Puiseux series

Summary

A Puiseux series is a formal Laurent series in a fractional power $X^{1/m}$ of the variable, for some positive integer $m$, see the definition. Puiseux series form a field that contains the field of formal Laurent series $k((X))$. By the Newton–Puiseux theorem, over an algebraically closed field of characteristic $0$ they give all roots of polynomial equations with Laurent series coefficients. They describe the branches of a plane algebraic curve near a point.