On Wednesday, September 4, 2024 at 1:41:30 PM UTC+9 Nils Bruin wrote:

... it may well depend on whether you're more algebraically or analytically 
oriented.


Yes. That may be a way to reconcile the conflicting views.

We may explicitly introduce technical distinction of "analytical fields" 
and "algebraic fields". 

Analytical fields are : RR, RDF, RBF,  ..., CC
Algebraic fields are: AA, QQbar, GF, Qp, ...

1. For an element x in analytical field P,  x^(1/n) returns the principal 
n-th root of x in P or in CC.
2. For an element x in algebraic field A,  x^(1/n) returns an n-th root of 
x in A or raises an error if there is none. 

and we live happily ever after.




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