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| 1. Write a category `HenslianRings` (or maybe `HenselianRingsWithUniformizer`) as a place to write C2-C5. Also a category for polynomials over such rings... | 1. Write a category `HenslianRings` (or maybe `HenselianRingsWithUniformizer`) as a place to write 2-5. Also a category for polynomials over such rings... |
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| 1. Write optimized versions of C1-C4 for polynomials over Zp and Qp. | 1. Write optimized versions of 2-5 for polynomials over Zp and Qp. |
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.