rational functions failing this condition.

I was trying to convert a rational function RR(X) to a polynomial of type RR|X,X^{-1}| b

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