Laurent polynomial

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In mathematics, a Laurent polynomial (named after Pierre Alphonse Laurent) in one variable over a field ${\displaystyle \mathbb {F} }$ is a linear combination of positive and negative powers of the variable with coefficients in ${\displaystyle \mathbb {F} }$. Laurent polynomials in ${\displaystyle X}$ form a ring denoted ${\displaystyle \mathbb {F} [X,X^{-1}]}$.^[1] They differ from ordinary polynomials in that they may have terms of negative degree. The construction of Laurent polynomials may be iterated, leading to the ring of Laurent polynomials in several variables. Laurent polynomials are of particular importance in the study of complex variables.