Use symbols instead of strings for variables in toric geometry

[lkastner]

Fixes #4159

[fingolfin]

Thank you!

Left some optional comments, feel free to ignore.

But regarding the CI errors, here is one:

LoadError: MethodError: no method matching polynomial_ring(::QQField, ::Vector{Any}; cached::Bool)

Closest candidates are:
  polynomial_ring(::Ring, ::Vector{Symbol}; kw...)
   @ AbstractAlgebra ~/oscar-runners/runner-28/julia/packages/AbstractAlgebra/5aJmh/src/MPoly.jl:1506
  polynomial_ring(::Ring, ::Union{AbstractArray{<:Union{Char, AbstractString, Symbol}}, Pair{<:Union{Char, AbstractString, Symbol}}}, Union{AbstractArray{<:Union{Char, AbstractString, Symbol}}, Pair{<:Union{Char, AbstractString, Symbol}}}...; kv...)
   @ AbstractAlgebra ~/oscar-runners/runner-28/julia/packages/AbstractAlgebra/5aJmh/src/misc/VarNames.jl:300
  polynomial_ring(::Ring, ::Tuple{Vararg{Union{AbstractArray{<:Union{Char, AbstractString, Symbol}}, Pair{<:Union{Char, AbstractString, Symbol}}}}}; kv...)
   @ AbstractAlgebra ~/oscar-runners/runner-28/julia/packages/AbstractAlgebra/5aJmh/src/misc/VarNames.jl:302
  ...

Stacktrace:
  [1] _construct_generic_sample
    @ ~/oscar-runners/runner-28/_work/Oscar.jl/Oscar.jl/experimental/FTheoryTools/src/auxiliary.jl:393

The code triggering this:

function _construct_generic_sample(base_grading::Matrix{Int64}, base_vars::Vector{String}, d::Int, fiber_ambient_space::NormalToricVariety, fiber_twist_divisor_classes::ZZMatrix)
  base_space = family_of_spaces(polynomial_ring(QQ, base_vars, cached = false)[1], base_grading, d)
  ambient_space_vars = vcat(base_vars, coordinate_names(fiber_ambient_space))
  coordinate_ring_ambient_space = polynomial_ring(QQ, ambient_space_vars, cached = false)[1]
...

I suspect that base_vars and coordinate_names(fiber_ambient_space) now have different types (one a Vector{String} one a Vector{Symbol}).

Two solutions come to mind (and perhaps both should be implemented):
1 also drop the vcat in that method and instead write

  coordinate_ring_ambient_space = polynomial_ring(QQ, base_vars, coordinate_names(fiber_ambient_space); cached = false)[1]

2. ensure that the Vector{String} there is also changed into a Vector{Symbol}

[HereAround]

@lkastner and I discussed this PR earlier today. We agreed, that I would take this over to suffer through the necessary changes in FTheoryTools. Thus, I just committed some suggestions from code review and rebased to #5263.

[lgoettgens]

The changes look mostly fine to me, thanks for working on this @HereAround! In a few places, I think the changes to docstrings make it harder for users to use specific kwargs (see comments).

I can not judge if this really resolves #4159 as I am not familiar enough with the surrounding code that was not touched here.

[HereAround]

@lgoettgens seems happy. I checked with @lkastner on slack, who also seems happy. I shall thus assume that this PR is good to go and will now merge it.