Polar quotients of a plane curve and the Newton algorithm (Q1772513)

For \(f\in k[[X,Y]]\) with \(\operatorname{ord}f(0,Y)>1\), and \(k\) algebraically closed of characteristic zero, the author shows how to compute the systems of polar quotients \(\overline {\mathcal Q}(f,X)\) (and the multiplicities) inductively, using a version of the Newton algorithm. This generalises earlier work of the author and others; in particular, \(f\) is not required to be irreducible. Several examples are worked out in detail.