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mathjuliagalois-fieldfinite-field

Converting FqFieldElem to an integer

I'm a beginner in Julia and I am working with the Nemo library to do stuff over finite fields.

I would like to compute the characters of a given finite field and to do so I have to compute quantities like

exp(2*pi*im*absolute_tr(a)/p)

However the type of absolute_tr(a) is FqFieldElem since it's an element of the prime subfield (here Z/pZ) of my finite field so this raises an error.

I would like to transform this integer modulo p to an int but I can't find any methods to do so (despite it being printed on the console as an integer...).

Solution

  • It isn't unambiguously defined how to map a field element into an Int. But, the following works by first going through a Nemo way to embed the field into Z:

    julia> R = GF(7)
Prime field of characteristic 7

julia> a = R(3)
3

julia> Int(lift(ZZ, a))
3

julia> typeof(Int(lift(ZZ, a)))
Int64