Laurent polynomial

A Laurent polynomial is an extension of the regular polynomial concept that allows variables to have negative as well as positive exponents. For example, instead of just \( x^2 + 3x + 2 \), a Laurent polynomial could be \( x^{-1} + 4x + 5 \) (where \( x^{-1} \) means \( 1/x \)). This flexibility makes Laurent polynomials useful in areas like algebra, complex analysis, and number theory, as they can describe functions with behaviors around singularities or poles. They are sums of terms with coefficients multiplied by variables raised to both positive and negative integer powers.