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Is this very important? Since there is no AbstractRational it is not so easy to do this. A package extension could be used, but that seems overkill.
I tried with signedroot(RationalRoot, half(1)), but that does not work because Base.rationalize(::HalfInteger) is not defined. That would probably be a useful addition to HalfIntegers.jl
Would it be interesting to support HalfIntegers.jl?
Currently, I see the following:
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