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| * ''Goal'' -- * ''Type'' -- * ''Priority'' -- * ''Difficulty'' -- * ''Prerequisites'' -- |
* ''Goal'' -- Define Hensel lifting for roots and factorizations of polynomials over Henselian rings. * ''Type'' -- basic features * ''Priority'' -- High * ''Difficulty'' -- Medium-Easy * ''Prerequisites'' -- [[../PolynomialPrecision | p-adic polynomial precision]] |
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| * ''Contributors'' -- * ''Progress'' - |
* ''Contributors'' -- David Roe * ''Progress'' - not started |
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| This is easy once the implementation of polynomials stabilizes... |
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1. Write a category HenslianRings (or maybe HenselianRingsWithUniformizer) as a place to write C2-C5. 1. Write a function that lifts a root of a polynomial (defined to sufficient precision) up one precision. 1. Write a function that lifts a root of a polynomial (defined to sufficient precision) to double precision. 1. Write a function that lifts a coprime factorization up one precision. 1. Write a function that lifts a coprime factorization to double precision. 1. Write functions that determine precisions of the resulting objects given the precision of the original polynomial. 1. Write optimized versions of C1-C4 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 C2-C5.
- 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 C1-C4 for polynomials over Zp and Qp.