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Usability wishes for QQab #3976

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fingolfin opened this issue Jul 26, 2024 · 0 comments
Open
4 tasks

Usability wishes for QQab #3976

fingolfin opened this issue Jul 26, 2024 · 0 comments

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@fingolfin
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Based on interactions with a user (Gunter Malle) today, here are some ideas for making life more comfortable for users. Consider this starting point:

julia> QQAb, E = abelian_closure(QQ)
(Abelian closure of Q, Generator of abelian closure of Q)

julia> x = E(5) + E(5)^4
-ζ(5)^3 - ζ(5)^2 - 1

julia> conj(x)
-ζ(5)^3 - ζ(5)^2 - 1

julia> conj(x) == x
true
  • implement is_real(:: QQAbFieldElem)
julia> is_real(x)
ERROR: MethodError: no method matching isreal(::QQAbFieldElem{AbsSimpleNumFieldElem})
  • implement > comparison -- by fixing an embedding into QQBar esp. $\mathbb{C}$, based on discussion with @fieker we could use the "standard embedding" (of course experts will immediately argue there are many embeddings, and of course complex_embeddings and real_embeddings for number fields are a thing and important -- but experts probably won't be using abelian_closure to start with)

  • implement coercion to QQBar -- this again requires choosing an embedding, but if we do that anyway, we may as well also support it here

  • make it easy to get a numerical approximation, e.g. by adding coercion to ComplexField / RealField

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