### People

Sebastian Pauli, Brian Sinclair, Maurizio Monge, David Roe, Xavier Caruso

### Description

Implement a native Sage algorithm for local field polynomial factorization. For more detail, see http://wiki.sagemath.org/padics/PolynomialFactoring.

### Current Progress

A functioning version of the algorithm is up: See #12561.

Initial doctests show that some examples are incorrectly returned as irreducible.

### A question

Given a polynomial P, can we derive from this algorithm a way to compute the graph (embedded in the Berkovich line) whose edges are the roots of P?