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| * ''Prerequisites'' -- [[../PolynomialPrecision | p-Adic polynomial precision] and [[../HenselLifting | Hensel lifting]]. In addition, the second half of the project depends on [[../GeneralExtensions | General extension rings]] | * ''Prerequisites'' -- [[../PolynomialPrecision | p-Adic polynomial precision]] and [[../HenselLifting | Hensel lifting]]. In addition, the second half of the project depends on [[../GeneralExtensions | General extension rings]] |
Goal -- Implement algorithms for factoring polynomials over local fields. Define extensions of local fields using any polynomial.
Type -- basic features
Priority -- High
Difficulty -- High
Prerequisites -- p-Adic polynomial precision and Hensel lifting. In addition, the second half of the project depends on General extension rings
Background -- Hensel lifting, newton polygons, p-adic factoring algorithms.
Contributors -- David Roe
Progress -
Related Tickets --
Discussion
Tasks
- Implement round 4 (or some other p-adic factoring algorithm) for polynomials over Zp. Compare results against results from pari. Find right precisions for factors.
- Write functions to extract the unramified and Eisenstein pieces from an irreducible polynomial over Zp using the internals of the factoring algorithm.
- Write a new p-adic parent class and printer that allows the "generator" of an extension to be arbitrary (rather than a uniformizer for an Eisenstein extension).
Change the extension factory in sage.rings.padics.factory to allow creation of such extensions.
- Implement factoring for polynomials over other Henselian rings.