Solving non-separable polynomials over the field of Puiseux series via golden lifting

Abstract

We develop an iterative method to calculate the roots of arbitrary polynomials over the field of Puiseux series including non-separable ones. The method works by transforming the polynomial and its roots into a special form and then extracting a new, univariate polynomial that contains information about our roots. We also provide a working implementation of the algorithm in Python.