implement general Newton's method root finding for power series rings

[ncalexan]

Extracting a square root of a power series is implemented in power_series_ring_element.pyx. Could we have the more general "improving a root of a polynomial" Newton's method?

My use case is calculating Puiseaux expansions around points of algebraic curves.

CC: @robertwb @williamstein

Component: commutative algebra

Keywords: power series root newton method

Author: Nick Alexander

Issue created by migration from https://trac.sagemath.org/ticket/6397

[ncalexan]

Author: Nick Alexander

[ncalexan]

comment:1

Here's a stand-alone implementation that needs to be plugged into the hell that is polynomial.roots().

[ncalexan]

Attachment: trac_6397-power-series-newton-ncalexan-1.pyx.gz