*Goal*-- Define Hensel lifting for roots and factorizations of polynomials over Henselian rings.*Type*-- basic features*Priority*-- High*Difficulty*-- Medium-Easy*Prerequisites*-- p-adic polynomial precision*Background*--*Contributors*-- David Roe*Progress*- not started*Related Tickets*--

## Discussion

This is easy once the implementation of polynomials stabilizes...

## Tasks

Write a category

`HenslianRings`(or maybe`HenselianRingsWithUniformizer`) as a place to write 2-5. Also a category for polynomials over such rings...- Write a function that lifts a root of a polynomial (defined to sufficient precision) up one precision.
- Write a function that lifts a root of a polynomial (defined to sufficient precision) to double precision.
- Write a function that lifts a coprime factorization up one precision.
- Write a function that lifts a coprime factorization to double precision.
- Write functions that determine precisions of the resulting objects given the precision of the original polynomial.
- Write optimized versions of 2-5 for polynomials over Zp and Qp.