Parametrize FunctionField as FunctionField{T, U}

[alexey-orlov-math]

Adds a second type parameter U <: PolyRingElem{T} to Generic.FunctionField and Generic.FunctionFieldElem, mirroring RationalFunctionField{T, U}. Unlike the latter (whose U may be uni- or multivariate), here U is restricted to the univariate polynomial element type

[thofma]

If the tests pass, can we treat this PR as "nonbreaking"? We would like to use this downstream soonish. Any thoughts on that @fingolfin or @lgoettgens?

[codecov]

Codecov Report

❌ Patch coverage is 92.42424% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.12%. Comparing base (2657ac7) to head (f4e3f67).

Files with missing lines	Patch %	Lines
src/generic/FunctionField.jl	91.93%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2414      +/-   ##
==========================================
- Coverage   88.13%   88.12%   -0.01%     
==========================================
  Files         130      130              
  Lines       32948    32943       -5     
==========================================
- Hits        29038    29031       -7     
- Misses       3910     3912       +2     

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[alexey-orlov-math]

failures in Hecke CI are expected:

Got exception outside of a @test
  MethodError: no method matching base_field_type(::Type{AbstractAlgebra.Generic.FunctionField{FqFieldElem, FqPolyRingElem}})
  
  Closest candidates are:
    base_field_type(::DataType)
     @ Hecke ~/.julia/packages/Hecke/bT28F/src/Hecke.jl:572
    base_field_type(::Any)
     @ Hecke ~/.julia/packages/Hecke/bT28F/src/Hecke.jl:571
    base_field_type(::Type{AbsNonSimpleNumField})
     @ Hecke ~/.julia/packages/Hecke/bT28F/src/Map/NumField.jl:187
    ...

we need to be exact here (i have a pr, waiting for this to land and version upgrade i guess?)

[alexey-orlov-math]

Hecke changes to follow
https://github.com/thofma/Hecke.jl/pull/2275/changes

[lgoettgens]

If the tests pass, can we treat this PR as "nonbreaking"? We would like to use this downstream soonish. Any thoughts on that @fingolfin or @lgoettgens?

I would be fine with it, but it seems like downstream CI is unhappy...

[alexey-orlov-math]

If the tests pass, can we treat this PR as "nonbreaking"? We would like to use this downstream soonish. Any thoughts on that @fingolfin or @lgoettgens?

I would be fine with it, but it seems like downstream CI is unhappy...

yes and it will be fixed by
thofma/Hecke.jl#2275

this is due to the way julia resolves "overloads" - current base_field_type is "underspecified" for function field so it cannot decide. I assume (i dunno about the process) that we would need to update version and use updated version in the same pr