Display confusion between PrimeField and BinaryField

[Keno]

I'm not sure if this is intended or a bug, but either way it's confusing.

julia> @GaloisField ℤ/256ℤ
𝔽₂₅₆

julia> @GaloisField 𝔽₂₅₆
(𝔽₂₅₆, ##423)

The former 𝔽₂₅₆ is a PrimeField (even though 256 isn't prime?) while the latter is a BinaryField. They print the same, but behave completely differently.

[tkluck]

Thanks for flagging. I've been hesitant to add isprime assertions in the constructors, but after timing this I don't see a reason:

julia> @btime isprime($(prevprime(typemax(Int128))))
  68.619 μs (4 allocations: 2.49 KiB)
true

That would then throw an error in your first example. Would that solve your confusion?

[Keno]

It would solve my confusion, though of course ℤ/256ℤ is sometimes quite useful, so perhaps we should just add a ModP datatype to support things of that form that aren't finite fields and just make it work. Perhaps this isn't the correct package for that, but I figure PrimeField has all the code to support ModP anyway.

[tkluck]

of course ℤ/256ℤ is sometimes quite useful, so perhaps we should just add a ModP datatype to support things of that form that aren't finite fields and just make it work.

I agree that it might be useful, but it immediately asks for new methods and functionality (chinese remainder theorem, is_zero_divisor, ideals, etc). So yep, probably not the right package.

I'll leave the issue open until I added isprime to the constructor.