first draft at generic tate

[thofma]

No description provided.

[codecov]

Codecov Report

Patch coverage: 60.16% and project coverage change: -0.05% ⚠️

Comparison is base (4129516) 74.41% compared to head (f0d72db) 74.37%.
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1144      +/-   ##
==========================================
- Coverage   74.41%   74.37%   -0.05%     
==========================================
  Files         346      346              
  Lines      110373   110465      +92     
==========================================
+ Hits        82130    82154      +24     
- Misses      28243    28311      +68     

Files Changed	Coverage Δ
src/EllCrv/Misc.jl	35.50% <0.00%> (-5.33%)	⬇️
src/EllCrv/MinimalModels.jl	71.04% <3.57%> (-6.23%)	⬇️
src/EllCrv/LocalData.jl	89.59% <97.22%> (+3.42%)	⬆️

... and 32 files with indirect coverage changes

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[thofma]

Tests will need Nemocas/Nemo.jl#1517.

[thofma]

Tate should be working now for rational function fields. I have also added some tentative functions to reduce a model, which might be helpful (they are at the bottom of the file):

function reduce_model(E::EllCrv{<: AbstractAlgebra.Generic.RationalFunctionFieldElem})
  Kt = base_field(E)
  Rt = base_ring(Kt.fraction_field)
  d = discriminant(E)
  E, = minimal_model(E, degree)
  for (g, e) in factor(d, Rt)
    g = AbstractAlgebra.MPolyFactor.make_monic(g)
    E, = minimal_model(E, g)
  end
  return E
 Check warning on line 629 in src/EllCrv/MinimalModels.jl
end

function _minimize(E::EllCrv{<: AbstractAlgebra.Generic.RationalFunctionFieldElem})
  Kt = base_field(E)
  Rt = base_ring(Kt.fraction_field)
  d = discriminant(E)
  for (g, e) in factor(d, Rt)
    g = AbstractAlgebra.MPolyFactor.make_monic(g)
    E = _minimize(E, Kt(g), e)
  end
  return E
end

function _minimize(E::EllCrv, u, e)
  v = one(u)
  if abs(e) > 11
    v = u^(fdiv(ZZ(e), 12))
  end
  if -12 < e < 0
    v *= inv(u)
  end
  E, = transform_rstu(E, [0, 0, 0, v])
  return E
end