is a linear combination of positive and negative powers of the variable with coefficients in
[1] They differ from ordinary polynomials in that they may have terms of negative degree.
Laurent polynomials are of particular importance in the study of complex variables.
A Laurent polynomial with coefficients in a field
is an integer (not necessarily positive) and only finitely many coefficients
Such expressions can be added, multiplied, and brought back to the same form by reducing similar terms.
Formulas for addition and multiplication are exactly the same as for the ordinary polynomials, with the only difference that both positive and negative powers of
are non-zero, all sums in effect have only finitely many terms, and hence represent Laurent polynomials.