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Traditionally, polynomials cannot have negative exponents. So what gives? Inspired by this.

user29418
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    Laurent series with only finitely many nonzero terms are called Laurent polynomials. Laurent polynomials are not necessarily polynomials. Despite that, the word polynomial appearing in the name still suggests a great deal about the structure. – JMoravitz Oct 18 '18 at 00:44
  • I see, so it's just standard nomenclature being context specific. – user29418 Oct 20 '18 at 07:44

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By definition, a polynomial has only nonnegative powers of its variables, while Laurent series have some powers of negative degree. Thus Laurent series and polynomials are disjoint.

If, however, there are only finitely many positive and negative powers in a Laurent series, it may be called a Laurent polynomial.

Parcly Taxel
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A Laurent polynomial is an expression of the form $p(x,x^{-1})$, where $p$ is a polynomial in two variables.

A Laurent polynomial is a Laurent series with only finitely many terms.

lhf
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