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Towards generic roots over local fields #1599

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This is my attempt of generalizing the implementation of roots over local fields in characteristic 0 to other local fields.
The main theoretical problem is that I do not know how to do a squarefree factorization in a non-perfect field of characteristic $p > 0$.

I open this pull request so that the code is not lost. I don't expect that I will continue working on this in the near future.

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codecov bot commented Sep 10, 2024

Codecov Report

Attention: Patch coverage is 15.16245% with 235 lines in your changes missing coverage. Please review.

Project coverage is 75.59%. Comparing base (25ef213) to head (589a16f).

Files with missing lines Patch % Lines
src/LocalField/roots.jl 0.00% 208 Missing ⚠️
src/LocalField/Poly.jl 30.76% 27 Missing ⚠️
Additional details and impacted files
@@            Coverage Diff             @@
##           master    #1599      +/-   ##
==========================================
- Coverage   75.78%   75.59%   -0.19%     
==========================================
  Files         362      363       +1     
  Lines      113906   114143     +237     
==========================================
- Hits        86320    86291      -29     
- Misses      27586    27852     +266     
Files with missing lines Coverage Δ
src/Misc/nmod_poly.jl 63.11% <100.00%> (+0.22%) ⬆️
src/NumFieldOrd/NfOrd/MaxOrd/Polygons.jl 89.04% <100.00%> (+0.01%) ⬆️
src/LocalField/Poly.jl 61.22% <30.76%> (-2.15%) ⬇️
src/LocalField/roots.jl 0.00% <0.00%> (ø)

... and 30 files with indirect coverage changes

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