padics/HenselLifting

• 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

1. Write a category HenslianRings (or maybe HenselianRingsWithUniformizer) as a place to write 2-5. Also a category for polynomials over such rings...

2. Write a function that lifts a root of a polynomial (defined to sufficient precision) up one precision.
3. Write a function that lifts a root of a polynomial (defined to sufficient precision) to double precision.
4. Write a function that lifts a coprime factorization up one precision.
5. Write a function that lifts a coprime factorization to double precision.
6. Write functions that determine precisions of the resulting objects given the precision of the original polynomial.
7. Write optimized versions of 2-5 for polynomials over Zp and Qp.